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Lattice Codes for CRYSTALS-Kyber (2308.13981v3)

Published 27 Aug 2023 in cs.IT and math.IT

Abstract: This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to 32.6%, and a reduction of the DFR by a factor of up to 2{85}. Given the same plaintext size as the original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by 24.49%, while the DFR is decreased by a factor of 2{39}. The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.

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References (22)
  1. National Institute of Standards and Technology: Module-Lattice-based Key Encapsulation Mechanism Standard. Federal Information Processing Standards Publication (FIPS) NIST FIPS 203 ipd. (2023) https://doi.org/10.6028/NIST.FIPS.203.ipd Bos et al. [2018] Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J.M., Schwabe, P., Seiler, G., Stehlé, D.: CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM. In: 2018 IEEE European Symposium on Security and Privacy (EuroS&P), pp. 353–367 (2018). https://doi.org/10.1109/EuroSP.2018.00032 D’Anvers et al. [2018] D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: Module-LWR Based Key Exchange, CPA-Secure Encryption and CCA-Secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) Progress in Cryptology – AFRICACRYPT 2018, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16 Alkim et al. [2021] Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J.M., Schwabe, P., Seiler, G., Stehlé, D.: CRYSTALS - Kyber: A CCA-Secure Module-Lattice-Based KEM. In: 2018 IEEE European Symposium on Security and Privacy (EuroS&P), pp. 353–367 (2018). https://doi.org/10.1109/EuroSP.2018.00032 D’Anvers et al. [2018] D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: Module-LWR Based Key Exchange, CPA-Secure Encryption and CCA-Secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) Progress in Cryptology – AFRICACRYPT 2018, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16 Alkim et al. [2021] Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: Module-LWR Based Key Exchange, CPA-Secure Encryption and CCA-Secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) Progress in Cryptology – AFRICACRYPT 2018, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16 Alkim et al. [2021] Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. 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Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. 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Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. 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Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. 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IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. 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Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: Module-LWR Based Key Exchange, CPA-Secure Encryption and CCA-Secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) Progress in Cryptology – AFRICACRYPT 2018, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16 Alkim et al. [2021] Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. 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In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  3. D’Anvers, J.-P., Karmakar, A., Sinha Roy, S., Vercauteren, F.: Saber: Module-LWR Based Key Exchange, CPA-Secure Encryption and CCA-Secure KEM. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) Progress in Cryptology – AFRICACRYPT 2018, pp. 282–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_16 Alkim et al. [2021] Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. 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Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  4. Alkim, E., Bos, J.W., Ducas, L., Longa, P., Mironov, I., Naehrig, M., Nikolaenko, V., Peikert, C., Raghunathan, A., Stebila, D.: FrodoKEM: Learning With Errors Key Encapsulation. NIST Round 3 specification (2021). https://frodokem.org/ D’Anvers et al. [2019] D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. 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[1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  5. D’Anvers, J.-P., Guo, Q., Johansson, T., Nilsson, A., Vercauteren, F., Verbauwhede, I.: Decryption Failure Attacks on IND-CCA Secure Lattice-Based Schemes. In: Lin, D., Sako, K. (eds.) Public-Key Cryptography – PKC 2019, pp. 565–598. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17259-6_19 Avanzi et al. [2021] Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. 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IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  6. Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J., Schwabe, P., Seiler, G., Stehlé, D.: Algorithm specifications and supporting documentation (version 3.02). Tech. rep., Submission to the NIST post-quantum project (2021). https://pq-crystals.org/kyber/resources.shtml D’Anvers and Batsleer [2022] D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. 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Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  7. D’Anvers, J.-P., Batsleer, S.: Multitarget Decryption Failure Attacks and Their Application to Saber and Kyber. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography – PKC 2022, pp. 3–33. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-97121-2_1 Fritzmann et al. [2019] Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Fritzmann, T., Pöppelmann, T., Sepulveda, J.: Analysis of error-correcting codes for lattice-based key exchange. In: Cid, C., Jacobson Jr., M.J. (eds.) Selected Areas in Cryptography – SAC 2018, pp. 369–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10970-7_17 Papadopoulos and Wang [2023] Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. 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Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. 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[2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Papadopoulos, I., Wang, J.: Polar codes for Module-LWE public key encryption: The case of Kyber. Cryptography 7(1) (2023) https://doi.org/10.3390/cryptography7010002 Lyu et al. [2023] Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. 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Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. 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Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. 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[1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lyu, S., Liu, L., Ling, C., Lai, J., Chen, H.: Lattice Codes for Lattice-Based PKE. In: Des. Codes Cryptogr. (2023). https://doi.org/10.1007/s10623-023-01321-6 D’Anvers et al. [2019] D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. 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[1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) D’Anvers, J.-P., Tiepelt, M., Vercauteren, F., Verbauwhede, I.: Timing Attacks on Error Correcting Codes in Post-Quantum Schemes. In: Proceedings of ACM Workshop on Theory of Implementation Security Workshop. TIS’19, pp. 2–9. Association for Computing Machinery, New York, NY, USA (2019). https://doi.org/10.1145/3338467.3358948 Walters and Roy [2020] Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. 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[2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. 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In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. 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Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. 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[1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. 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Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  12. Walters, M., Roy, S.S.: Constant-time BCH error-correcting code. In: 2020 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1–5 (2020). https://doi.org/10.1109/ISCAS45731.2020.9180846 van Poppelen [2016] Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  13. Poppelen, A.: Cryptographic decoding of the Leech lattice. Cryptology ePrint Archive, Paper 2016/1050 (2016). https://eprint.iacr.org/2016/1050 Gupta et al. [2021] Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  14. Gupta, N., Jati, A., Chauhan, A.K., Chattopadhyay, A.: PQC Acceleration Using GPUs: FrodoKEM, NewHope, and Kyber. IEEE Transactions on Parallel and Distributed Systems 32(3), 575–586 (2021) https://doi.org/10.1109/TPDS.2020.3025691 Huang et al. [2020] Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. 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Prentice-Hall, Inc., USA (2004) Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. 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Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  15. Huang, Y., Huang, M., Lei, Z., Wu, J.: A pure hardware implementation of CRYSTALS-KYBER PQC algorithm through resource reuse. IEICE Electron. Express 17, 20200234 (2020) https://doi.org/10.1587/elex.17.20200234 Costa et al. [2022] Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  16. Costa, V.L.R.D., Camponogara, Â., López, J., Ribeiro, M.V.: The Feasibility of the CRYSTALS-Kyber Scheme for Smart Metering Systems. IEEE Access 10, 131303–131317 (2022) https://doi.org/10.1109/ACCESS.2022.3229521 Costache et al. [2022] Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  17. Costache, A., Curtis, B.R., Hales, E., Murphy, S., Ogilvie, T., Player, R.: On the precision loss in approximate homomorphic encryption. Cryptology ePrint Archive, Paper 2022/162 (2022). https://eprint.iacr.org/2022/162 Ding et al. [2022] Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  18. Ding, X., Esgin, M.F., Sakzad, A., Steinfeld, R.: An injectivity analysis of Crystals-Kyber and implications on quantum security. In: Information Security and Privacy, pp. 332–351. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22301-3_17 Conway and Sloane [1999] Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  19. Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices, and Groups, 3rd edn. Springer, New York (1999). https://doi.org/10.1007/978-1-4757-6568-7 Vardy and Be’ery [1993] Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  20. Vardy, A., Be’ery, Y.: Maximum likelihood decoding of the Leech lattice. IEEE Transactions on Information Theory 39(4), 1435–1444 (1993) https://doi.org/10.1109/18.243466 Caire et al. [1998] Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  21. Caire, G., Taricco, G., Biglieri, E.: Bit-interleaved coded modulation. IEEE Trans. Inf. Theory 44(3), 927–946 (1998) https://doi.org/10.1109/18.669123 Lin and Costello [2004] Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004) Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
  22. Lin, S., Costello, D.J.: Error Control Coding, Second Edition. Prentice-Hall, Inc., USA (2004)
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