Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Quantum Money from Abelian Group Actions (2307.12120v4)

Published 22 Jul 2023 in quant-ph and cs.CR

Abstract: We give a construction of public key quantum money, and even a strengthened version called quantum lightning, from abelian group actions, which can in turn be constructed from suitable isogenies over elliptic curves. We prove security in the generic group model for group actions under a plausible computational assumption, and develop a general toolkit for proving quantum security in this model. Along the way, we explore knowledge assumptions and algebraic group actions in the quantum setting, finding significant limitations of these assumptions/models compared to generic group actions.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (64)
  1. Scott Aaronson. Quantum copy-protection and quantum money. In Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC ’09, pages 229–242, Washington, DC, USA, 2009. IEEE Computer Society.
  2. Quantum money from hidden subspaces. In Howard J. Karloff and Toniann Pitassi, editors, 44th ACM STOC, pages 41–60. ACM Press, May 2012.
  3. Cryptographic group actions and applications. In Shiho Moriai and Huaxiong Wang, editors, ASIACRYPT 2020, Part II, volume 12492 of LNCS, pages 411–439. Springer, Heidelberg, December 2020.
  4. Candidate trapdoor claw-free functions from group actions with applications to quantum protocols. In Eike Kiltz and Vinod Vaikuntanathan, editors, TCC 2022, Part I, volume 13747 of LNCS, pages 266–293. Springer, Heidelberg, November 2022.
  5. Strengths and weaknesses of quantum computing. SIAM J. Comput., 26(5):1510–1523, Oct 1997.
  6. A cryptographic test of quantumness and certifiable randomness from a single quantum device. In Mikkel Thorup, editor, 59th FOCS, pages 320–331. IEEE Computer Society Press, October 2018.
  7. Factoring and pairings are not necessary for iO: Circular-secure LWE suffices. Cryptology ePrint Archive, Report 2020/1024, 2020. https://eprint.iacr.org/2020/1024.
  8. Shalev Ben-David and Or Sattath. Quantum tokens for digital signatures, 2016. https://arxiv.org/abs/1609.09047.
  9. Return of GGH15: Provable security against zeroizing attacks. In Amos Beimel and Stefan Dziembowski, editors, TCC 2018, Part II, volume 11240 of LNCS, pages 544–574. Springer, Heidelberg, November 2018.
  10. A lower bound on the length of signatures based on group actions and generic isogenies. In Carmit Hazay and Martijn Stam, editors, EUROCRYPT 2023, Part V, volume 14008 of LNCS, pages 507–531. Springer, Heidelberg, April 2023.
  11. CSI-FiSh: Efficient isogeny based signatures through class group computations. In Steven D. Galbraith and Shiho Moriai, editors, ASIACRYPT 2019, Part I, volume 11921 of LNCS, pages 227–247. Springer, Heidelberg, December 2019.
  12. Amit Behera and Or Sattath. Almost public quantum coins. Cryptology ePrint Archive, Report 2020/452, 2020. https://eprint.iacr.org/2020/452.
  13. Quantum security analysis of CSIDH. In Anne Canteaut and Yuval Ishai, editors, EUROCRYPT 2020, Part II, volume 12106 of LNCS, pages 493–522. Springer, Heidelberg, May 2020.
  14. An efficient key recovery attack on SIDH. In Carmit Hazay and Martijn Stam, editors, EUROCRYPT 2023, Part V, volume 14008 of LNCS, pages 423–447. Springer, Heidelberg, April 2023.
  15. Constructing elliptic curve isogenies in quantum subexponential time. Journal of Mathematical Cryptology, 8(1):1–29, 2014.
  16. Orienting supersingular isogeny graphs. Journal of Mathematical Cryptology, 14:414–437, 10 2020.
  17. CSIDH: An efficient post-quantum commutative group action. In Thomas Peyrin and Steven Galbraith, editors, ASIACRYPT 2018, Part III, volume 11274 of LNCS, pages 395–427. Springer, Heidelberg, December 2018.
  18. Jean-Marc Couveignes. Hard homogeneous spaces. Cryptology ePrint Archive, Report 2006/291, 2006. https://eprint.iacr.org/2006/291.
  19. Non-quantum cryptanalysis of the noisy version of aaronson–christiano’s quantum money scheme. IET Information Security, 13(4):362–366, 2019.
  20. Ivan Damgård. Towards practical public key systems secure against chosen ciphertext attacks. In Joan Feigenbaum, editor, CRYPTO’91, volume 576 of LNCS, pages 445–456. Springer, Heidelberg, August 1992.
  21. SCALLOP: Scaling the CSI-FiSh. In Alexandra Boldyreva and Vladimir Kolesnikov, editors, PKC 2023, Part I, volume 13940 of LNCS, pages 345–375. Springer, Heidelberg, May 2023.
  22. Luca De Feo and Steven D. Galbraith. SeaSign: Compact isogeny signatures from class group actions. In Yuval Ishai and Vincent Rijmen, editors, EUROCRYPT 2019, Part III, volume 11478 of LNCS, pages 759–789. Springer, Heidelberg, May 2019.
  23. Generic models for group actions. In Alexandra Boldyreva and Vladimir Kolesnikov, editors, PKC 2023, Part I, volume 13940 of LNCS, pages 406–435. Springer, Heidelberg, May 2023.
  24. Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. Journal of Mathematical Cryptology, 8(3):209–247, 2014.
  25. Luca De Feo and Michael Meyer. Threshold schemes from isogeny assumptions. In Aggelos Kiayias, Markulf Kohlweiss, Petros Wallden, and Vassilis Zikas, editors, PKC 2020, Part II, volume 12111 of LNCS, pages 187–212. Springer, Heidelberg, May 2020.
  26. On quantum algorithms for noncommutative hidden subgroups. Advances in Applied Mathematics, 25(3):239–251, 2000.
  27. Quantum money from knots. In Shafi Goldwasser, editor, ITCS 2012, pages 276–289. ACM, January 2012.
  28. The algebraic group model and its applications. In Hovav Shacham and Alexandra Boldyreva, editors, CRYPTO 2018, Part II, volume 10992 of LNCS, pages 33–62. Springer, Heidelberg, August 2018.
  29. Graph-induced multilinear maps from lattices. In Yevgeniy Dodis and Jesper Buus Nielsen, editors, TCC 2015, Part II, volume 9015 of LNCS, pages 498–527. Springer, Heidelberg, March 2015.
  30. Quantum complexity for discrete logarithms and related problems. Cryptology ePrint Archive, Paper 2023/1054, 2023. https://eprint.iacr.org/2023/1054.
  31. Indistinguishability obfuscation from well-founded assumptions. In Samir Khuller and Virginia Vassilevska Williams, editors, 53rd ACM STOC, pages 60–73. ACM Press, June 2021.
  32. On the equivalence of generic group models. In Joonsang Baek, Feng Bao, Kefei Chen, and Xuejia Lai, editors, ProvSec 2008, volume 5324 of LNCS, pages 200–209. Springer, Heidelberg, October / November 2008.
  33. Daniel M. Kane. Quantum money from modular forms, 2018. https://arxiv.org/abs/1809.05925.
  34. Publicly verifiable quantum money from random lattices, 2022. https://arxiv.org/abs/2207.13135v2.
  35. Quantum money from quaternion algebras. Cryptology ePrint Archive, Report 2021/1294, 2021. https://eprint.iacr.org/2021/1294.
  36. Breaking and making quantum money: Toward a new quantum cryptographic protocol. In Andrew Chi-Chih Yao, editor, ICS 2010, pages 20–31. Tsinghua University Press, January 2010.
  37. Another round of breaking and making quantum money: How to not build it from lattices, and more. In Carmit Hazay and Martijn Stam, editors, EUROCRYPT 2023, Part I, volume 14004 of LNCS, pages 611–638. Springer, Heidelberg, April 2023.
  38. Andrew Lutomirski. An online attack against wiesner’s quantum money, 2010. https://arxiv.org/abs/1010.0256.
  39. Revisiting post-quantum Fiat-Shamir. In Alexandra Boldyreva and Daniele Micciancio, editors, CRYPTO 2019, Part II, volume 11693 of LNCS, pages 326–355. Springer, Heidelberg, August 2019.
  40. Ueli M. Maurer. Abstract models of computation in cryptography (invited paper). In Nigel P. Smart, editor, 10th IMA International Conference on Cryptography and Coding, volume 3796 of LNCS, pages 1–12. Springer, Heidelberg, December 2005.
  41. An attack on SIDH with arbitrary starting curve. Cryptology ePrint Archive, Report 2022/1026, 2022. https://eprint.iacr.org/2022/1026.
  42. Full quantum equivalence of group action DLog and CDH, and more. In Shweta Agrawal and Dongdai Lin, editors, ASIACRYPT 2022, Part I, volume 13791 of LNCS, pages 3–32. Springer, Heidelberg, December 2022.
  43. L1subscript𝐿1{L_{1}}italic_L start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT-norm ball for CSIDH: Optimal strategy for choosing the secret key space. Cryptology ePrint Archive, Report 2020/181, 2020. https://eprint.iacr.org/2020/181.
  44. Simple two-round OT in the explicit isogeny model. Cryptology ePrint Archive, Report 2023/269, 2023. https://eprint.iacr.org/2023/269.
  45. Lorenz Panny. Csi-fish really isn’t polynomial-time, 2023. https://yx7.cc/blah/2023-04-14.html.
  46. Chris Peikert. He gives C-sieves on the CSIDH. In Anne Canteaut and Yuval Ishai, editors, EUROCRYPT 2020, Part II, volume 12106 of LNCS, pages 463–492. Springer, Heidelberg, May 2020.
  47. Oded Regev. On lattices, learning with errors, random linear codes, and cryptography. In Harold N. Gabow and Ronald Fagin, editors, 37th ACM STOC, pages 84–93. ACM Press, May 2005.
  48. Bhaskar Roberts. Security analysis of quantum lightning. In Anne Canteaut and François-Xavier Standaert, editors, EUROCRYPT 2021, Part II, volume 12697 of LNCS, pages 562–567. Springer, Heidelberg, October 2021.
  49. Damien Robert. Breaking SIDH in polynomial time. In Carmit Hazay and Martijn Stam, editors, EUROCRYPT 2023, Part V, volume 14008 of LNCS, pages 472–503. Springer, Heidelberg, April 2023.
  50. Phillip Rogaway. Formalizing human ignorance. In Phong Q. Nguyen, editor, Progress in Cryptology - VIETCRYPT 06, volume 4341 of LNCS, pages 211–228. Springer, Heidelberg, September 2006.
  51. Public-Key Cryptosystem Based On Isogenies. Cryptology ePrint Archive, Report 2006/145, 2006. https://eprint.iacr.org/2006/145.
  52. Franchised quantum money. In Mehdi Tibouchi and Huaxiong Wang, editors, ASIACRYPT 2021, Part I, volume 13090 of LNCS, pages 549–574. Springer, Heidelberg, December 2021.
  53. Peter W. Shor. Algorithms for quantum computation: Discrete logarithms and factoring. In 35th FOCS, pages 124–134. IEEE Computer Society Press, November 1994.
  54. Victor Shoup. Lower bounds for discrete logarithms and related problems. In Walter Fumy, editor, EUROCRYPT’97, volume 1233 of LNCS, pages 256–266. Springer, Heidelberg, May 1997.
  55. Vladimir Shpilrain. Cryptanalysis of stickel’s key exchange scheme. In Edward A. Hirsch, Alexander A. Razborov, Alexei Semenov, and Anatol Slissenko, editors, Computer Science – Theory and Applications, pages 283–288, Berlin, Heidelberg, 2008. Springer Berlin Heidelberg.
  56. E. Stickel. A new method for exchanging secret keys. In Third International Conference on Information Technology and Applications (ICITA’05), volume 2, pages 426–430, 2005.
  57. Stephen Wiesner. Conjugate coding. SIGACT News, 15(1):78–88, January 1983.
  58. A. Winter. Coding theorem and strong converse for quantum channels. IEEE Trans. Inf. Theor., 45(7):2481–2485, November 1999.
  59. Candidate obfuscation via oblivious LWE sampling. In Anne Canteaut and François-Xavier Standaert, editors, EUROCRYPT 2021, Part III, volume 12698 of LNCS, pages 127–156. Springer, Heidelberg, October 2021.
  60. Verifiable quantum advantage without structure. In 63rd FOCS, pages 69–74. IEEE Computer Society Press, October / November 2022.
  61. Mark Zhandry. How to record quantum queries, and applications to quantum indifferentiability. In Alexandra Boldyreva and Daniele Micciancio, editors, CRYPTO 2019, Part II, volume 11693 of LNCS, pages 239–268. Springer, Heidelberg, August 2019.
  62. Mark Zhandry. Quantum lightning never strikes the same state twice. In Yuval Ishai and Vincent Rijmen, editors, EUROCRYPT 2019, Part III, volume 11478 of LNCS, pages 408–438. Springer, Heidelberg, May 2019.
  63. Mark Zhandry. Redeeming reset indifferentiability and applications to post-quantum security. In Mehdi Tibouchi and Huaxiong Wang, editors, ASIACRYPT 2021, Part I, volume 13090 of LNCS, pages 518–548. Springer, Heidelberg, December 2021.
  64. Mark Zhandry. To label, or not to label (in generic groups). In Yevgeniy Dodis and Thomas Shrimpton, editors, CRYPTO 2022, Part III, volume 13509 of LNCS, pages 66–96. Springer, Heidelberg, August 2022.
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now