On black-box separations of quantum digital signatures from pseudorandom states (2402.08194v1)
Abstract: It is well-known that digital signatures can be constructed from one-way functions in a black-box way. While one-way functions are essentially the minimal assumption in classical cryptography, this is not the case in the quantum setting. A variety of qualitatively weaker and inherently quantum assumptions (e.g. EFI pairs, one-way state generators, and pseudorandom states) are known to be sufficient for non-trivial quantum cryptography. While it is known that commitments, zero-knowledge proofs, and even multiparty computation can be constructed from these assumptions, it has remained an open question whether the same is true for quantum digital signatures schemes (QDS). In this work, we show that there $\textit{does not}$ exist a black-box construction of a QDS scheme with classical signatures from pseudorandom states with linear, or greater, output length. Our result complements that of Morimae and Yamakawa (2022), who described a $\textit{one-time}$ secure QDS scheme with classical signatures, but left open the question of constructing a standard $\textit{multi-time}$ secure one.
- Can you sign a quantum state? Quantum, 5:603, 2021.
- Pseudorandom (function-like) quantum state generators: New definitions and applications. In Theory of Cryptography: 20th International Conference, TCC 2022, Chicago, IL, USA, November 7–10, 2022, Proceedings, Part I, pages 237–265. Springer, 2023.
- Pseudorandom strings from pseudorandom quantum states. arXiv preprint arXiv:2306.05613, 2023.
- Cryptography from pseudorandom quantum states. In Advances in Cryptology–CRYPTO 2022: 42nd Annual International Cryptology Conference, CRYPTO 2022, Santa Barbara, CA, USA, August 15–18, 2022, Proceedings, Part I, pages 208–236. Springer, 2022.
- On the computational hardness needed for quantum cryptography. arXiv preprint arXiv:2209.04101, 2022.
- Local random quantum circuits are approximate polynomial-designs. In Communications in Mathematical Physics, pages 397–434, 2016.
- The power of a single haar random state: constructing and separating quantum pseudorandomness. To appear, 2024.
- Query-optimal estimation of unitary channels in diamond distance. arxiv preprint arxiv:2302.14066, 2023.
- Russell Impagliazzo. A personal view of average-case complexity. In Proceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference, pages 134–147. IEEE, 1995.
- Limits on the provable consequences of one-way permutations. In Proceedings of the twenty-first annual ACM symposium on Theory of computing, pages 44–61, 1989.
- Pseudorandom quantum states. In Advances in Cryptology–CRYPTO 2018: 38th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19–23, 2018, Proceedings, Part III 38, pages 126–152. Springer, 2018.
- Pseudorandom quantum states. In Advances in Cryptology – CRYPTO 2018, pages 126–152. Springer, 2018.
- William Kretschmer. Quantum pseudorandomness and classical complexity. In 16th Conference on the Theory of Quantum Computation, Communication and Cryptography, 2021.
- Commitments from quantum one-wayness. arXiv preprint arXiv:2310.11526, 2023.
- Elizabeth S. Meckes. The random matrix theory of the classical compact groups. Cambridge Tracts in Mathematics, pages 6–9, 2019.
- One-wayness in quantum cryptography. arXiv preprint arXiv:2210.03394, 2022.
- Quantum commitments and signatures without one-way functions. In Advances in Cryptology–CRYPTO 2022: 42nd Annual International Cryptology Conference, CRYPTO 2022, Santa Barbara, CA, USA, August 15–18, 2022, Proceedings, Part I, pages 269–295. Springer, 2022.
- Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, USA, 10th edition, 2011.
- Notions of reducibility between cryptographic primitives. In Theory of Cryptography Conference, pages 1–20. Springer, 2004.
- Mark Zhandry. Secure identity-based encryption in the quantum random oracle model. In Advances in Cryptology–CRYPTO 2012: 32nd Annual International Cryptology Conference, CRYPTO 2012, Berlin, Heidelberg, pages 758–775. Springer, 2012.