证论文的正确性。目前一些论坛、公众号、知乎等平台也有很多人发表了一些相关见解,大家都是在分析如果论文中的算法是正确的,会带来哪些影响,至于论文算法的正确性问题,还没人能下定结论。其中,著名密码学家 N. P. Smart 发表了博客文章《Implications of the Proposed Quantum Attack on LWE》[14],详细介绍了此攻击的影响和一些观点,总结如下: 这篇论文目前尚未经过同行评审,即使被验证是正确的,也要依赖于量子计算机,因此只要量子计算机还未问世,对目前在使用的密码方案均无影响。 按照论文中给出的结果:仍无法攻破此前 NIST 给出的标准化算法 Kyber, Dilithium,但 NIST 可能会重新评估这些算法的参数。 对于常用的 RLWE 同态加密算法,如 BFV/CKKS/BGV,这些算法是在这篇论文的攻击能力之内的。不过,不管从是学术界还是工业界的视角,同态加密技术的“同态性”比其“抗量子性”更具吸引力,很少人会为追求“抗量子性”而使用 RLWE 同态加密算法,就像基于椭圆曲线的密码方案依赖于离散对数困难问题,而求解该问题的量子算法很早就被提出了,但学术界,工业界仍然在研究、使用这些方案。 最新消息:陈老师论文计算存在问题,格密码警报暂时解除。 [1] https://ethresear.ch/t/how-to-hard-fork-to-save-most-users-funds-in-a-quantum-emergency/18901/9 [2] Benioff P. The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines[J]. Journal of statistical physics, 1980, 22: 563-591. [3] Shor P W. Algorithms for quantum computation: discrete logarithms and factoring[C]//Proceedings 35th annual symposium on foundations of computer science. Ieee, 1994: 124-134. [4] Grover L K. A fast quantum mechanical algorithm for database search[C]//Proceedings of the twenty-eighth annual ACM symposium on Theory of computing. 1996: 212-219. [5] Bernstein, D.J. (2009). Introduction to post-quantum cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds) Post-Quantum Cryptography. Springer, Berlin, Heidelberg. [6] Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography[J]. Reviews of modern physics, 2002, 74(1): 145. [7] https://csrc.nist.gov/Projects/post-quantum-cryptography/post-quantum-cryptography-standardization [8] https://csrc.nist.gov/News/2022/pqc-candidates-to-be-standardized-and-round-4 [9] https://csrc.nist.gov/News/2023/three-draft-fips-for-post-quantum-cryptography [10] Huelsing, A., Butin, D., Gazdag, S., Rijneveld, J., and A. Mohaisen, "XMSS: eXtended Merkle Signature Scheme", RFC 8391, DOI 10.17487/RFC8391, May 2018, . [11] McGrew, D., Curcio, M., and S. Fluhrer, "Leighton-Micali Hash-Based Signatures", RFC 8554, DOI 10.17487/RFC8554, April 2019, . [12] Chen Y. Quantum Algorithms for Lattice Problems[J]. Cryptology ePrint Archive, 2024. [13] Regev O. On lattices, learning with errors, random linear codes, and cryptography[J]. Journal of the ACM (JACM), 2009, 56(6): 1-40. [14] https://nigelsmart.github.io/LWE.html 本文由 ZAN Team(X 账号 @zan_team)的 Dongni 和 Jiaxing 共同撰写。 来源:金色财经lg...