Quantum Algorithm for the Invariant Estimate of the Closeness of Classical Ciphers to the One-Time Pad

Pleiades Publishing Ltd - Tập 117 - Trang 75-82 - 2023
S. N. Molotkov1,2
1Academy of Cryptography of the Russian Federation, Moscow, Russia
2Osipyan Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Russia

Tóm tắt

An invariant measure of the closeness of a block cipher to the perfect (ideal) cipher of the one-time pad has been proposed. The measure is the same for any implementation of the one-time pad. A quantum algorithm based on the determination of the eigenvalue (phase) of the quantum state has been proposed to estimate the closeness of the block cipher to ideal in terms of the proposed measure with high probability and accuracy.

Tài liệu tham khảo

D. Deutsch and R. Jozsa, Proc. R. Soc. London, Ser. A 439 (1907), 553 (1992). P. W. Shor, SIAM J. Comput. 26, 1484 (1997). L. K. Grover, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing—STOC’96 (ACM Press, New York, 1996), p. 212. D. R. Simon, SIAM J. Comput. 26, 1474 (1997). M. Kaplan, G. Leurent, A. Leverrier, and M. Naya-Plasencia, arXiv: 1602.05973 [quant-ph] (2016). A. Ambainis, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (IEEE, 2014), p. 22. https://ieeexplore.ieee.org/document/1366221. A. W. Harrow, A. Hassidim, and S. Lloyd, Phys. Rev. Lett. 103, 150502 (2009). D. Dervovic, M. Herbster, P. Mountney, S. Severini, N. Usher, and L. Wossnig, arXiv: 0311001 [quant-ph] (2014). M. Grassl, B. Langenberg, M. Roetteler, and R. Steinwand, arXiv: 1512.04965 [quant-ph] (2015). M. Almazrooie, A. Samsudin, R. Abdullah, and K. N. Mutter, SpringerPlus 5, 1494 (2016). M. Almazrooie, A. Samsudin, R. Abdullah, and K. N. Mutter, in Proceedings of the 2018 7th International Conference on Software and Computer Applications (ACM, New York, 2018), p. 204. D. V. Denisenko, G. B. Marshalko, M. V. Nikitenkova, V. I. Rudskoi, and V. A. Shishkin, J. Exp. Theor. Phys. 128, 552 (2019). V. Gheorghiu and M. Mosca, A Resource Estimation Framework for Quantum Attacks against Cryptographic Functions—Recent Developments. https://globalriskinstitute.org. Accessed 2021. M. Piani and M. Mosca, Quantum Threat Timeline Report (2020). https://globalriskinstitute.org. M. Piani and M. Mosca, Quantum Threat Timeline Report (2019). https://globalriskinstitute.org. V. Gheorghiu and M. Mosca, Global Risk Institute Quantum Risk Assessment Report (2020). https://globalriskinstitute.org. V. Gheorghiu and M. Mosca, Global Risk Institute Quantum Risk Assessment Report, Part 4 (2018). https://globalriskinstitute.org. V. Gheorghiu and M. Mosca, Global Risk Institute Quantum Risk Assessment Report, Part 3 (2018). https://globalriskinstitute.org. V. Gheorghiu and M. Mosca, Global Risk Institute Quantum Risk Assessment Report, Part 2 (2018). https://globalriskinstitute.org. V. Gheorghiu and M. Mosca, Global Risk Institute Quantum Risk Assessment Report, Part 1 (2017). https://globalriskinstitute.org. Y.-A. Chen and X.-S. Gao, arXiv: 1712.06239 [quant-ph] (2018). A. Ambainis, arXiv: 1010.4458 [quant-ph] (2010). A. M. Childs, R. Kothari, and R. D. Somma, SIAM J. Comput. 46, 1920 (2017). L. Wossnig, Z. Zhao, and A. Prakash, Phys. Rev. Lett. 120, 050502 (2018). G. Brassard, P. Hoyer, and A. Tapp, ACM SIGACT News 28 (2), 14 (1997). A. Chailloux, M. Naya-Plasencia, and A. Schrottenloher, Preprint (2017). https://eprint.iacr.org/2017/847. G. Brassard, P. Hoyer, and A. Tapp, arXiv: 0005055 [quant-ph] (2000). T. Häner and M. Soeken, arXiv: 2006.03845 [quant-ph] (2020). M. Roetteler and R. Steinwandt, Inf. Process. Lett. 115, 40 (2015). A. Hosoyamada and E. Aoki, in On Quantum Related-Key Attacks on Iterated Even-Mansour Ciphers, Ed. by S. Obana and K. Chida, Lect. Notes Comput. Sci. 10418, 3 (2017). X. Bonnetain, M. Naya-Plasencia, and A. Schrottenloher, Preprint (2018). https://eprint.iacr.org/2018/1067.pdf. A. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation (MTsNMO-CheRo, Moscow, 1999; Am. Math. Soc., Philadelphia, 2002). G. Leander and A. May, in Advances in Cryptology— ASIACRYPT 2017 23rd International Conference on the Theory and Applications of Cryptology and Information Security, Hong Kong, China, December 3–7, 2017 (Springer, 2017), Part II. G. S. Vernam, J. IEEE 55, 109 (1926). V. A. Kotel’nikov, Report (1941). https://cryptography-museum.ru. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948); Bell Syst. Tech. J. 27, 623 (1948); Report (1945). https://www.iacr.org > shannon > shannon45. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th ed. (Cambridge Univ. Press, Cambridge, 2010). S. N. Molotkov, Laser Phys. Lett. 19, 045201 (2022). S. N. Molotkov, Laser Phys. Lett. 19, 075203 (2022). I. M. Arbekov and S. N. Molotkov, J. Exp. Theor. Phys. 125, 50 (2017). S. N. Molotkov, JETP Lett. 103, 345 (2016).