Abstract
Post-quantum cryptography has attracted much attention from worldwide cryptologists. However, most research works are related to public-key cryptosystem due to Shor’s attack on RSA and ECC ciphers. At CRYPTO 2016, Kaplan et al. showed that many secret-key (symmetric) systems could be broken using a quantum period finding algorithm, which encouraged researchers to evaluate symmetric systems against quantum attackers. In this paper, we continue to study symmetric ciphers against quantum attackers. First, we convert the classical advanced slide attacks (introduced by Biryukov and Wagner) to a quantum one, that gains an exponential speed-up in time complexity. Thus, we could break 2/4K-Feistel and 2/4K-DES in polynomial time. Second, we give a new quantum key-recovery attack on full-round GOST, which is a Russian standard, with \(2^{114.8}\) quantum queries of the encryption process, faster than a quantum brute-force search attack by a factor of \(2^{13.2}\).
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Notes
The way to select \(\alpha \) is the same as Sect. 3.2.1.
References
Benoist J. C.: Quantum circuit representation of Grover’s algorithm. Wikimedia, Inc. http://en.wikipedia.org/wiki/File: Grovers algorithm.svg. Accessed 5 Jan 2011
Biham E., Shamir A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3–72 (1991).
Biryukov A., Wagner D.: Slide attacks. In: Knudsen L. (ed.) Fast Software Encryption, FSE 1999, vol. 1636, pp. 245–259. Lecture Notes in Computer ScienceSpringer, Berlin, Heidelberg (1999).
Biryukov A., Wagner D.: Advanced slide attacks. In: Preneel B. (ed.) Advances in Cryptology—EUROCRYPT 2000, vol. 1807, pp. 589–606. Lecture Notes in Computer ScienceSpringer, Berlin, Heidelberg (2000).
Boneh D., Zhandry M.: Quantum-secure message authentication codes. In: T. Johansson, P. Q. Nguyen (eds.) Advances in Cryptology—EUROCRYPT 2013, 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26–30, 2013. Proceedings, volume 7881 of Lecture Notes in Computer Science, pp. 592–608. Springer (2013)
Boneh D., Zhandry M.: Secure signatures and chosen ciphertext security in a quantum computing world. In: Canetti R., Garay J.A. (eds.) Advances in Cryptology—CRYPTO 2013, vol. 8043, pp. 361–379. Lecture Notes in Computer ScienceSpringer, Berlin (2013).
Bonnetain X., Naya-Plasencia M., Schrottenloher A.: On Quantum Slide Attacks. Cryptology ePrint Archive, Report 2018/1067. To appear at SAC (2019)
Brassard G., Hoyer P., Mosca M., et al.: Quantum amplitude amplification and estimation. arXiv:quant-ph/0005055 (2000)
Chailloux A., Naya-Plasencia M., Schrottenloher A.: An efficient quantum collision search algorithm and implications on symmetric cryptography. Cryptology ePrint Archive, Report 2017/847 (2017)
Damgård I., Funder J., Nielsen J.B., Salvail L.: Superposition attacks on cryptographic protocols. In: Padró C. (ed.) ICITS 2013, vol. 8317, pp. 142–161. LNCSSpringer, Heidelberg (2014).
Dinur I., Dunkelman O., Shamir A.: Improved attacks on full GOST. In: Canteaut A. (ed.) Fast Software Encryption, FSE 2012, vol. 7549, pp. 9–28. Lecture Notes in Computer ScienceSpringer, Berlin (2012).
Dong X., Dong B., Wang X.: Quantum Attacks on Some Feistel Block Ciphers. Cryptology ePrint Archive, Report 2018/504.
Dong X., Wang X.: Quantum key-recovery attack on Feistel structures. Sci. China Inf. Sci. 61(10), 102501 (2018). https://doi.org/10.1007/s11432-017-9468-y.
Dong X., Li Z., Wang X.: Quantum cryptanalysis on some generalized Feistel schemes. Sci. China Inf. Sci. 62(2), 22501 (2018).
Feistel H., Notz W.A., Smith J.L.: Some cryptographic techniques for machine-to-machine data communications. Proc. IEEE 63(11), 1545–1554 (1975).
Grover L. K: A fast quantum mechanical algorithm for database search. In: Miller G L, eds. Proceedings of STOC 1996. ACM, pp. 212–219 (1996)
Hosoyamada A., Sasaki Y.: Quantum Demiric-Selçuk Meet-in-the-Middle Attacks. Applications to 6-Round Generic Feistel Constructions. In: Catalano D, De Prisco R, (eds.), Security and Cryptography for Networks—11th International Conference, SCN 2018. Lecture Notes in Computer Science, vol. 11035. Springer, Cham, pp. 386–403 (2018)
Hosoyamada A., Sasaki Y.: Cryptanalysis against symmetric-key schemes with online classical queries and offline quantum computations. In: Smart N.P. (ed.) CT-RSA 2018, vol. 10808, pp. 198–218. LNCSSpringer, Cham (2018).
Hosoyamada A., Sasaki Y., Xagawa K.: Quantum multicollision-finding algorithm. IACR Cryptol. ePrint Arch. 2017, 864 (2017).
International Organization for Standardization (ISO).: International Standard-ISO/IEC 18033-3, Information technology-Security techniques-Encryption algorithms-Part 3: Block ciphers (2010)
Isobe T.: A single-key attack on the full GOST block cipher. In: Joux A. (ed.) Fast Software Encryption, FSE 2011, vol. 6733, pp. 290–305. Lecture Notes in Computer ScienceSpringer-Verlag, Berlin (2011).
Ito G., Hosoyamada A., Matsumoto R., Sasaki Y., Iwata T.: Quantum chosen-ciphertext attacks against feistel ciphers. In: Matsui M (eds.) Topics in Cryptology—CT-RSA 2019—The Cryptographers’ Track at the RSA Conference 2019, San Francisco, CA, USA, March 4–8, 2019, Proceedings. Lecture Notes in Computer Science, vol. 11405. Springer, pp. 391–411 (2019)
Kaplan M., Leurent G., Leverrier A., Naya-Plasencia M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw M., Katz J. (eds.) Advances in Cryptology—CRYPTO 2016, vol. 9815, pp. 207–237. Lecture Notes in Computer ScienceSpringer, Berlin (2016).
Kaplan M., Leurent G., Leverrier A., Naya-Plasencia M.: Quantum differential and linear cryptanalysis. IACR Trans. Symmetric Cryptol. 1, 71–94 (2016).
Kara O.: Reflection cryptanalysis of some ciphers. In: Chowdhury D.R., Rijmen V., Das A. (eds.) Progress in Cryptology—INDOCRYPT 2008, vol. 5365, pp. 294–307. Lecture Notes in Computer ScienceSpringer, Berlin (2008).
Kuwakado H., Morii M.: Quantum distinguisher between the 3-round feistel cipher and the random permutation. In: International symposium on information theory, ISIT 2010. IEEE, pp. 2682–2685 (2010)
Kuwakado H., Morii M.: Security on the quantum-type even-mansour cipher. In: International symposium on information theory and its applications, ISITA 2012. IEEE, pp. 312–316 (2012)
Leander G., May A.: Grover meets simon—quantumly attacking the FX-construction. In: Takagi T., Peyrin T. (eds.) Advances in Cryptology—ASIACRYPT 2017, Part II, vol. 10625, pp. 161–178. Lecture Notes in Computer ScienceCham, Springer (2017).
Matsui M.: Linear cryptanalysis method of DES sipher. In: Helleseth T. (ed.) EUROCRYPT 1993, vol. 765, pp. 386–397. LNCSSpringer, Heidelberg (1994).
Moody D.: The Ship Has Sailed: the NIST Post-quantum Cryptography “Competition”(Invited talk). In: Advances in Cryptology—ASIACRYPT 2017. Springer, Berlin (2017)
National Soviet Bureau of Standards: Information Processing System—Cryptographic Protection—Cryptographic Algorithm GOST 28147–89 (1989)
Nielsen M. A, Chuang I.: Quantum computation and quantum information. aapt.scitation.org (2002)
Rivest R.L., Shamir A., Adleman L.: A Method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978).
Santoli T., Schaffner C.: Using simon’s algorithm to attack symmetric-key cryptographic primitives. Quantum Inf. Comput. 17(1&2), 65–78 (2017).
Shor P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997).
Simon D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997).
Strubell E.: An Introduction to Quantum Algorithms. https://people.cs.umass.edu/~strubell/doc/quantum_tutorial.pdf
Zhandry M.: How to construct quantum random functions. In: 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012, New Brunswick, NJ, USA, October 20–23, 2012, pp. 679–687. IEEE Computer Society (2012)
Acknowledgements
We would like to thank the anonymous reviewers for their important comments on this paper. This work is supported by National Key Research and Development Program of China (No. 2017YFA0303903), the National Natural Science Foundation of China (No. 61902207), the National Cryptography Development Fund (No. MMJJ20180101, MMJJ20170121).
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Dong, X., Dong, B. & Wang, X. Quantum attacks on some feistel block ciphers. Des. Codes Cryptogr. 88, 1179–1203 (2020). https://doi.org/10.1007/s10623-020-00741-y
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DOI: https://doi.org/10.1007/s10623-020-00741-y