Abstract
Post-quantum cryptography has drawn considerable attention from cryptologists on a global scale. At Asiacrypt 2017, Leander and May combined Grover’s and Simon’s quantum algorithms to break the FX-based block ciphers, which were introduced by Kilian and Rogaway to strengthen DES. In this study, we investigate the Feistel constructions using Grover’s and Simon’s algorithms to generate new quantum key-recovery attacks on different rounds of Feistel constructions. Our attacks require 20.25nr−0.75n quantum queries to break an r-round Feistel construction. The time complexity of our attacks is less than that observed for quantum brute-force search by a factor of 20.75n. When compared with the best classical attacks, i.e., Dinur et al.’s attacks at CRYPTO 2015, the time complexity is reduced by a factor of 20.5n without incurring any memory cost.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Shor P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput, 1997, 26: 1484–1509
Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Commun ACM, 1978, 21: 120–126
Even S, Mansour Y. A construction of a cipher from a single pseudorandom permutation. J Cryptol, 1997, 10: 151–161
Kuwakado H, Morii M. Security on the quantum-type even-mansour cipher. In: Proceedings of International Symposium on Information Theory and Its Applications, Honolulu, 2012. 312–316
Kaplan M, Leurent G, Leverrier A, et al. Breaking symmetric cryptosystems using quantum period finding. In: Advances in Cryptology -CRYPTO 2016. Berlin: Springer-Verlag, 2016. 207–237
Moody D. The ship has sailed: the NIST post-quantum cryptography “competition” (invited talk). In: Advances in Cryptology-ASIACRYPT 2017. Berlin: Springer, 2017
Boneh D, Zhandry M. Secure signatures and chosen ciphertext security in a quantum computing world. In: Advances in Cryptology -CRYPTO 2013. Berlin: Springer, 2013. 361–379
Grover L K. A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of Computing, Philadelphia, 1996. 212–219
Simon D R. On the power of quantum computation. SIAM J Comput, 1997, 26: 1474–1483
Feistel H, Notz W A, Smith J L. Some cryptographic techniques for machine-to-machine data communications. Proc IEEE, 1975, 63: 1545–1554
International Organization for Standardization (ISO). Information Technology-Security Techniques-Encryption Algorithms-Part 3: Block Ciphers. International Standard-ISO/IEC 18033–3. 2010. https://doi.org/www.iso.org/standard/54531.html
Luby M G, Rackoff C. How to construct pseudorandom permutations from pseudorandom functions. SIAM J Comput, 1988, 17: 373–386
Kuwakado H, Morii M. Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: Proceedings of International Symposium on Information Theory, Austin, 2010. 2682–2685
Dinur I, Dunkelman O, Keller N, et al. New attacks on Feistel structures with improved memory complexities. In: Advances in Cryptology -CRYPTO 2015, Part I. Berlin: Springer, 2015. 433–454
Brassard G, Hoyer P, Mosca M, et al. Quantum amplitude amplification and estimation. 2000. ArXiv:quant-ph/0005055
Leander G, May A. Grover meets simon -quantumly attacking the FX-construction. In: Advances in Cryptology -ASIACRYPT 2017, Part II. Berlin: Springer, 2017. 161–178
Kilian J, Rogaway P. How to protect DES against exhaustive key search. In: Advances in Cryptology -CRYPTO 1996. Berlin: Springer, 1996. 252–267
Borghoff J, Canteaut A, G¨uneysu T, et al. PRINCE — a low-latency block cipher for pervasive computing applications — extended abstract. In: Advances in Cryptology -ASIACRYPT 2012. Berlin: Springer, 2012. 208–225
Albrecht M R, Driessen B, Kavun E B, et al. Block ciphers - focus on the linear layer (feat. PRIDE). In: Advances in Cryptology - CRYPTO 2014. Berlin: Springer, 2014. 57–76
Acknowledgements
This work was supported by National Key Research and Development Program of China (Grant No. 2017YFA0303903), National Natural Science Foundation of China (Grant No. 61672019), Fundamental Research Funds of Shandong University (Grant No. 2016JC029), National Cryptography Development Fund (Grant No. MMJJ20170121), Zhejiang Province Key R&D Project (Grant No. 2017C01062), and Project Funded by China Postdoctoral Science Foundation (Grant No. 2017M620807).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dong, X., Wang, X. Quantum key-recovery attack on Feistel structures. Sci. China Inf. Sci. 61, 102501 (2018). https://doi.org/10.1007/s11432-017-9468-y
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-017-9468-y