Abstract
Differential cryptanalysis is one of the most popular methods in attacking block ciphers. However, there are still some limitations in traditional differential cryptanalysis. On the other hand, researches of quantum algorithms have made great progress nowadays. This paper proposes two methods to apply quantum algorithms in differential cryptanalysis, and analysis their efficiencies and success probabilities. One method is using quantum algorithm in the high probability differential finding period for every S-Box. The second method is taking the encryption as a whole, using quantum algorithm in this process.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptology 4(1), 3–72 (1991)
Knudsen, L.R.: Truncated and higher order differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995)
Biryukov, A.: Impossible differential attack. In: van Tilborg, H.C.A., Jajodia, S. (eds.) Encyclopedia of Cryptography and Security, p. 597. Springer, New York (2011)
Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. In: Proceedings of the Royal Society of London, Volume A, vol. 439, pp. 553–558 (1992)
Bernstein, E., Vazirani, U.: Quantum complexity theory. In: Proceedings of the 25th Annual ACM Symposium on Theory of Computing, pp. 11–20. ACM Press, New York (1993)
Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26, 1474–1483 (1997)
Shor, P.W.: Polynomial-time algorithm for prime factorization and discrete logarithms on quantum computer. SIAM J. Comput. 26, 1484–1509 (1997). A primary version appeared in FOCS, 124–134 (1994)
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)
Atici, A., Servedio, R.: Quantum algorithms for learning and testing juntas. Quantum Inf. Process. 6(5), 323–348 (2007)
Chakraborty, S., Fischer, E., Matsliah, A., de Wolf., R.: New results on quantum property testing. In: FSTTCS, pp. 145–156 (2010)
Hillery, M., Anderson, E.: Quantum tests for the linearity and permutation invariance of Boolean functions. Phys. Rev. A 84, 062326 (2011)
Floess, D., Andersson, E., Hillery, M.: Quantum algorithms for testing and learning Boolean functions. Math. Struct. Comp. Sci. 23, 386–398 (2013)
Aharonov, D., Jones, V., Landau, Z.: A polynomial quantum algorithm for approximating the Jones polynomial. Algorithmica 55, 395–421 (2009). Preliminary version in Proceedings of the 38th Annual ACM Symposium on Theory of Computing STOC, pp. 427–436 (2006)
Nakajima, Y., Kawano, Y., Sekigawa, H.: Efficient quantum circuits for approximating the Jones polynomial. Quantum Inf. Comput. 8(5), 489–500 (2008)
Li, H.W., Yang, L.: A quantum algorithm to approximate the linear structures of Boolean functions. arXiv:1404.0611v2 [quant-ph], 20 Jan 2015
Roetteler, M., Steinwandt, R.: A note on quantum related-key attacks. Inf. Process. Lett. 115, 40–44 (2015)
Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014)
Zhou, Q., Lu, S.F., Zhang, Z.G., Sun, J.: Quantum differential cryptanalysis. Quantum Inf. Process. 14(6), 2101–2109 (2015)
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 61173157.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, H., Yang, L. (2015). Quantum Differential Cryptanalysis to the Block Ciphers. In: Niu, W., et al. Applications and Techniques in Information Security. ATIS 2015. Communications in Computer and Information Science, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48683-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-48683-2_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-48682-5
Online ISBN: 978-3-662-48683-2
eBook Packages: Computer ScienceComputer Science (R0)