logo

SCIENCE CHINA Information Sciences, Volume 61, Issue 3: 032106(2018) https://doi.org/10.1007/s11432-016-9075-6

Impossible differential attack on Simpira v2

More info
  • ReceivedDec 17, 2016
  • AcceptedMar 16, 2017
  • PublishedAug 30, 2017

Abstract

Simpira v2 is a family of cryptographic permutations proposed at ASIACRYPT 2016, and can be used to construct high throughput block ciphers by using the Even-Mansour construction, permutation-based hashing, and wide-block authenticated encryption. This paper shows a 9-round impossible differential of Simpira-4. To the best of our knowledge, this is the first 9-round impossible differential.To determine some efficient key recovery attacks on its block cipher mode (Even-Mansour construction with Simpira-4), we use some 6/7-round shrunken impossible differentials. Based on eight 6-round impossible differentials,we propose a series of 7-round key recovery attacks on the block cipher mode; each 6-round impossible differential helps recover 32 bits of the master key (512 bits), and in total, half of the master key bits are recovered. The attacks require $2^{57}$ chosen plaintexts and $2^{57}$ 7-round encryptions.Furthermore, based on ten 7-round impossible differentials, we add one round on the top or at the bottom to mount ten 8-round key recovery attacks on the block cipher mode. This helps recover the full key space (512 bits) with a data complexity of $2^{170}$ chosen plaintexts and time complexity of $2^{170}$ 8-round encryptions. Those are the first attacks on the round-reduced Simpira v2 and do not threaten the Even-Mansour mode with the full 15-round Simpira-4.


Acknowledgment

This work was supported by National Basic Research Program of China (973 Program) (Grant No. 2013CB834205), National Natural Science Foundation of China (Grant No. 61672019), Fundamental Research Funds of Shandong University (Grant No. 2016JC029), and Foundation of Science and Technology on Information Assurance Laboratory (Grant No. KJ-15-002).


References

[1] Daemen J, Rijmen V. The Design of Rijndael. Berlin: Springer, 2002. Google Scholar

[2] Mala H, Dakhilailian M, Rijmen V, et al. Improved impossible differential cryptanalysis of 7-round AES-128. In: Proceedings of International Conference on Cryptology in India. Berlin: Springer-Verlag, 2010. 282--291. Google Scholar

[3] Lu J Q, Dunkelman O, Keller N, et al. New impossible differential attacks on AES. In: Proceedings of International Conference on Cryptology in India. Berlin: Springer-Verlag, 2008. 279--293. Google Scholar

[4] Zhang W T, Wu W L, Feng D G. New results on impossible differential cryptanalysis of reduced AES. In: Proceedings of International Conference on Information Security and Cryptology. Berlin: Springer-Verlag, 2007. 239--250. Google Scholar

[5] Daemen J, Knudsen L, Rijmen V. The block cipher Square. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer-Verlag, 1997. 149--165. Google Scholar

[6] Gilber H, Minier M. A collision attack on 7 rounds of Rijndael. In: Proceedings of AES Candidate Conference, New York, 2000. 230--241. Google Scholar

[7] Dunkelman O, Keller N, Shamir A. Improved single-key attacks on 8-round AES-192 and AES-256. In: Advances in Cryptology — ASIACRYPT 2010. Berlin: Springer-Verlag, 2010. 158--176. Google Scholar

[8] Derbez P, Fouque P, Jean J. Improved key recovery attacks on reduced-round AES in the single-key setting. In: Advances in Cryptology — EUROCRYPT 2013. Berlin: Springer-Verlag, 2013. 371--387. Google Scholar

[9] Li L B, Jia K T, Wang X Y. Improved single-key attacks on 9-round AES-192/256. In: Fast Software Encryption. Berlin: Springer-Verlag, 2015. 127--146. Google Scholar

[10] Biryukov A, Khovratovich D. Related-key cryptanalysis of the full AES-192 and AES-256. In: Advances in Cryptology — ASIACRYPT 2009. Berlin: Springer-Verlag, 2009. 1--18. Google Scholar

[11] Biryukov A, Khovratovich D, Nikoli$\acute{\rm~~c}$ I. Distingsuiher and related-key attack on the full AES-256. In: Advances in Cryptology — CRYPTO 2009. Berlin: Springer-Verlag, 2009. 231--249. Google Scholar

[12] Sun B, Liu M C, Guo J, et al. New insights on AES-like SPN ciphers. In: Advances in Cryptology — CRYPTO 2016. Berlin: Springer-Verlag, 2016. 605--624. Google Scholar

[13] Grassi L, Rechberger C, Rønjom S. Subspace trail cryptanalysis and its applications to AES. IACR Trans Symmetric Cryptol, 2016, 2016: 192--225. Google Scholar

[14] Gueron S, Mouha N. Simpira v2: a family of efficient permutations using the AES round function. In: Advances in Cryptology — ASIACRYPT 2016. Berlin: Springer-Verlag, 2016. 95--125. Google Scholar

[15] Dunkelman O, Keller N, Shamir A. Minimalism in cryptography: the Even-Mansour scheme revisited. In: Advances in Cryptology — EUROCRYPT 2012. Berlin: Springer-Verlag, 2012. 336--354. Google Scholar

[16] Even S, Mansour Y. A construction of a cipher from a single pseudorandom permutation. J Cryptology, 1997, 10: 151--161. Google Scholar

[17] Dobraunig C, Eichlseder M, Mendel F. Cryptanalysis of Simpira v1. In: Selected Areas in Cryptography, Newfoundland, 2016, in press. Google Scholar

[18] R${\o}$njom S. Invariant subspaces in Simpira. Cryptology ePrint Archive, Report, 2016. http://eprint.iacr.org/2016/248.pdf. Google Scholar

[19] Knudsen L R. DEAL — a 128-bit block cipher. Complexity, 1998, 258: 216. Google Scholar

[20] Biham E, Biryukov A, Shamir A. Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In: Advances in Cryptology — EUROCRYPT 1999. Berlin: Springer-Verlag, 1999. 12--23. Google Scholar

[21] Sun S W, Hu L, Wang M Q, et al. Constructing mixed-integer programming models whose feasible region is exactly the set of all valid differential characteristics of SIMON. Cryptology ePrint Archive, Report, 2015. http://eprint.iacr.org/2015/122.pdf. Google Scholar

[22] Sun S W, Hu L, Wang M Q, et al. Mixed integer programming models for finite automaton and its application to additive differential patterns of exclusive-or. Cryptology ePrint Archive, Report, 2016. http://eprint.iacr.org/2016/338.pdf. Google Scholar

[23] Cui T T, Jia K T, Fu K, et al. New automatic search tool for impossible differentials and zero-correlation linear approximations. Cryptology ePrint Archive, Report, 2016. http://eprint.iacr.org/2016/689.pdf. Google Scholar

[24] Daemen J, Rijmen V. Understanding two-round differentials in aes. In: Proceedings of International Conference on Security and Crytography for Networks. Berlin: Springer-Verlag, 2006. 78--94. Google Scholar

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1