Impossible differential attack on Simpira v2
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, permutationbased 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 257 chosen plaintexts and 257 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 2170 chosen plaintexts and time complexity of 2170 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.
KeywordsSimpira-4 impossible differential attack super S-box the Even-Mansour construction security claim
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).
- 5.Daemen J, Knudsen L, Rijmen V. The block cipher Square. In: Proceedings of International Workshop on Fast Software Encryption. Berlin: Springer-Verlag, 1997. 149–165Google Scholar
- 6.Gilber H, Minier M. A collision attack on 7 rounds of Rijndael. In: Proceedings of AES Candidate Conference, New York, 2000. 230–241Google Scholar
- 13.Grassi L, Rechberger C, Rønjom S. Subspace trail cryptanalysis and its applications to AES. IACR Trans Symmetric Cryptol, 2016, 2016: 192–225Google Scholar
- 18.Rønjom S. Invariant subspaces in Simpira. Cryptology ePrint Archive, Report, 2016. http://eprint.iacr.org/2016/248. pdfGoogle Scholar
- 19.Knudsen L R. DEAL — a 128-bit block cipher. Complexity, 1998, 258: 216Google 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.pdfGoogle 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.pdfGoogle 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.pdfGoogle Scholar