Cryptology ePrint Archive: Report 2019/126

New Automatic search method for Truncated-differential characteristics: Application to Midori, SKINNY and CRAFT

AmirHossein E. Moghaddam and Zahra Ahmadian

Abstract: In this paper, using Mixed Integer Linear Programming, a new automatic search tool for truncated differential characteristic is presented. Our method models the problem of finding a maximal probability truncated differential characteristic, which is able to distinguish the cipher from a pseudo random permutation.

Using this method, we analyse Midori64, SKINNY64/X and CRAFT block ciphers, for all of which the existing results are improved. In all cases, the truncated differential characteristic is much more efficient than the (upper bound of) bit-wise differential characteristic proven by the designers, for any number of rounds. More specifically, the highest possible rounds, for which an efficient differential characteristic can exist for Midori64, SKINNY64/X and CRAFT are 6, 7 and 10 rounds respectively, for which differential characteristics with maximum probabilities of $2^{-60}$, $2^{-52}$ and $2^{-62.61}$ (may) exist. Using our new method, we introduce new truncated differential characteristics for these ciphers with respective probabilities $2^{-54}$, $2^{-4}$ and $2^{-24}$ at the same number of rounds. Moreover, the longest truncated differential characteristics found for SKINNY64/X and CRAFT have 10 and 12 rounds, respectively. This method can be used as a new tool for differential analysis of SPN block ciphers.

Category / Keywords: secret-key cryptography / Truncated Differential, MILP, SPN

Date: received 5 Feb 2019, last revised 9 Jun 2019

Contact author: zahraahmadian at yahoo com

Available format(s): PDF | BibTeX Citation

Version: 20190609:145143 (All versions of this report)

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