New Automatic Search Method for Truncated-Differential Characteristics Application to Midori, SKINNY and CRAFT. (15th June 2020)

• Record Type: Journal Article
• Authors: Ebrahimi Moghaddam, AmirHossein; Ahmadian, Zahra
• Is Part Of: Computer journal. Volume 63:Number 12(2020)
• Page Start: 1813
• Page End: 1825
• Publication Date: 2020-06-15
• Subjects: truncated differential -- MILP -- SPN; Computers -- Periodicals; 005.1
• DOI: 10.1093/comjnl/bxaa004
• Languages: English
• ISSNs: 0010-4620

Abstract

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, being able to distinguish the cipher from a pseudo-random permutation. Using this method, we analyze 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.