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Title:
Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds
Authors: Anne Canteaut, Eran Lambooij, Samuel Neves, Shahram Rasoolzadeh, Yu Sasaki, Marc Stevens
Abstract:The current paper studies the probability of differential characteristics for an unkeyed (or with a fixed key) construction. Most notably, it focuses on the gap between two probabilities of differential characteristics: probability with independent S-box assumption, p_{ind}, and exact probability, p_{exact}. It turns out that p_{exact} is larger than p_{ind} in Feistel network with some S-box based inner function. The mechanism of this gap is then theoretically analyzed. The gap is derived from interaction of S-boxes in three rounds, and the gap depends on the size and choice of the S-box. In particular the gap can never be zero when the S-box is bigger than six bits. To demonstrate the power of this improvement, a related-key differential characteristic is proposed against a lightweight block cipher RoadRunneR. For the 128-bit key version, p_{ind} of 2^{-48} is improved to p_{exact} of 2^{-43}. For the 80-bit key version, p_{ind} of 2^{-68} is improved to p_{exact} of 2^{-62}. The analysis is further extended to SPN with an almost-MDS binary matrix in the core primitive of the authenticated encryption scheme Minalpher: p_{ind} of 2^{-128} is improved to p_{exact} of 2^{-96}, which allows to extend the attack by two rounds.
ePrint: https://eprint.iacr.org/2017/478
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