### Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds

Anne Canteaut, Eran Lambooij, Samuel Neves, Shahram Rasoolzadeh, Yu Sasaki, and 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.

Available format(s)
Publication info
Keywords
differential cryptanalysisindependent S-boxfixed keyunkeyed constructionexact probabilityRoadRunneRMinalpher
Contact author(s)
sasaki yu @ lab ntt co jp
sneves @ dei uc pt
anne canteaut @ inria fr
e lambooij @ student tue nl
marc stevens @ cwi nl
History
Short URL
https://ia.cr/2017/478

CC BY

BibTeX

@misc{cryptoeprint:2017/478,
author = {Anne Canteaut and Eran Lambooij and Samuel Neves and Shahram Rasoolzadeh and Yu Sasaki and Marc Stevens},
title = {Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds},
howpublished = {Cryptology ePrint Archive, Paper 2017/478},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/478}},
url = {https://eprint.iacr.org/2017/478}
}

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