International Association for Cryptologic Research

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Paper: Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds

Authors:
Anne Canteaut , Inria
Eran Lambooij , Technische Universiteit Eindhoven
Samuel Neves , CISUC, Dept. of Informatics Engineering, University of Coimbra
Shahram Rasoolzadeh , Ruhr-Universität Bochum
Yu Sasaki , NTT Secure Platform Laboratories
Marc Stevens , CWI Amsterdam
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DOI: 10.13154/tosc.v2017.i2.203-227
URL: https://tosc.iacr.org/index.php/ToSC/article/view/644
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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, pind, and exact probability, pexact. It turns out that pexact is larger than pind 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, pind of 2−48 is improved to pexact of 2−43. For the 80-bit key version, pind of 2−68 is improved to pexact 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: pind of 2−128 is improved to pexact of 2−96, which allows to extend the attack by two rounds.
BibTeX
@article{tosc-2017-28465,
  title={Refined Probability of Differential Characteristics Including Dependency Between Multiple Rounds},
  journal={IACR Trans. Symmetric Cryptol.},
  publisher={Ruhr-Universität Bochum},
  volume={2017, Issue 2},
  pages={203-227},
  url={https://tosc.iacr.org/index.php/ToSC/article/view/644},
  doi={10.13154/tosc.v2017.i2.203-227},
  author={Anne Canteaut and Eran Lambooij and Samuel Neves and Shahram Rasoolzadeh and Yu Sasaki and Marc Stevens},
  year=2017
}