Abstract
In this paper we propose new techniques related to division property. We describe for the first time a practical algorithm for computing the propagation tables of 16-bit Super-Sboxes, increasing the precision of the division property by removing a lot of false division trails. We also improve the complexity of the procedure introduced by Lambin et al. (Design, Codes and Cryptography, 2020) to extend a cipher with linear mappings and show how to decrease the number of transitions to look for. While search procedures for integral distinguishers most often rely on MILP or SAT solvers for their ease of programming the propagation constraints, such generic solvers can only handle small 4/8-bit Sboxes. Thus we developed an ad-hoc tool handling larger Sboxes and all the improvements described in the paper. As a result, we found new integral distinguishers on SKINNY-64, HIGHT and Midori-64.
Highlights
Integral cryptanalysis exploits distinguishers computing the sum of ciphertexts corresponding to a set of plaintexts spanning a linear subspace
Midori is a lightweight block cipher designed by Banik et al and presented at ASIACRYPT’15
We focused on SKINNY-64, the internal state of the 128-bit version being too big to be handled by our tool
Summary
Integral cryptanalysis exploits distinguishers computing the sum of ciphertexts corresponding to a set of plaintexts spanning a linear subspace. This technique was originally introduced by Knudsen in [DKR97] as a specific attack against the byte-oriented structure of the block cipher SQUARE. Division property captures that if for a subset X of Fn2 each monomial my appearing in mz satisfies x∈X my(x) = 0 x∈X mz(x) = 0. Several variants of this property were used to find integral distinguishers.
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