Welcome to the resource topic for 2020/334
Title:
4-Uniform Permutations with Null Nonlinearity
Authors: Christof Beierle, Gregor Leander
Abstract:We consider n-bit permutations with differential uniformity of 4 and null nonlinearity. We first show that the inverses of Gold functions have the interesting property that one component can be replaced by a linear function such that it still remains a permutation. This directly yields a construction of 4-uniform permutations with trivial nonlinearity in odd dimension. We further show their existence for all n = 3 and n \geq 5 based on a construction in [1]. In this context, we also show that 4-uniform 2-1 functions obtained from admissible sequences, as defined by Idrisova in [8], exist in every dimension n = 3 and n \geq 5. Such functions fulfill some necessary properties for being subfunctions of APN permutations. Finally, we use the 4-uniform permutations with null nonlinearity to construct some 4-uniform 2-1 functions from \mathbb{F}_2^n to \mathbb{F}_2^{n-1} which are not obtained from admissible sequences. This disproves a conjecture raised by Idrisova.
ePrint: https://eprint.iacr.org/2020/334
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