Author:
Beierle Christof,Leander Gregor
Abstract
AbstractWe 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 ≥ 5 based on a construction in Alsalami (Cryptogr. Commun. 10(4): 611–628, 2018). In this context, we also show that 4-uniform 2-1 functions obtained from admissible sequences, as defined by Idrisova in (Cryptogr. Commun. 11(1): 21–39, 2019), exist in every dimension n = 3 and n ≥ 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 $\mathbb {F}_{2}^{n}$
F
2
n
to $\mathbb {F}_{2}^{n-1}$
F
2
n
−
1
which are not obtained from admissible sequences. This disproves a conjecture raised by Idrisova.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Computer Networks and Communications
Cited by
8 articles.
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