4-Uniform Permutations with Null Nonlinearity

Christof Beierle; Gregor Leander

Paper 2020/334

4-Uniform Permutations with Null Nonlinearity

Christof Beierle and Gregor Leander

Abstract

We consider -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 and 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 and . 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 to which are not obtained from admissible sequences. This disproves a conjecture raised by Idrisova.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Cryptography and Communications
DOI: 10.1007/s12095-020-00434-2
Keywords: Boolean function Cryptographic S-boxes APN permutations Gold functions
Contact author(s): christof beierle @ rub de
gregor leander @ rub de
History: 2020-04-20: revised; 2020-03-18: received; See all versions
Short URL: https://ia.cr/2020/334
License: CC BY

BibTeX

@misc{cryptoeprint:2020/334,
      author = {Christof Beierle and Gregor Leander},
      title = {4-Uniform Permutations with Null Nonlinearity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2020/334},
      year = {2020},
      doi = {10.1007/s12095-020-00434-2},
      url = {https://eprint.iacr.org/2020/334}
}