Investigations on $c$-Boomerang Uniformity and Perfect Nonlinearity

Pantelimon Stanica

Investigations on $c$-Boomerang Uniformity and Perfect Nonlinearity

Information Theory 2020-04-27 v1 math.IT Number Theory

Authors: Pantelimon Stanica

Abstract

We defined in~\cite{EFRST20} a new multiplicative $c$ -differential, and the corresponding $c$ -differential uniformity and we characterized the known perfect nonlinear functions with respect to this new concept, as well as the inverse in any characteristic. The work was continued in~\cite{RS20}, investigating the $c$ -differential uniformity for some further APN functions. Here, we extend the concept to the boomerang uniformity, introduced at Eurocrypt '18 by Cid et al.~\cite{Cid18}, to evaluate S-boxes of block ciphers, and investigate it in the context of perfect nonlinearity and related functions.

Keywords

c-differential uniformity c-boomerang uniformity perfect nonlinearity apn functions s-boxes block ciphers

Cite

@article{arxiv.2004.11859,
  title  = {Investigations on $c$-Boomerang Uniformity and Perfect Nonlinearity},
  author = {Pantelimon Stanica},
  journal= {arXiv preprint arXiv:2004.11859},
  year   = {2020}
}

Comments

31 pages, 1 figure

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