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arXiv · 1909.03628

$C$-differentials, multiplicative uniformity and (almost) perfect $c$-nonlinearity

Pal Ellingsen·Patrick Felke·Constanza Riera·Pantelimon Stanica·Anton Tkachenko
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Abstract

In this paper we define a new (output) multiplicative differential, and the corresponding $c$-differential uniformity. With this new concept, even for characteristic $2$, there are perfect $c$-nonlinear (PcN) functions. We first characterize the $c$-differential uniformity of a function in terms of its Walsh transform. We further look at some of the known perfect nonlinear (PN) and show that only one remains a PcN function, under a different condition on the parameters. In fact, the $p$-ary Gold PN function increases its $c$-differential uniformity significantly, under some conditions on the parameters. We then precisely characterize the $c$-differential uniformity of the inverse function (in any dimension and characteristic), relevant for the Rijndael (and Advanced Encryption Standard) block cipher.

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Pal Ellingsen, Patrick Felke, Constanza Riera, Pantelimon Stanica, Anton Tkachenko. 2019-09-09. $C$-differentials, multiplicative uniformity and (almost) perfect $c$-nonlinearity. https://arxiv.org/abs/1909.03628

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