Title: On sets determining the differential spectrum of mappings

Authors: Pascale Charpin; Gohar M. Kyureghyan

Addresses: INRIA, SECRET Project-team, 2 rue Simone Iff, 75012 Paris, France ' Institute for Mathematics, University of Rostock, 18051 Rostock, Germany

Abstract: In this paper, we study computational aspects for determining the differential uniformity of mappings on finite fields of characteristic 2. In particular, we show: (1) A mapping has differential uniformity 2 (i.e. it is almost perfect non-linear) if and only if its difference mappings defined by the elements of a fixed hyperplane are 2-to-1. (2) For a large family of mappings of a special shape, it is enough to consider difference mappings defined by the elements from a suitable multiplicative subgroup.

Keywords: APN mappings; bent function; Boolean function; cryptographic criteria; differential uniformity; hyperplane; monomial binomial; permutation.

DOI: 10.1504/IJICOT.2017.083844

International Journal of Information and Coding Theory, 2017 Vol.4 No.2/3, pp.170 - 184

Received: 28 Nov 2016
Accepted: 30 Nov 2016

Published online: 20 Apr 2017 *

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