On sets determining the differential spectrum of mappings
Pascale Charpin, Gohar Kyureghyan · International Journal of Information and Coding Theory · 2017
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.