On sets determining the differential spectrum of mappings
type: Item
instance of: scholarly article
title: On sets determining the differential spectrum of mappings
zbMATH Open document ID: 1406.94036
DOI: 10.1504/IJICOT.2017.10004710
author: Pascale Charpin
author: Gohar M. Kyureghyan
published in: International Journal of Information and Coding Theory
publication date: 2018-08-24T00:00:00Z
review text: Summary: 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 nonlinear) 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.
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 11T06
Mathematics Subject Classification ID: 68P25
Mathematics Subject Classification ID: 94C10
zbMATH DE Number: 6924909
zbMATH Keywords: APN mappings
zbMATH Keywords: bent function
zbMATH Keywords: Boolean function
zbMATH Keywords: cryptographic criteria
zbMATH Keywords: differential uniformity
zbMATH Keywords: hyperplane
zbMATH Keywords: monomial binomial
zbMATH Keywords: permutation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6924909