Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography
type: Item
instance of: scholarly article
title: Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography
zbMATH Open document ID: 0936.94009
DOI: 10.1023/A:1008337029047
author: Paul Camion
author: Anne Canteaut
published in: Designs, Codes and Cryptography
publication date: 2000-05-22T00:00:00Z
review text: Correlation-immune functions and resilient functions are known to be important concepts for some applications in cryptography. In the paper the notions of correlation-immune functions and resilient functions are extended to functions over any finite alphabet; also some other results are given as well. First, three characterizations of correlation-immune functions over a finite alphabet are given. An orthogonal array characterization, a characterization by means of characters and a matrix characterization are presented. Then the properties of the algebraic normal form of correlation-immune functions over a finite field are investigated and construction of \(t\)-resilient functions with optimal nonlinearity order over any finite field is given. The next section is devoted to the construction of new correlation-immune functions by composition of correlation-immune functions of smaller order. Finally links between correlation-immune functions and several other cryptographic notions like perfect local randomizers or multipermutations are explored.
reviewed by: Jozef Vyskoč
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 1332720
zbMATH Keywords: resilient functions
zbMATH Keywords: correlation-immune functions
zbMATH Keywords: orthogonal arrays
zbMATH Keywords: multipermutations
MaRDI profile type: Publication
full work available at URL: a:1008337029047
OpenAlex ID: W1534088294
description: scientific article; zbMATH DE number 1332720