On propagation characteristics of resilient functions

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding

Abstract

In this paper we derive several important results towards a better understanding of propagation characteristics of resilient Boolean functions. We first introduce a new upper bound on nonlinearity of a given resilient function depending on the propagation criterion. We later show that a large class of resilient functions admit a linear structure; more generally, we exhibit some divisibility properties concerning the Walsh-spectrum of the derivatives of any resilient function. We prove that, fixing the order of resiliency and the degree of propagation criterion, a high algebraic degree is a necessary condition for construction of functions with good autocorrelation properties. We conclude by a study of the main constructions of resilient functions. We notably show how to avoid linear structures when a linear concatenation is used and when the recursive construction introduced in [11] is chosen.

Details

Authors
  • P Charpin
  • Enes Pasalic
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • Boolean functions, linear space, resiliency, nonlinearity, propagation characteristics
Original languageEnglish
Title of host publicationLecture Notes in Computer Science (Selected Areas in Cryptography. Revised Papers)
PublisherSpringer
Pages175-195
Volume2595
StatePublished - 2003
Peer-reviewedYes
Event9th Annual International Workshop, SAC 2002 - St. John's, Newfoundland, Canada
Duration: 2002 Aug 152002 Aug 16

Publication series

Name
Volume2595
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference9th Annual International Workshop, SAC 2002
CountryCanada
CitySt. John's, Newfoundland
Period2002/08/152002/08/16