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On Propagation Characteristics of Resilient Functions

  • Pascale Charpin
  • Enes Pasalic
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2595)

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.

Keywords

Boolean functions nonlinearity propagation characteristics resiliency linear space 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Pascale Charpin
    • 1
  • Enes Pasalic
    • 2
  1. 1.INRIAprojet CODES, Domaine de VoluceauLe Chesnay CedexFrance
  2. 2.Department of Information TechnologyLund UniversityLundSweden

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