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Reports (Research Report) Year : 2002

On propagation characteristics of resilient functions

Enes Pasalic
  • Function : Author

Abstract

In this paper we derive several important results towards a better understandi- ng 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 autocorrelati- on 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 is chosen.
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Dates and versions

inria-00072051 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00072051 , version 1

Cite

Pascale Charpin, Enes Pasalic. On propagation characteristics of resilient functions. [Research Report] RR-4537, INRIA. 2002. ⟨inria-00072051⟩
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