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On propagation characteristics of resilient functions

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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https://hal.inria.fr/inria-00072051
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Submitted on : Tuesday, May 23, 2006 - 7:39:03 PM
Last modification on : Friday, February 4, 2022 - 3:10:36 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:50:42 PM

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  • HAL Id : inria-00072051, version 1

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

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