On propagation characteristics of resilient functions

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


title = "On propagation characteristics of resilient functions",
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, linear space, resiliency, nonlinearity, propagation characteristics",
author = "P Charpin and Enes Pasalic",
year = "2003",
doi = "10.1007/3-540-36492-7_13",
language = "English",
volume = "2595",
publisher = "Springer",
pages = "175--195",
booktitle = "Lecture Notes in Computer Science (Selected Areas in Cryptography. Revised Papers)",