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  is chosen.
|Conference||9th Annual International Workshop, SAC 2002|
|City||St. John's, Newfoundland|
|Period||2002/08/15 → 2002/08/16|
- Electrical Engineering, Electronic Engineering, Information Engineering
- Boolean functions
- linear space
- propagation characteristics