Two Classes of 1-Resilient Prime-Variable Rotation Symmetric Boolean Functions

Abstract

Recent research has shown that the class of rotation symmetric Boolean functions is beneficial to cryptographics. In this paper, for an odd prime p, two sufficient conditions for p-variable rotation symmetric Boolean functions to be 1-resilient are obtained, and then several concrete constructions satisfying the conditions are presented. This is the first time that resilient rotation symmetric Boolean functions have been systematically constructed. In particular, we construct a class of 2-resilient rotation symmetric Boolean functions when p=2^m+1 for m ≥ 4. Moreover, several classes of 1-order correlation immune rotation symmetric Boolean functions are also got.