Several classes of even-variable 1-resilient rotation symmetric Boolean functions with high algebraic degree and nonlinearity

Abstract

Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, some classes of 2m-variable (m is an odd integer) 1-resilient rotation symmetric Boolean functions are got, whose nonlinearity and algebraic degree are studied. For the first time, we obtain 2m-variable 1-resilient rotation symmetric Boolean functions having high nonlinearity and optimal algebraic degree. In addition, we obtain a class of non-linear rotation symmetric 1-resilient function for every n≥5, and a class of quadratic rotation symmetric (k−1)-resilient function of n=3k variables, where k is an integer.