A novel construction of 2-resilient rotation symmetric Boolean functions

Abstract

In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t - 1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et.al. Several situations are examined, as the direct corollaries, three classes of (4t - 1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.