The lower bound of the weightwise nonlinearity profile of a class of weightwise perfectly balanced functions

Abstract Boolean functions satisfying good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. Although the nonlinearity of Boolean functions can be calculated rapidly by Walsh transform, the nonlinearity of the Boolean functions with restricted input seems to be very difficult to calculate. In this paper, a class of weightwise perfectly balanced Boolean functions with very simple algebraic normal form is proposed. Then, the cryptographic properties of the weightwise perfectly balanced Boolean functions are discussed. Especially, the lower bound of the weightwise nonlinearity of these 2 m -variable functions is given for any positive integer m .