A systematic method of constructing weightwise almost perfectly balanced Boolean functions on an arbitrary number of variables

Abstract

Boolean functions satisfying good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the well-known FLIP stream cipher. In this paper, we present a systematic method of constructing weightwise almost perfectly balanced Boolean functions on an arbitrary number of variables, which equal the direct sum of several known weightwise perfectly balanced Boolean functions. At the same time, we show two concrete constructions of weightwise almost perfectly balanced Boolean functions, whose k-weight nonlinearities and algebraic immunities are discussed at the end of this paper.