Construction of Odd-Variable Boolean Functions with Optimum Algebraic Immunity

Abstract

Recently, algebraic attacks becomes a major attack method to threat to cryptography security. In order to resist algebraic attacks, algebraic immunity as a Boolean function cryptographic property has been put out. This makes that Boolean functions should have high algebraic immunity to resist algebraic attacks. In this paper, a specific decomposition method of the space is proposed. By the method, we construct a class of odd number of variables Boolean functions with optimal algebraic immunity.