Several Algorithms to find Annihilators of Boolean Function

Algebraic attack is new and efficient in cryptoanalysis, and it is a challenge to both cipher designers and attackers. The key step of algebraic attack on stream ciphers is to build low-degree overdefined equations and this course can be changed to find low-degree annihilators of the combination functions of the key stream generator. In this paper the sufficient and necessary conditions of the existence of low degree multiplies for a given Boolean function f is analysed and three algorithms to find annihilators of a Boolean function f are presented.