A Characteristic Set Method for Solving Boolean Equations and Applications in Cryptanalysis of Stream Ciphers1

We present a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, we give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. We also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, we use our method to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.