A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers*

Abstract

This paper presents a characteristic set method for solving Boolean equations, which is more e-cient and has better properties than the general characteristic set method. In particular, the authors 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. The authors 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, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear fllter generators. Extensive experiments show that the method is quite efiective.