A CHARACTERISTIC SET METHOD FOR SOLVING BOOLEAN EQUATIONS AND APPLICATIONS IN CRYPTANALYSIS OF STREAM CIPHERS

This paper presents a characteristic set method for solving Boolean equations,which ismore efficient and has better properties than the general characteristic set method.In particular,theauthors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equationsystem and an explicit formula for the number of solutions of a Boolean equation system.The authorsalso prove that a characteristic set can be computed with a polynomial number of multiplications ofBoolean polynomials in terms of the number of variables.As experiments,the proposed method is usedto solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators.Extensive experiments show that the method is quite effective.