Abstract
This paper presents a characteristic set method for solving Boolean equations, which is more efficient 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 filter generators. Extensive experiments show that the method is quite effective.
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*This research is partially supported by a National Key Basic Research Project of China under Grant No. 2004CB318000.
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CHAI, F., GAO, XS. & YUAN, C. A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers*. J Syst Sci Complex 21, 191–208 (2008). https://doi.org/10.1007/s11424-008-9103-0
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DOI: https://doi.org/10.1007/s11424-008-9103-0