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A CHARACTERISTIC SET METHOD FOR SOLVING BOOLEAN EQUATIONS AND APPLICATIONS IN CRYPTANALYSIS OF stream ciphers

Journal of Systems Science & Complexity 2008年第2期21卷 191-208页

作者： Fengjuan CHAI Xiao-Shan GAO Chunming YUAN Key Laboratory of Mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is 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.

关键词： Boolean equation characteristic set method cryptanalysis finite field stream ciphers.

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Linearization of Multi-Valued Nonlinear Feedback Shift Registers

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Journal of Systems Science & Complexity 2017年第2期30卷 494-509页

作者： WANG Haiyan ZHONG Jianghua LIN Dongdai State Key Laboratory of Information Security Institute of Information EngineeringChinese Academy of SciencesBeijing 100093China

Nonlinear feedback shift registers(NFSRs) have been used in many stream ciphers.for cryptographic security. The linearization of NFSRs is to describe their state transitions using some matrices. Such matrices are called their state transition matrices. Compared to extensive work on binary NFSRs, much less work has been done on multi-valued NFSRs. This paper uses a semi-tensor product approach to investigate the linearization of multi-valued NFSRs, by viewing them as logical networks. A new state transition matrix is found for a multi-valued NFSR, which can be simply computed from the truth table of its feedback function. The new state transition matrix is easier to compute and is more explicit than the existing results. Some properties of the state transition matrix are provided as well, which are helpful to theoretically analyze multi-valued NFSRs.

关键词： Logic network nonlinear feedback shift register semi-tensor product state transition matrix stream ciphers.

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维普期刊数据库

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DISTRIBUTION OF ONE-ERROR LINEAR COMPLEXITY OF BINARY SEQUENCES FOR ARBITRARY PRIME PERIOD

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Journal of Systems Science & Complexity 2012年第6期25卷 1223-1233页

作者： Lin TAN Wenfeng QI Hong XU Department of Applied Mathematics Zhengzhou Information Science and Technology Institute

Complexity measures for sequences, such as the linear complexity and the k-error linear complexity, play an important role in stream ciphers. This contribution studies the distribution of 1-error linear complexity of binary sequences with arbitrary prime period. For any odd prime N, the authors present all possible values of 1-error linear complexity of N-periodic binary sequences, and derive the exact formulas to count the number of N-periodic binary sequences with any given 1-error linear complexity.

关键词： k-error linear complexity linear complexity periodic sequences stream ciphers.

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维普期刊数据库

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