On the efficiency of solving Boolean polynomial systems with the characteristic set method. (March 2021)

• Record Type: Journal Article
• Authors: Huang, Zhenyu; Sun (c), Yao; Lin, Dongdai
• Is Part Of: Journal of symbolic computation. Volume 103(2021)
• Page Start: 66
• Page End: 94
• Publication Date: 2021-03
• Subjects: Boolean polynomial system -- Characteristic set method -- Computation complexity -- Zero decomposition -- Cryptanalysis; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.11.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain pseudo-remainders. Three important techniques are applied in the algorithm. The first one is eliminating variables by new generated linear polynomials. The second one is optimizing the strategy of choosing polynomial for zero decomposition. The third one is to compute add-remainders to eliminate the leading variable of new generated monic polynomials. By analyzing the depth of the zero decomposition tree, we present some complexity bounds of this algorithm, which are lower than the complexity bounds of previous characteristic set algorithms. Extensive experimental results show that this new algorithm is more efficient than previous characteristic set algorithms for solving Boolean polynomial systems.