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Abstract
Solving the satisfiability problems of Boolean polynomial equations is still an open challenge in the fields of mathematics and computer science. In this paper, our goal is to propose a non-algebraic method for solving maximal Boolean polynomial equations (Max-PoSSo problem). By leveraging channel coding theory and dynamic programming, we propose three deterministic and robust algorithms for solving the satisfiability problems of Boolean polynomial equations. Comparisons are made among the three proposed algorithms and Genetic and Grobner algorithms. Simulation results show that the proposed algorithms exhibit better performance in terms of the largest number of Boolean polynomials equal to 0 compared to the benchmark schemes in the literature.
Highlights
Solving Boolean polynomial equations is one of the major elements for algebraic side-channel attacks, known as side channel cryptanalysis, which was proposed by Kocher [1] in the late 1990s
Three deterministic and robust algorithms have been proposed to solve the problem of the satisfiability of Boolean polynomial equations based on coding theory
The number of Boolean polynomials equal to 0 obtained by the proposed algorithms has been significantly increased compared to the benchmark scheme in [21]
Summary
Solving Boolean polynomial equations is one of the major elements for algebraic side-channel attacks, known as side channel cryptanalysis, which was proposed by Kocher [1] in the late 1990s. It is an attack method based on information gained from the implementation of a computer system. The algebraic attack is to set the cryptographic information as a variable, establish a set of polynomial equations by considering the relationship between the known information and the cryptographic information, and recover the cryptographic information through solving the set of polynomial equations. Algebraic side-channel attacks reduce the attack complexity via introducing side channel information, thereby improve. The challenge in algebraic side-channel attacks is that polynomial equations are difficult to solve
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