Development of hybrid approach for solving MQ problem: Intermediate hybrid approach

Abstract

Multivariate polynomial public cryptography is a form of post-quantum cryptography that represents one of the candidates for next-generation cryptography. Solving a multivariate simultaneous system of quadratic equations (MQ problem) serves as the basis of security for multivariate public-key cryptography, and evaluating its computational complexity is an important topic. The hybrid approach is a method for solving MQ problems, which combines exhaustive search and Gröbner basis computation. We propose a new algorithm as an alternative to the hybrid approach, wherein the Gröbner basis computation is performed, the assignment calculation is performed subsequently, and the Gröbner basis computation is performed again.