Polynomial selection of F₄ for solving the MQ problem

Abstract

The multivariate quadratic (MQ) polynomial problem involves finding solutions to a system of MQ equations. The construction of an efficient algorithm for solving the MQ problem is an important research topic in the security evaluation of multivariate public key cryptosystems. Gröbner basis computation is often used to solve the MQ problem; the F₄ algorithm is a representative algorithm for computing Gröbner bases. In this article, we examine a polynomial selection strategy for efficiently solving the MQ problem using the F₄ algorithm.