Modeling an Optimization Problem to Solve a System of Algebraic Equations for Cryptanalysis

Abstract

In this paper, we construct an optimization problem to solve a system of algebraic equations over a finite field. Given a system of equations over finite field, we derive a system of equations over the real numbers from the given system. We construct a model of an unconstrained optimization problem by using a penalty function. We also show that an optimal solution to the unconstrained optimization problem is the solution of the original system of algebraic equations over a finite field.