International Association
for Cryptologic Research

This paper explores the use of a system of equations to factor semiprime numbers. Semiprime numbers are a special type of omposite number that are the product of two prime numbers. Factoring semiprime numbers is important in cryptography and number theory. In this study, we present a method that applies a system of polynomial equations to factor semiprime number $M$. Where $M$ can be any semiprime number. In fact, we build a family of systems where each system compose from three polynomial equations with three variables. The results of this study show that a solution for one system results with a complete factorization for a semiprime number. It may be possible to apply well known algorithms, such as Grobner method to solve one of those systems for a particular semiprime number $M$.