Applying System of Equations to Factor Semiprime Number

Abstract

This paper explores the use of a system of equations to factor semiprime num- bers. Semiprime numbers are a special type of composite 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 ap-plies 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 Gr ?obner method [1], to solve one of those systems for a particular semiprime number M.