AN ALGERAIC TRANSFORMATION METHOD TO SOLVING EQUATIONS IN THE EXTENDED GALOIS FIELD

Abstract

This article proposes a method to solve cubic and quartic equations over finite fields using its algebraic transformations on quadratic equations. The obtained results can be generalized to solve equations over finite fields of any size and at the same time allow to reduce the complexity and processing delay significantly compared to traditional methods, so that it can be applied in high-speed communication systems.