A METHOD OF SOLVING EQUATIONS OVER THE FINITE FIELDS USING THE SOLUSIONS OF AFFINE POLYNOMIALS

Abstract

Several problems such as decoding BCH, Reed-Solomon, Goppa codes and
decrypt code-based cryptosystems relate to solving equations over finite fields.
Finding of polynomials over finite fields is highly complicated because numerical
methods to find roots of polynomials over infinite fields can not be used. On the
other hand, affine polynomials are linear and finding their roots, therefore, is
much easier than of the other polynomials. The paper proposes a novel method
to find roots of polynomials over extended Galois fields using roots of affine
polynomials. This method can reduce processing time significantly compared to
traditional methods, and therefore, can be more suitable for high speed
communication systems.