Factoring polynomial over finite fields

Abstract

Factoring polynomials over finite fields has influenced on many areas of computer science and computational mathematics such as computer algebra, algebraic coding theory, computational number theory, cryptography. In cryptography there are numerous examples. Index calculus method for computing the discrete logarithms over finite fields. Finding roots of polynomial for the same problem in order to establish ismorphisms between different representations of the same field. computing the number of points on elliptic curves, building arithmetic public key cryptosystem, designing cyclic redundancy code, studying decoding algorithm for algebraic code such as BCH code.