Factorization of polynomials modulo a prime
Pham, Autumn Thu · ProQuest Demo Repository
The factorization of polynomials is a classical mathematical question. The quest of finding the factorization of a polynomial modulo a prime is of interest for problems in computer science, algebraic number theory and cryptology. For example, in computer science, it is used in analyzing in geometric optimization problems. In algebraic number theory, it determined the factorization of integers. In cryptology, it is used for computing key parameters of cryptosystems. With the advent of high speed computers, the twentieth century saw the development of various techniques for this task with the goal of accomplishing the factorization in a minimal amount of time and with maximal efficiency. In this thesis, we first consider the factorization of the special polynomials, xn – 1. We establish results about the degrees and the number of irreducible factors. We then discuss some algorithms developed by Berlekamp, Zassenhaus, Shoup and others for factorizing arbitrary polynomials.