Improvements on Cantor-Zassenhaus Factorization Algorithm

TL;DR

This paper presents a simplified and more efficient version of the Cantor-Zassenhaus polynomial factorization algorithm, reducing computational effort and improving success rate estimates over finite fields.

Contribution

A new simplified version of the Cantor-Zassenhaus algorithm that requires less computational cost and provides improved attempt estimates for factorization over finite fields.

Findings

Requires fewer computational resources than previous versions.

Achieves success with fewer attempts, especially for polynomials over finite fields.

Applicable to both characteristic 2 and odd prime fields.

Abstract

After revisiting Cantor-Zassenhaus polynomial factorization algorithm, we describe a new simplified version of it, which requires less computational cost. Moreover we show that it is able to find a factor of a fully splitting polynomial of degree $t$ over $\mathbb F_{2^m}$ with $O(\frac{2^m}{3^{t}})$ attempts and over $\mathbb F_{p^m}$ for odd $p$ with $O(\frac{p^m}{2^{t}})$ attempts.