Improvements on Cantor-Zassenhaus Factorization Algorithm

Details Improvements on Cantor-Zassenhaus Factorization Algorithm Improvements on Cantor-Zassenhaus Factorization Algorithm

2010-12-23

arxiv.org/abs/1012.5322v2

Mathematics

Number Theory

extended and revised version; case s>1 added

Scientific paper

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.

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