an:06680379
Zbl 1373.16046
Caruso, Xavier; Le Borgne, J??r??my
A new faster algorithm for factoring skew polynomials over finite fields
EN
J. Symb. Comput. 79, Part 2, 411-443 (2017).
00362780
2017
j
16S36 16Z05 16H05
skew polynomial; factorization; Azumaya algebra
Summary: In this paper, we provide an algorithm for the factorization of skew polynomials over finite fields. It is faster than the previously known algorithm, which was due to [\textit{M. Giesbrecht}, J. Symb. Comput. 26, No. 4, 463--486 (1998; Zbl 0941.68160)]. There are two main improvements. The first one is obtained through a careful study of the structure of the quotients of a skew polynomial ring, using theoretical results relating skew polynomial rings and Azumaya algebras. The second improvement is provided by giving faster sub-algorithms for the arithmetic in skew polynomial rings, such as multiplication, division, and extended Euclidean division.
Zbl 0941.68160