On a new factorization algorithm for polynomials over finite fields

Authors:
Harald Niederreiter and Rainer Göttfert

Journal:
Math. Comp. **64** (1995), 347-353

MSC:
Primary 11T06; Secondary 11Y16

DOI:
https://doi.org/10.1090/S0025-5718-1995-1265019-6

MathSciNet review:
1265019

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Abstract: A new deterministic factorization algorithm for polynomials over finite fields was recently developed by the first author. The bottleneck in this algorithm is the last stage in which the irreducible factors of the polynomial are derived from the solutions of a system of linear equations. An efficient approach to the last stage was designed by the second author for the case of finite fields of characteristic 2. In this paper, we describe a different approach to the last stage which works for arbitrary fields of positive characteristic. In particular, we obtain in this way an acceleration of the factorization algorithm of the first author which makes this algorithm polynomial time for fixed characteristic.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1995-1265019-6

Keywords:
Polynomial factorization,
finite fields,
arithmetic complexity

Article copyright:
© Copyright 1995
American Mathematical Society