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A new efficient factorization algorithm for polynomials over small finite fields

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We present a new deterministic factorization algorithm for polynomials over a finite prime fieldF p . As in other factorization algorithms for polynomials over finite fields such as the Berlekamp algorithm, the key step is the “linearization” of the factorization problem, i.e., the reduction of the problem to a system of linear equations. The theoretical justification for our algorithm is based on a study of the differential equationy (p−1)+y p=0 of orderp−1 in the rational function fieldF p(x). In the casep=2 the new algorithm is more efficient than the Berlekamp algorithm since there is no set-up cost for the coefficient matrix of the system of linear equations.

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Authors and Affiliations

  1. Institute for Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010, Vienna, Austria

    Harald Niederreiter

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  1. Harald Niederreiter
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Niederreiter, H. A new efficient factorization algorithm for polynomials over small finite fields. AAECC 4, 81–87 (1993). https://doi.org/10.1007/BF01386831

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  • DOI: https://doi.org/10.1007/BF01386831

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