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Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2

Fast multiplication of polynomials over fields of characteristic 2

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Summary

Polynomial multiplication of degree N can be accomplished in time O (N · log N) provided the scalar field contains suitable roots of unity. Otherwise at least O (N · log N · log log N) is obtained by a modified version of the Schönhage-Strassen multiplication which employs computations modulo 1 + xn (where N = 2n), if the field contains 2−1, or modulo 1 + xn + x2N, if 3−1 exists. The latter method covering all fields of characteristic 2 is presented here in detail.

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Literatur

  1. Aho, A. V., Hopcroft, J. E., Ullman, J. D.: The design and analysis of computer algorithms. Reading (Mass.): Addison-Wes'ley 1974

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  2. Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281–292 (1971)

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Authors and Affiliations

  1. Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen, Bundesrepublik Deutschland

    Arnold Schönhage

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  1. Arnold Schönhage
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Schönhage, A. Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2. Acta Informatica 7, 395–398 (1977). https://doi.org/10.1007/BF00289470

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  • DOI: https://doi.org/10.1007/BF00289470

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