Acta Informatica

, Volume 7, Issue 4, pp 395–398 | Cite as

Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2

  • Arnold Schönhage
Article

Fast multiplication of polynomials over fields of characteristic 2

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. 1.
    Aho, A. V., Hopcroft, J. E., Ullman, J. D.: The design and analysis of computer algorithms. Reading (Mass.): Addison-Wes'ley 1974Google Scholar
  2. 2.
    Schönhage, A., Strassen, V.: Schnelle Multiplikation großer Zahlen. Computing 7, 281–292 (1971)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Arnold Schönhage
    • 1
  1. 1.Mathematisches Institut der Universität TübingenTübingenBundesrepublik Deutschland

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