Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2
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Fast multiplication of polynomials over fields of characteristic 2
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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