On the Bounds of the Bilinear Complexity of Multiplication in Some Finite Fields

Authors:
Stéphane Ballet;Jean Chaumine
Affiliations:
Université de la Polynésie Française, Laboratoire de Géométrie Algébrique et Applications à la Théorie de l’Information, B.P. 6570, 9 ...;Université de la Polynésie Française, Laboratoire de Géométrie Algébrique et Applications à la Théorie de l’Information, B.P. 6570, 9 ...
Venue:
Applicable Algebra in Engineering, Communication and Computing
Year:
2004

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Abstract

From the existence of a tower of algebraic function fields, we improve upper bounds on the bilinear complexity of multiplication in all the extensions of the finite fields ** and ** where p is a prime ≥5. In particular, we improve asymptotic upper bounds on this complexity for prime finite fields of characteristic p5.