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Rings of Low Multiplicative Complexity

โœ Scribed by Joseph H. Silverman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
159 KB
Volume
6
Category
Article
ISSN
1071-5797

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โœฆ Synopsis

The complexity of the multiplication operation in "nite "elds is of interest for both theoretical and practical reasons. For example, an optimal normal basis for % , has complexity 2N!1. A construction described in J. H. Silverman, (&&Cryptographic Hardware and Embedded Systems,'' Lecture Notes in Computer Science, Vol. 1717, pp. 122}134, Springer}Verlag, Berlin, 1999.) allows multiplication of complexity N#1 to be performed in %

, by working in a larger ring R of dimension N#1 over %

. In this paper we give a complete classi"cation of all such rings and show that this construction is the only one which also has a certain useful permutability property.

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