HP Labs Technical Reports

Reduced Ideals in Function Fields

Smart, Nigel P.

HPL-98-201

Keyword(s): function fields; divisor class group; reduced ideals; cryptography

Abstract: Please Note. This abstract contains mathematical formulae which cannot be represented here. Let F denote a function field of transcendence degree one over a finite field k. We assume that the field is tamely ramified at infinity, that the valuations at infinity of a set of fundamental units are known and we have gcd(f 1 ,U,f s ) = 1, where fi denotes the degree of a place at infinity. In such a situation we describe a simple arithmetic in the divisor class group. One draw back of this arithmetic is that we do not obtain a unique representative for each divisor class. The method makes use of multiplication and reduction of reduced fractional ideals.

19 Pages

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