Reduced Ideals in Function Fields

Smart, Nigel P.

HP Development Company

关键词: function fields;    divisor class group;    reduced ideals;    cryptography;   

RP-ID  :  HPL-98-201

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

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.