A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves 论文

摘要

The aim of this paper is to show that the computation of the discrete logarithm in the m-torsion part of the divisor class group of a curve X over a finite field ko (with char(ko) prime to m), or over a local field k with residue field ko, can be reduced to the computation of the discrete logarithm in k0(4m)* . For this purpose we use a variant of the (tame) Tate pairing for Abelian varieties over local fields. In the same way the problem to determine all linear combinations of a finite set of elements in the divisor class group of a curve over k or ko which are divisible by m is reduced to the computation of the discrete logarithm in ko(Cm)* -