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

Gerhard Frey and Hans-Georg Rück
Mathematics of Computation
Vol. 62, No. 206 (Apr., 1994), pp. 865-874
DOI: 10.2307/2153546
Stable URL: http://www.jstor.org/stable/2153546
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Remark Concerning m-Divisibility and the Discrete Logarithm in the Divisor Class Group of Curves
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Abstract

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 k0 (with $\operatorname{char}(k_0)$ prime to m), or over a local field k with residue field k0, can be reduced to the computation of the discrete logarithm in k0m)*. 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 k0 which are divisible by m is reduced to the computation of the discrete logarithm in k0m)*.

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