Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A remark concerning $ m$-divisibility and the discrete logarithm in the divisor class group of curves


Authors: Gerhard Frey and Hans-Georg Rück
Journal: Math. Comp. 62 (1994), 865-874
MSC: Primary 11G20; Secondary 14G15, 94A60
MathSciNet review: 1218343
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11G20, 14G15, 94A60

Retrieve articles in all journals with MSC: 11G20, 14G15, 94A60


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1218343-6
PII: S 0025-5718(1994)1218343-6
Article copyright: © Copyright 1994 American Mathematical Society