Discrete Logarithms in Generalized Jacobians

S.  D.  Galbraith; B.  A.  Smith

Paper 2006/333

Discrete Logarithms in Generalized Jacobians

S. D. Galbraith and B. A. Smith

Abstract

Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of groups. We then argue that generalized Jacobians offer poorer security and efficiency than standard Jacobians.

Note: Here is a revised version of the note.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Also put on arxiv
Keywords: elliptic curves algebraic tori jacobians
Contact author(s): Steven Galbraith @ rhul ac uk
History: 2006-10-17: revised; 2006-10-05: received; See all versions
Short URL: https://ia.cr/2006/333
License: CC BY

BibTeX

@misc{cryptoeprint:2006/333,
      author = {S.  D.  Galbraith and B.  A.  Smith},
      title = {Discrete Logarithms in Generalized Jacobians},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/333},
      year = {2006},
      url = {https://eprint.iacr.org/2006/333}
}