Discrete Logarithms in Generalized Jacobians

S.  D.  Galbraith; B.  A.  Smith

Paper 2006/333 Original: eprint.iacr.org/2006/333 ↗

Discrete Logarithms in Generalized Jacobians

S. D. Galbraith

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2006-10-17: last updated; 2006-10-05: published
Short URL: https://ia.cr/2006/333
License: https://creativecommons.org/licenses/by/4.0/

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}
}