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 curvesalgebraic torijacobians
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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2006/333}},
      url = {https://eprint.iacr.org/2006/333}
}
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