International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Discrete Logarithms in Generalized Jacobians

Steven D. Galbraith
B. A. Smith
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Abstract: D\'ech\`ene 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.
  title={Discrete Logarithms in Generalized Jacobians},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / elliptic curves, algebraic tori, jacobians},
  note={Also put on arxiv 13438 received 2 Oct 2006, last revised 17 Oct 2006},
  author={Steven D. Galbraith and B. A. Smith},