Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / elliptic curves, algebraic tori, jacobians

Publication Info: Also put on arxiv

Date: received 2 Oct 2006, last revised 17 Oct 2006

Contact author: Steven Galbraith at rhul ac uk

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Note: Here is a revised version of the note.

Version: 20061017:100227 (All versions of this report)

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