Discrete Logarithms in Generalized Jacobians

Details Discrete Logarithms in Generalized Jacobians Discrete Logarithms in Generalized Jacobians

2006-10-02

arxiv.org/abs/math/0610073v1

Mathematics

Number Theory

Scientific paper

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.

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