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Gaudry's Variant against Cab Curves

Seigo ARITA

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Summary :

Gaudry has described a new algorithm (Gaudry's variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry's variant solves for the DLP in time O(q2+ε). This paper shows that Cab curves can be attacked with a modified form of Gaudry's variant and presents the timing results of such attack. However, Gaudry's variant cannot be effective in all of the Cab curve cryptosystems. This paper also provides an example of a Cab curve that is unassailable by Gaudry's variant.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.9 pp.1809-1814
Publication Date
2000/09/25
Publicized
Online ISSN
DOI
Type of Manuscript
PAPER
Category
Information Security

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