Gaudry’s variant against cab curves

Abstract

Gaudry has described a new algorithm (Gaudry’s variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For hyperelliptic curves of small genus on finite field GF(q), Gaudry’s variant solves for the DLP in O(q2 logγ(q)) time. 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 provides an example of a Cab curve that is unassailable by Gaudry’s variant.