Gaudry's variant against C-ab curves

Gaudry has described a new algorithm (Gaudry's variant) fur thf discrete lo garithm 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(q(2+c)). This paper shows that C-ab 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 C-ab, curve cryptosystems. This paper also provides an example of a C-ab curve th at is unassailable by Gaudry's variant.