## Cryptology ePrint Archive: Report 2004/161

Improvement of ThLeriault Algorithm of Index Calculus for Jacobian of Hyperelliptic Curves of Small Genus

Ko-ichi Nagao

Abstract: Gaudry present a variation of index calculus attack for solving the DLP in the Jacobian of hyperelliptic curves. Harley and ThLerialut improve these kind of algorithm. Here, we will present a variation of these kind of algorithm, which is faster than previous ones. Its complexity is $O(2-\frac{2}{g}+\epsilon)$. Recently, P. Gaudry and E. Thom'e http://eprint.iacr.org/2004/153/ present the algorithm, whose complexity is same as our results. So I submit my manuscript to this eprint archive.

Category / Keywords: public-key cryptography / Index calculus attack, Jacobian, Hyperelliptic curve, DLP