## 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

**Date: **received 8 Jul 2004

**Contact author: **nagao at kanto-gakuin ac jp

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

**Version: **20040709:162024 (All versions of this report)

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