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

Ko-ichi Nagao

Paper 2004/161

Improvement of Thériault 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 Thériault 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. Thomé 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.

Metadata

Available format(s): PDF PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Index calculus attack Jacobian Hyperelliptic curve DLP
Contact author(s): nagao @ kanto-gakuin ac jp
History: 2004-07-09: received
Short URL: https://ia.cr/2004/161
License: CC BY

BibTeX

@misc{cryptoeprint:2004/161,
      author = {Ko-ichi Nagao},
      title = {Improvement of Thériault Algorithm of Index Calculus for Jacobian of Hyperelliptic Curves of Small Genus},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/161},
      year = {2004},
      url = {https://eprint.iacr.org/2004/161}
}