Paper 2004/118 Original: eprint.iacr.org/2004/118 ↗
Fast addition on non-hyperelliptic genus $3$ curves
Abstract
We present a fast addition algorithm in the Jacobian of a genus $3$ non-hyperelliptic curve over a field of any characteristic. When the curve has a rational flex and $\textrm{char}(k) > 5$, the computational cost for addition is $148M+15SQ+2I$ and $165M+20SQ+2I$ for doubling. An appendix focuses on the computation of flexes in all characteristics. For large odd $q$, we also show that the set of rational points of a non-hyperelliptic curve of genus $3$ can not be an arc.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2004-05-19: last updated
- 2004-05-19: published
- Short URL
- https://ia.cr/2004/118
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/118,
author = {Stéphane Flon and Roger Oyono and Christophe Ritzenthaler},
title = {Fast addition on non-hyperelliptic genus $3$ curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/118},
year = {2004},
url = {https://eprint.iacr.org/2004/118}
}