Paper 2004/107 Original: eprint.iacr.org/2004/107 ↗
Classification of genus 2 curves over $\mathbb{F}_{2^n}$ and optimization of their arithmetic
Abstract
To obtain efficient cryptosystems based on hyperelliptic curves, we studied genus 2 isomorphism classes of hyperelliptic curves in characteristic 2. We found general and optimal form for these curves, just as the short Weierstrass form for elliptic curves. We studied the security and the arithmetic on their jacobian. We also rewrote and optimized the formulas of Lange in characteristic 2, and we introduced a new system of coordinate. Therefore, we deduced the best form of hyperelliptic curves of genus 2 in characteristic 2 to use in cryptography.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2004-05-07: last updated
- 2004-05-07: published
- Short URL
- https://ia.cr/2004/107
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/107,
author = {Bertrand BYRAMJEE and Sylvain DUQUESNE},
title = {Classification of genus 2 curves over $\mathbb{F}_{2^n}$ and optimization of their arithmetic},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/107},
year = {2004},
url = {https://eprint.iacr.org/2004/107}
}