Paper 2004/107
Classification of genus 2 curves over $\mathbb{F}_{2^n}$ and optimization of their arithmetic
Bertrand BYRAMJEE and Sylvain DUQUESNE
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 PS
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- hyperelliptic curvesgenus 2characteristic 2isomorphism classes.
- Contact author(s)
- duquesne @ math univ-montp2 fr
- History
- 2004-05-07: received
- Short URL
- https://ia.cr/2004/107
- License
-
CC BY
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} }