### 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.

Available format(s)
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
Short URL
https://ia.cr/2004/107

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},
note = {\url{https://eprint.iacr.org/2004/107}},
url = {https://eprint.iacr.org/2004/107}
}

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