Paper 2007/057
Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians
David Freeman
Abstract
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. Our algorithm works for arbitrary embedding degrees $k$ and prime subgroup orders $r$. The resulting abelian surfaces are defined over prime fields $\F_q$ with $q \approx r^4$. We also provide an algorithm for constructing genus 2 curves over prime fields $\F_q$ with ordinary Jacobians $J$ having the property that $J[r] \subset J(\F_{q})$ or $J[r] \subset J(\F_{q^k})$ for any even $k$.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- pairing-friendly curvesembedding degreegenus 2 curveshyperelliptic curvesCM methodcomplex multiplication
- Contact author(s)
- dfreeman @ math berkeley edu
- History
- 2007-02-20: received
- Short URL
- https://ia.cr/2007/057
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/057,
author = {David Freeman},
title = {Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians},
howpublished = {Cryptology ePrint Archive, Paper 2007/057},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/057}},
url = {https://eprint.iacr.org/2007/057}
}
