### Constructing pairing-friendly hyperelliptic curves using Weil restriction

David Mandell Freeman and Takakazu Satoh

##### Abstract

A pairing-friendly curve is a curve over a finite field whose Jacobian has small embedding degree with respect to a large prime-order subgroup. In this paper we construct pairing-friendly genus 2 curves over finite fields $\mathbb{F}_q$ whose Jacobians are ordinary and simple, but not absolutely simple. We show that constructing such curves is equivalent to constructing elliptic curves over $\mathbb{F}_q$ that become pairing-friendly over a finite extension of $\mathbb{F}_q$. Our main proof technique is Weil restriction of elliptic curves. We describe adaptations of the Cocks-Pinch and Brezing-Weng methods that produce genus 2 curves with the desired properties. Our examples include a parametric family of genus 2 curves whose Jacobians have the smallest recorded $\rho$-value for simple, non-supersingular abelian surfaces.

Note: Submission version.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. (None)
Keywords
pairing-friendly curvesWeil restriction
Contact author(s)
satohaar @ mathpc-satoh math titech ac jp
History
2009-11-27: last of 4 revisions
See all versions
Short URL
https://ia.cr/2009/103

CC BY

BibTeX

@misc{cryptoeprint:2009/103,
author = {David Mandell Freeman and Takakazu Satoh},
title = {Constructing pairing-friendly hyperelliptic curves using Weil restriction},
howpublished = {Cryptology ePrint Archive, Paper 2009/103},
year = {2009},
note = {\url{https://eprint.iacr.org/2009/103}},
url = {https://eprint.iacr.org/2009/103}
}

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