Welcome to the resource topic for 2009/103
Title:
Constructing pairing-friendly hyperelliptic curves using Weil restriction
Authors: David Mandell Freeman, 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.
ePrint: https://eprint.iacr.org/2009/103
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