Constructing pairing-friendly hyperelliptic curves using Weil restriction

David Mandell Freeman; Takakazu Satoh

Paper 2009/103

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 $F_{q}$ whose Jacobians are ordinary and simple, but not absolutely simple. We show that constructing such curves is equivalent to constructing elliptic curves over $F_{q}$ that become pairing-friendly over a finite extension of $F_{q}$ . 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 $ρ$ -value for simple, non-supersingular abelian surfaces.

Note: Submission version.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. (None)
Keywords: pairing-friendly curves Weil restriction
Contact author(s): satohaar @ mathpc-satoh math titech ac jp
History: 2009-11-27: last of 4 revisions; 2009-03-02: received; See all versions
Short URL: https://ia.cr/2009/103
License: 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},
      url = {https://eprint.iacr.org/2009/103}
}