Constructing pairing-friendly genus 2 curves with ordinary Jacobians

Authors:
David Freeman
Affiliations:
Department of Mathematics, University of California, Berkeley, Berkeley, CA
Venue:
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Year:
2007

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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 is modeled on the Cocks-Pinch method for constructing pairing-friendly elliptic curves [5], and works for arbitrary embedding degrees k and prime subgroup orders r. The resulting abelian surfaces are defined over prime fields Fq with q ≈ r4. We also provide an algorithm for constructing genus 2 curves over prime fields Fq with ordinary Jacobians J having the property that J[r] ⊂ J(Fq) or J[r] ⊂ J(F qk) for any even k.