Constructing Pairing-Friendly Genus 2 Curves with Ordinary Jacobians

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(Fqk ) for any even k.

• Type: Conference
• Year: 2007
• Where: PAIRING
• Authors: David Freeman
• Keywords: Cryptography, Embedding Degrees, PAIRING 2007, Pairing-friendly Elliptic Curves, Prime fields