Welcome to the resource topic for 2007/057
Title:
Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians
Authors: David Freeman
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 works for arbitrary embedding degrees k and prime subgroup orders r. The resulting abelian surfaces are defined over prime fields \F_q with q \approx r^4. We also provide an algorithm for constructing genus 2 curves over prime fields \F_q with ordinary Jacobians J having the property that J[r] \subset J(\F_{q}) or J[r] \subset J(\F_{q^k}) for any even k.
ePrint: https://eprint.iacr.org/2007/057
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