Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians

@article{Freeman2007ConstructingPG,
  title={Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians},
  author={David Freeman},
  journal={IACR Cryptology ePrint Archive},
  year={2007},
  volume={2007},
  pages={57}
}
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 Fq with q ≈ r. We also provide an… CONTINUE READING