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

Authors:
David Freeman
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URL: http://eprint.iacr.org/2007/057
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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 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 $k$.
BibTeX
@misc{eprint-2007-13339,
  title={Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / pairing-friendly curves, embedding degree, genus 2 curves, hyperelliptic curves, CM method, complex multiplication},
  url={http://eprint.iacr.org/2007/057},
  note={ dfreeman@math.berkeley.edu 13561 received 16 Feb 2007},
  author={David Freeman},
  year=2007
}