## Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians (2007)

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Venue: | In: proceedings of Pairing 2007, LNCS 4575 |

Citations: | 11 - 2 self |

### BibTeX

@INPROCEEDINGS{Freeman07constructingpairing-friendly,

author = {David Freeman},

title = {Constructing pairing-friendly genus 2 curves over prime fields with ordinary Jacobians},

booktitle = {In: proceedings of Pairing 2007, LNCS 4575},

year = {2007},

pages = {152--176},

publisher = {Springer}

}

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### Abstract

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 ≈ r 4. 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 q k) for any even k. 1