Constructing pairing-friendly elliptic curves with embedding degree 10
<|reference_start|>Constructing pairing-friendly elliptic curves with embedding degree 10: We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham. We show that our framework incorporates existing constructions for k = 3, 4, 6, and 12, and we give evidence that the method is unlikely to produce infinite families of curves with embedding degree k > 12.<|reference_end|>
@article{freeman2006constructing,
    title={Constructing pairing-friendly elliptic curves with embedding degree 10},
    author={David Freeman},
    journal={arXiv preprint arXiv:math/0601487},
    year={2006},
    archivePrefix={arXiv},
    eprint={math/0601487},
    primaryClass={math.NT cs.CR}
}