Constructing pairing-friendly elliptic curves with embedding degree 10
数论
2007-05-23 v1 密码学与安全
摘要
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.
引用
@article{arxiv.math/0601487,
title = {Constructing pairing-friendly elliptic curves with embedding degree 10},
author = {David Freeman},
journal= {arXiv preprint arXiv:math/0601487},
year = {2007}
}