Constructing Families of Pairing-Friendly Elliptic Curves

Freeman, David

HP Development Company

关键词: cryptography;    pairings;    elliptic curves;    embedding degree;   

RP-ID  :  HPL-2005-155

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

We present a general method for constructing families of elliptic curves with prescribed embedding degree and prime order. We demonstrate this method by constructing curves of embedding degree k = 10, a value which has not previously appeared in the literature, and we show that our method applies to existing constructions for k = 3, 4, 6, and 12. We give evidence that our method is unlikely to produce infinite families of curves for embedding degrees k > 12. 15 Pages