2006 | OriginalPaper | Buchkapitel
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
verfasst von : David Freeman
Erschienen in: Algorithmic Number Theory
Verlag: Springer Berlin Heidelberg
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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 [6]. 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.