Constructing pairing-friendly elliptic curves with embedding degree 10
- Author(s): Freeman, D
- et al.
Published Web Locationhttp://springerlink.com/content/w836740j18132577/fulltext.pdf
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.