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 [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.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: David Freeman
• Keywords: Algorithms, ANTS 2006, Elliptic Curves, Embedding Degree, Prescribed Embedding Degree