Cryptology ePrint Archive: Report 2006/026

Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10

David Freeman

Abstract: 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.

Category / Keywords: public-key cryptography / elliptic curves, embedding degree, pairings

Date: received 19 Jan 2006

Contact author: dfreeman at math berkeley edu

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Version: 20060127:175951 (All versions of this report)

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