Cryptology ePrint Archive: Report 2005/236

Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves

Pu Duan and Shi Cui and Choong Wah Chan

Abstract: Finding suitable non-supersingular elliptic curves becomes an important issue for the growing area of pairing-based cryptosystems. For this purpose, many methods have been proposed when embedding degree k and cofactor h are taken different values. In this paper we propose a new method to find pairing-friendly elliptic curves without restrictions on embedding degree k and cofactor h. We propose the idea of effective polynomial families for finding the curves through different kinds of Pell equations or special forms of D(x)V^2(x). In addition, we discover some efficient families which can be used to build pairing-friendly elliptic curves over extension fields, e.g. Fp^2 and Fp^4.

Category / Keywords: public-key cryptography / elliptic curves, pairing-based cryptosystems

Date: received 20 Jul 2005, last revised 27 Aug 2005

Contact author: pg03460751 at ntu edu sg, dp@pmail ntu edu sg

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Version: 20050828:012529 (All versions of this report)

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