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Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves
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| 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. |
BibTeX
@misc{eprint-2005-12571,
title={Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / elliptic curves, pairing-based cryptosystems},
url={http://eprint.iacr.org/2005/236},
note={ pg03460751@ntu.edu.sg, dp@pmail.ntu.edu.sg 13023 received 20 Jul 2005, last revised 27 Aug 2005},
author={Pu Duan and Shi Cui and Choong Wah Chan},
year=2005
}