Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves (original) (raw)

Paper 2005/236

Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves

Pu Duan, 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.

BibTeX

@misc{cryptoeprint:2005/236, author = {Pu Duan and Shi Cui and Choong Wah Chan}, title = {Effective Polynomial Families for Generating More Pairing-Friendly Elliptic Curves}, howpublished = {Cryptology {ePrint} Archive, Paper 2005/236}, year = {2005}, url = {https://eprint.iacr.org/2005/236} }