Constructing pairing-friendly elliptic curves using Gröbner basis reduction

Authors:
Waldyr D. Benits, Jr.;Steven D. Galbraith
Affiliations:
Mathematics Department, Royal Holloway University of London, Egham, Surrey, UK;Mathematics Department, Royal Holloway University of London, Egham, Surrey, UK
Venue:
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Year:
2007

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Abstract

The problem of constructing elliptic curves suitable for pairing applications has received a lot of attention. One of the most general methods to solve this problem is due to Scott. We propose a variant of this method which replaces an exhaustive search with a Gröbner basis calculation. This makes the method potentially able to generate a larger set of families of parameters. We present some new families of parameters for pairing-friendly elliptic curves.