Constructing pairing-friendly elliptic curves using Gröbner basis reduction

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 Grobner 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.