This talk is about efficient pairing computation on elliptic curves. I will discuss particularly implementation-friendly curves, the use of the polynomial parameter representation to compute pairings on BN curves, and reasons to use affine coordinates for pairings at high security levels.

This contains joint work with P. Barreto, G. Pereira, M. Simplício Jr, P. Schwabe, R. Niederhagen, K. Lauter, and P. Montgomery.