Optimal pairing computation over families of pairing-friendly elliptic curves

Abstract

Vercauteren introduced the concept of optimal pairing, which by definition can be computed by using at most (log 2 r)/φ(k) + log 2 k basic Miller iterations, where r is the order of the groups involved and k is the embedding degree Vercauteren (IEEE Trans Inf Theory 56(1):455-461, 2010). Freeman et al. summarized and proposed all of the new constructions of pairing-friendly elliptic curves that currently exist Freeman et al. (J Cryptol 23(2):224-280, 2010). In this paper, we give an optimal pairing for each family of pairing-friendly curves in Freeman et al. (J Cryptol 23(2):224-280, 2010) by taking the Ate or R-ate pairing approach. © 2011 Springer-Verlag.