We show an efficient implementation of the Tate, ate and R-ate pairings for the KSS curves with embedding degree $k=18$.
Use of Magma
In this webpage we will demonstrate using magma a step-by-step approach to the efficient implementation of pairings given a family of pairing friendly elliptic curves, and propose some specific optimisations for the chosen $k=18$ family of such curves in the computation of the Tate, ate and R-ate
pairings