International Association for Cryptologic Research
Since they appeared in cryptography, the efficient computation of pairings is a very active area of research. Originally defined over elliptic curves in weierstrass model, pairings have been computed in other models of elliptic curves (for example Edwards, Hu, Jacobi). They have also been studied in different systems of coordinates such as affine, jacobian, projective, chudnovsky or in original representation of finite fields RNS. The main algorithm to compute pairings is the miller algorithm. It is based on a double and add scheme.