Research on the miller loop optimization of SM9 bilinear pairings

SM9 is identity-based cryptography designed by bilinear pairing, which can effectively solve the certificates management problems of the PKI and constitutes an important part of Chinese commercial cryptography system. Due to the high complexity of bilinear pairing, SM9 still faces the problem of low efficiency, especially in resource-constrained environments, so performance becomes the key factor that hinders its wide application. This paper has explicitly analyzed detailed computation process of Miller loop in SM9 bilinear pairings and proposed the optimization methods for the point addition, point doubling and line function computation on BN curves. Furthermore, we compare the computational cost of Miller loop under the projective coordinate system and the Jacobian coordinate system and the results show that the latter can improve the efficiency by 5% than the former. The research is very important to optimize the SM9 the performance.