Improvements of the Ate-Pairing used for IBC

Compared to RSA, Elliptic curve cryptosystem provides the same security level with shorter key length, which makes the calculation complexity much smaller. Ate pairing is an optimized bilinear pairing with outstanding performance and it is playing more and more important role in elliptic curve cryptosystem. Therefore, the reduction of Miller loops to accelerate the computation of Ate-pairing is the fundamental purpose. In this paper, we explore the optimization of Ate-pairing. We improved the Ate pairing performance leading to the shortest Miller loop of r
^1/φ(k)
, which support former conjecture. These improvements could be useful when Ate pairing is used in IBC schemes requiring high-speed but facing limited hardware resources. Both the experiment result and previous manuscripts proved the correctness and validity of the optimization.