Refinements of Miller's Algorithm for Computing Weil/Tate Pairing.
Ian F. Blake, V. Kumar Murty, Guangwu Xu · IACR Cryptology ePrint Archive · 2004
In this paper we propose three refinements to Miller’s algorithm for computing Weil/Tate Pairing. The first one is an overall improvement and achieves its optimal behavior if the binary expansion of the involved integer has more zeros. If more ones are presented in the binary expansion, second improvement is suggested. The third one is especially efficient in the case base three. We also have some performance analysis. keywords: algorithm, elliptic curve, cryptography, Weil/Tate pairing