## Cryptology ePrint Archive: Report 2009/564

Optimal pairing revisited

Mingqiang Wang and Puwen Wei and Haifeng Zhang and Yuliang Zheng

Abstract: Vercauteren introduced a notion of optimal pairings. Up to know the only known optimal pairing is the optimal Ate pairing. In this paper, we give some properties of optimal pairing and provide an algorithm for finding an optimal pairing if there exists one which is defined on the given elliptic curve. Applying the cyclotomic polynomial, we construct some new optimal pairings and provide a construction method of pairing-friendly elliptic curves on which the optimal pairing can be defined. Our algorithm is explicit and works for arbitrary embedding degree $k$ and large prime subgroup orders $r$.

Category / Keywords: implementation /