Fast Symmetric Pairing Revisited

During the past decade pairing-based cryptosystems have been through a huge development, and the implementation of bilinear pairings has been improved greatly. Two pairing models, namely symmetric and asymmetric pairings, are widely used and have common cryptographic properties in most cryptosystems. Symmetric pairings are more convenient to construct cryptographic schemes, but asymmetric pairings are more efficient and suitable for implementation due to their flexible embedding degrees. In this paper we revisit symmetric pairings on supersingular elliptic curves over large characteristic fields. We show that a special family of supersingular elliptic curves with embedding degree 3 admits a kind of fast symmetric pairings, whose computational costs might be twice the costs for the current fastest asymmetric pairings.