Ate Pairing on Hyperelliptic CurvesRobert Granger, Florian Hess, Roger Oyono, Nicolas Theriault, Fre Vercauteren, Ate Pairing on Hyperelliptic Curves. Advances in Cryptology - EUROCRYPT 2007, pp. 430–447. May 2007. No electronic version available.
In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed.