Ate Pairing on Hyperelliptic Curves

Abstract. 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 automatically reduced, i.e. no final exponentiation is needed.

• Type: Conference
• Year: 2007
• Where: EUROCRYPT
• Authors: Robert Granger, Florian Hess, Roger Oyono, Nicolas Thériault, Frederik Vercauteren
• Keywords: Arbitrary Algebraic Curves, Cryptography, EUROCRYPT 2007, Hyperelliptic Curves, Loop Length