## Ate Pairing on Hyperelliptic Curves

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.

Editor(s):
Naor, Moni
Published in:
Advances in Cryptology - EUROCRYPT 2007, 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Barcelona, Spain, May 20-24, 2007. Proceedings, 430-447
Presented at:
Advances in Cryptology - EUROCRYPT 2007, Barcelona, Spain, May 20-24, 2007
Year:
2007
Publisher:
Springer-Verlag Berlin Heidelberg
Keywords:
Laboratories: