Ate Pairing on Hyperelliptic Curves

Authors:
R. Granger;F. Hess;R. Oyono;N. Thériault;F. Vercauteren
Affiliations:
Dept. Computer Science, University of Bristol, MVB, Woodland Road, Bristol, BS8 1UB, United Kingdom;Technische Universität Berlin, Fakultät II, Institut für Mathematik Sekr. MA 8-1, Strasse des 17. Juni 136, D-10623 Berlin, Germany;University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario, N2L 3G1, Canada;Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile;Department of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B-3001 Leuven-Heverlee, Belgium
Venue:
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Year:
2007

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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 gtimes shorter than for the Tate pairing, with gthe genus of the curve, and the pairing is automatically reduced, i.e. no final exponentiation is needed.