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On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

Published online by Cambridge University Press:  01 February 2010

R. Granger ,
D. Page  and
M. Stam
R. Granger
Affiliation:
University of Bristol, Department of Computer Science, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom, granger@cs.bris.ac.uk
D. Page
Affiliation:
University of Bristol, Department of Computer Science, Merchant Venturers Building, Woodland Road, Bristol, BS8 1UB, United Kingdom, page@cs.bris.ac.uk, http://www.cs.bris.ac.uk/~page/
M. Stam
Affiliation:
EPFL – IC –LACAL, Station 14, INJ 3.33, CH-1015 Lausanne, Switzerland, martijn.stam@epfl.ch

Abstract

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The value ot the late pairing on an elliptic curve over a finite field may be viewed as an element of an algebraic torus. Using this simple observation, we transfer techniques recently developed for torus-based cryptography to pairing-based cryptography, resulting in more efficient computations, and lower bandwidth requirements. To illustrate the efficacy of this approach, we apply the method to pairings on supersingular elliptic curves in characteristic three.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 64 - 85
Copyright
Copyright © London Mathematical Society 2006

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