Cryptology ePrint Archive: Report 2004/132

On Small Characteristic Algebraic Tori in Pairing-Based Cryptography

R. Granger and D. Page and M. Stam

Abstract: The output of the Tate 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.

Category / Keywords: Algebraic tori, Pairing-based cryptography

Publication Info: LMS Journal of Computation and Mathematics

Date: received 1 Jun 2004, last revised 18 Mar 2005

Contact author: granger at cs bris ac uk

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Version: 20050318:163033 (All versions of this report)

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