On Small Characteristic Algebraic Tori in Pairing-Based Cryptography
Robert Granger, Daniel Page, Martijn Stam · LMS Journal of Computation and Mathematics · 2006
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.