Improvement of Final Exponentiation for Pairings on BLS Curves with Embedding Degree 15

Abstract

To be suitable in practice, pairings are typically carried out by two steps, which consist of the Miller loop and final exponentiation. To improve the final exponentiation step of a pairing on the BLS family of pairing-friendly elliptic curves with embedding degree 15, the authors provide a new representation of the exponent. The proposal can achieve a more reduction of the calculation cost of the final exponentiation than the previous method by Fouotsa et al.