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

Yuki NANJO  Masaaki SHIRASE  Takuya KUSAKA  Yasuyuki NOGAMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E104-A   No.1   pp.315-318
Publication Date: 2021/01/01
Publicized: 2020/07/17
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020EAL2046
Type of Manuscript: LETTER
Category: Cryptography and Information Security
pairing-based cryptography,  BLS curves,  final exponentiation,  

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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.