Faster Beta Weil Pairing on BLS Pairing Friendly Curves with Odd Embedding Degree

Azebaze Guimagang Laurian; Fouotsa Emmanuel; El Mrabet Nadia; Pecha Njiahouo Aminatou

Paper 2022/769

Faster Beta Weil Pairing on BLS Pairing Friendly Curves with Odd Embedding Degree

Azebaze Guimagang Laurian

, University of Yaounde 1

Fouotsa Emmanuel

, University of Bamenda

El Mrabet Nadia

, Mines Saint-Etienne, CEA-Tech

Pecha Njiahouo Aminatou, Universit´e de Maroua

Abstract

Since the advent of pairing-based cryptography, various optimization methods that increase the speed of pairing computations have been exploited, as well as new types of pairings. This paper extends the work of Kinoshita and Suzuki who proposed a new formula for the -Weil pairing on curves with even embedding degree by eliminating denominators and exponents during the computation of the Weil pairing. We provide novel formulas suitable for the parallel computation for the -Weil pairing on curves with odd embedding degree which involve vertical line functions useful for sparse multiplications. For computations we used Miller's algorithm combined with storage and multifunction methods. Applying our framework to BLS-, BLS- and BLS- curves at respectively the bit, the bit and the bit security level, we obtain faster -Weil pairings than the previous state-of-the-art constructions. The correctness of all the formulas and bilinearity of pairings obtained in this work is verified by a SageMath code.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Beta-Weil pairing Optimal Ate pairing Multifunction technique Storage technique BLS curves.
Contact author(s): azebazelaurian @ yahoo fr
emmanuelfouotsa @ yahoo fr
nadia el-mrabet @ emse fr
aminap2001 @ yahoo fr
History: 2022-06-16: approved; 2022-06-15: received; See all versions
Short URL: https://ia.cr/2022/769
License: CC BY-NC

BibTeX

@misc{cryptoeprint:2022/769,
      author = {Azebaze Guimagang Laurian and Fouotsa Emmanuel and El Mrabet Nadia and Pecha Njiahouo Aminatou},
      title = {Faster Beta Weil Pairing on {BLS} Pairing Friendly Curves with Odd Embedding Degree},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/769},
      year = {2022},
      url = {https://eprint.iacr.org/2022/769}
}