Fast Final Exponentiation on BW and BLS Curves with Even Embedding Degrees at 128 bits security

Senegue Gomez Nyamsi; Emmanuel Fouotsa; Calvin Tcheka

Paper 2025/1387

Fast Final Exponentiation on BW and BLS Curves with Even Embedding Degrees at 128 bits security

Senegue Gomez Nyamsi, University of Dschang

Emmanuel Fouotsa, University of Bamenda

Calvin Tcheka, University of Dschang

Abstract

The final exponentiation is a crucial step in pairing computations, ensuring cor- rectness and uniqueness of results in pairing-based cryptographic protocols. In this work, we propose an efficient method for computing the hard part of the final exponentiation on BW10-511, BW14-351 and BLS12 curves at 128 bits security level. Our approach reduces the computation cost by optimizing the exponenti- ation sequence and minimizing the number of required multiplications through an improved addition chain strategy. The computation cost of our method for the final exponentiation on these curves is about 25.6%, 33.2% and 10% faster than the previously fastest result on BW10-511, BW14-351 and BLS12 curves respectively. The correctness of our formulas has been verified by a Magma code.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint.
Keywords: Addition chain Final exponentiation.
Contact author(s): nyamsigomez @ gmail com
emmanuelfouotsa @ yahoo fr
jtcheka @ yahoo fr
History: 2025-07-31: approved; 2025-07-30: received; See all versions
Short URL: https://ia.cr/2025/1387
License: CC BY-NC

BibTeX

@misc{cryptoeprint:2025/1387,
      author = {Senegue Gomez Nyamsi and Emmanuel Fouotsa and Calvin Tcheka},
      title = {Fast Final Exponentiation on {BW} and {BLS} Curves with Even Embedding Degrees at 128 bits security},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1387},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1387}
}