Paper 2026/885
Optimized Final Exponentiation for Optimal Ate Pairings Using Cyclotomic Cubing
Abstract
Pairing-based cryptography relies heavily on the efficiency of bilinear pairings, the computation of which is dominated by the final exponentiation step. This paper describes an efficient cubing operation in the cyclotomic subgroup of $\mathbb{F}_{q^6}$ for $q\equiv1\mod{6}$. As an application, we use existing results for computing Frobenius maps to optimize the cost of the optimal Ate pairing final exponentiation over the SG54 curve. Furthermore, we introduce a novel decomposition for the hard part of the final exponentiation for this curve. Additionally, we apply established methods for cyclotomic cubing to accelerate the final exponentiation for the BLS15 and BLS27 curves. Compared to previous works, our approach achieves efficiency gains of $24\%$ for SG54 and $22\%$ for the BLS15 and BLS27 curves.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Elliptic curvespairingsfinal exponentiationcyclotomic cubing.
- Contact author(s)
-
leila benabdelghani @ fsm rnu tn
haddajiwalid95 @ gmail com - History
- 2026-05-08: approved
- 2026-05-05: received
- See all versions
- Short URL
- https://ia.cr/2026/885
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/885,
author = {Leila Ben Abdelghani and Walid Haddaji},
title = {Optimized Final Exponentiation for Optimal Ate Pairings Using Cyclotomic Cubing},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/885},
year = {2026},
url = {https://eprint.iacr.org/2026/885}
}
