Paper 2020/875
Efficient Final Exponentiation via Cyclotomic Structure for Pairings over Families of Elliptic Curves
Daiki Hayashida, Kenichiro Hayasaka, and Tadanori Teruya
Abstract
The final exponentiation, which is the exponentiation by a fixed large exponent, must be performed in the Tate and (optimal) Ate pairing computation to ensure output uniqueness, algorithmic correctness, and security for pairing-based cryptography. In this paper, we propose a new framework of efficient final exponentiation for pairings over families of elliptic curves. Our framework provides two methods: the first method supports families of elliptic curves with arbitrary embedding degrees, and the second method supports families with specific embedding degrees of providing even faster algorithms. Applying our framework to several Barreto-Lynn-Scott families, we obtain faster final exponentiation than the previous state-of-the-art constructions.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MAJOR revision.
- Keywords
- pairingsfinal exponentiationcyclotomic polynomial
- Contact author(s)
- Hayashida Daiki @ df mitsubishielectric co jp
- History
- 2020-07-12: received
- Short URL
- https://ia.cr/2020/875
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/875,
author = {Daiki Hayashida and Kenichiro Hayasaka and Tadanori Teruya},
title = {Efficient Final Exponentiation via Cyclotomic Structure for Pairings over Families of Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/875},
year = {2020},
url = {https://eprint.iacr.org/2020/875}
}
