Paper 2008/490 Original: eprint.iacr.org/2008/490 ↗
On the final exponentiation for calculating pairings on ordinary elliptic curves
Abstract
When using pairing-friendly ordinary elliptic curves to compute the Tate and related pairings, the computation consists of two main components, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of ``truncated loop'' pairings like the R-ate pairing), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing friendly elliptic curves to reduce the computation required for the final exponentiation to a minimum.
Metadata
- Available format(s)
PDF- Category
- Implementation
- Publication info
- Preprint.
- History
- 2010-08-24: last updated
- 2008-11-24: published
- Short URL
- https://ia.cr/2008/490
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2008/490,
author = {Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J. Dominguez Perez and Ezekiel J. Kachisa},
title = {On the final exponentiation for calculating pairings on ordinary elliptic curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/490},
year = {2008},
url = {https://eprint.iacr.org/2008/490}
}