Paper 2012/247
On Efficient Pairings on Elliptic Curves over Extension Fields
Xusheng Zhang, Kunpeng Wang, and Dongdai Lin
Abstract
In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller's algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals's supersingular curves over composite extension fields in parallel implementation.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Published elsewhere. The 5th International Conference on Pairing-Based Cryptography (Pairing 2012)
- Keywords
- pairingelliptic curve over extension fieldmulti-pairing technique
- Contact author(s)
- xszhang is @ gmail com
- History
- 2012-05-03: received
- Short URL
- https://ia.cr/2012/247
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2012/247,
author = {Xusheng Zhang and Kunpeng Wang and Dongdai Lin},
title = {On Efficient Pairings on Elliptic Curves over Extension Fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/247},
year = {2012},
url = {https://eprint.iacr.org/2012/247}
}
