Paper 2013/562
Self-pairings on supersingular elliptic curves with embedding degree $three$
Binglong Chen and Chang-An Zhao
Abstract
Self-pairings are a special subclass of pairings and have interesting applications in cryptographic schemes and protocols. In this paper, we explore the computation of the self-pairings on supersingular elliptic curves with embedding degree $k = 3$. We construct a novel self-pairing which has the same Miller loop as the Eta/Ate pairing. However, the proposed self-pairing has a simple final exponentiation. Our results suggest that the proposed self-pairings are more efficient than the other ones on the corresponding curves. We compare the efficiency of self-pairing computations on different curves over large characteristic and estimate that the proposed self-pairings on curves with $k=3$ require $44\%$ less field multiplications than the fastest ones on curves with $k=2$ at AES 80-bit security level.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Elliptic curveTate pairingWeil pairingSelf-pairingPairing based cryptography.
- Contact author(s)
- zhaochan3 @ mail sysu edu cn
- History
- 2013-09-05: received
- Short URL
- https://ia.cr/2013/562
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2013/562,
author = {Binglong Chen and Chang-An Zhao},
title = {Self-pairings on supersingular elliptic curves with embedding degree $three$},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/562},
year = {2013},
url = {https://eprint.iacr.org/2013/562}
}
