Paper 2008/019
Computing Pairings Using x-Coordinates Only
Steven D. Galbraith and Xibin Lin
Abstract
To reduce bandwidth in elliptic curve cryptography one can transmit only $x$-coordinates of points (or $x$-coordinates together with an extra bit). For further computation using the points one can either recover the $y$-coordinates by taking square roots or one can use point multiplication formulae which use $x$-coordinates only. We consider how to efficiently use point compression in pairing-based cryptography. We give a method to compute compressed Weil pairings using $x$-coordinates only. We also show how to compute the compressed Tate and ate pairings using only one $y$-coordinate. Our methods are more efficient than taking square roots when the embedding degree is small. We implemented the algorithms in the case of embedding degree 2 curves over $\F_p$ where $p \equiv 3 \pmod{4}$ and found that our methods are $10-15\%$ faster than the analogous methods using square roots.
Metadata
- Available format(s)
-
PDF PS
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- elliptic curvespairingspoint compression.
- Contact author(s)
- linxibin @ mail2 sysu edu cn
- History
- 2008-01-22: received
- Short URL
- https://ia.cr/2008/019
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/019,
author = {Steven D. Galbraith and Xibin Lin},
title = {Computing Pairings Using x-Coordinates Only},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/019},
year = {2008},
url = {https://eprint.iacr.org/2008/019}
}