Paper 2009/580 Original: eprint.iacr.org/2009/580 ↗
A complete set of addition laws\\for incomplete Edwards curves
Abstract
Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1+P2.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2010-10-06: last updated
- 2009-12-01: published
- Short URL
- https://ia.cr/2009/580
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2009/580,
author = {Daniel J. Bernstein and Tanja Lange},
title = {A complete set of addition laws\\for incomplete Edwards curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2009/580},
year = {2009},
url = {https://eprint.iacr.org/2009/580}
}