Paper 2010/309
Co-Z Addition Formulae and Binary Ladders on Elliptic Curves
Raveen R. Goundar, Marc Joye, and Atsuko Miyaji
Abstract
Meloni recently introduced a new type of arithmetic on elliptic curves when adding projective points sharing the same Z-coordinate. This paper presents further co-Z addition formulae (and register allocations) for various point additions on Weierstrass elliptic curves. It explains how the use of conjugate point addition and other implementation tricks allow one to develop efficient scalar multiplication algorithms making use of co-Z arithmetic. Specifically, this paper describes efficient co-Z based versions of Montgomery ladder and Joye’s double-add algorithm. Further, the resulting implementations are protected against a large variety of implementation attacks.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Published elsewhere. Extended abstract appears in CHES 2010. This is the full version.
- Keywords
- Elliptic curvesMeloni’s techniqueJacobian coordinatesregular binary laddersimplementation attacksembedded systems.
- Contact author(s)
- raveen rg @ gmail com
- History
- 2010-05-27: revised
- 2010-05-25: received
- See all versions
- Short URL
- https://ia.cr/2010/309
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/309,
author = {Raveen R. Goundar and Marc Joye and Atsuko Miyaji},
title = {Co-Z Addition Formulae and Binary Ladders on Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/309},
year = {2010},
url = {https://eprint.iacr.org/2010/309}
}
