Paper 2010/311
Combining leak--resistant arithmetic for elliptic curves defined over and RNS representation
J. C. Bajard, S. Duquesne, and M. Ercegovac
Abstract
In this paper we combine the residue number system (RNS) representation
and the leak-resistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve
cryptography on embedded devices.\
% since they have leak-resistance properties.
It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-resistant arithmetic on elliptic curves (unified addition, Montgomery ladder) in order to minimize the number of modular reductions. We also improve the complexity of the RNS modular reduction step. As a result, we show how to obtain a competitive secured implementation.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- ellicptic curvesleak resistanceRNSarithmetic
- Contact author(s)
- sylvain duquesne @ univ-rennes1 fr
- History
- 2010-05-25: received
- Short URL
- https://ia.cr/2010/311
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/311, author = {J. C. Bajard and S. Duquesne and M. Ercegovac}, title = {Combining leak--resistant arithmetic for elliptic curves defined over $\F_p$ and {RNS} representation}, howpublished = {Cryptology {ePrint} Archive, Paper 2010/311}, year = {2010}, url = {https://eprint.iacr.org/2010/311} }