Paper 2015/408
Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
Franck Rondepierre
Abstract
This paper deals with the protection of elliptic curve scalar multiplications against side-channel analysis by using the atomicity principle. Unlike other atomic patterns, we investigate new formul\ae{} with same cost for both doubling and addition. This choice is particularly well suited to evaluate double scalar multiplications with the Straus-Shamir trick. Since fixed point multiplications highly benefit from this trick, our pattern allows a huge improvement in this case as other atomic patterns cannot use it. Surprisingly, in other cases our choice remains very efficient. Besides, we also point out a security threat when the curve parameter $a$ is null and propose an even more efficient pattern in this case.
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Published elsewhere. Major revision. CARDIS 2013
- DOI
- 10.1007/978-3-319-08302-5_12
- Keywords
- Elliptic CurvesScalar MultiplicationStraus-Shamir TrickSide-Channel AnalysisAtomicity
- Contact author(s)
- f rondepierre @ oberthur com
- History
- 2015-05-01: received
- Short URL
- https://ia.cr/2015/408
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/408,
author = {Franck Rondepierre},
title = {Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves},
howpublished = {Cryptology ePrint Archive, Paper 2015/408},
year = {2015},
doi = {10.1007/978-3-319-08302-5_12},
note = {\url{https://eprint.iacr.org/2015/408}},
url = {https://eprint.iacr.org/2015/408}
}
