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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
Creative Commons Attribution
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}
}
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