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Evaluation of ASIC Implementation of Physical Random Number Generators Using RS Latches Read chapter Read first chapter

2014 | OriginalPaper | Chapter

Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves

Author : Franck Rondepierre

Published in: Smart Card Research and Advanced Applications

Publisher: Springer International Publishing

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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 formulæ with same cost for both doubling and addition. This choice is particularly well suited to evaluate double scalar multiplications with the Straus-Shamir trick. Thus, in situations where this trick is used to evaluate single scalar multiplications our pattern allows an average improvement of \(40\,\%\) when compared with the most efficient atomic scalar multiplication published so far. 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.

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Appendix
Available only for authorised users
Footnotes
1
A trick from Montgomery [24] enables to evaluate several inverses at the cost of only one inversion and few multiplications: \(\frac{1}{a}=\frac{1}{ab}\cdot b\), \(\frac{1}{b}=\frac{1}{ab}\cdot a\).
 
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Metadata
Title
Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
Author
Franck Rondepierre
Copyright Year
2014
Book
Smart Card Research and Advanced Applications

Print ISBN: 978-3-319-08301-8

Electronic ISBN: 978-3-319-08302-5

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-08302-5_12

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