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2014 | OriginalPaper | Buchkapitel

Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves

verfasst von : Franck Rondepierre

Erschienen in: Smart Card Research and Advanced Applications

Verlag: 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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Titel: Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
verfasst von: Franck Rondepierre
Verlag: Springer International Publishing
Buch: Smart Card Research and Advanced Applications
Print ISBN: 978-3-319-08301-8

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

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-319-08302-5_12

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