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Published in:
2013 | OriginalPaper | Chapter
On the Use of Shamir’s Secret Sharing against Side-Channel Analysis
Authors : Jean-Sébastien Coron, Emmanuel Prouff, Thomas Roche
Published in: Smart Card Research and Advanced Applications
Publisher: Springer Berlin Heidelberg
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At CHES 2011 Goubin and Martinelli described a new countermeasure against side-channel analysis for AES based on Shamir’s secret-sharing scheme. In the present paper, we exhibit a flaw in this scheme and we show that it is always theoretically broken by a first-order side-channel analysis. As a consequence of this attack, only a slight adaptation of the scheme proposed by Ben-Or et al.at STOC in 1988 can securely process multiplications on data shared with Shamir’s technique. In the second part of this paper, we propose an improvement of this scheme that leads to a complexity
${\cal \tilde O}(d^2)$
instead of
${\cal O}(d^3)$
, where
d
is the number of shares per data.