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A Side-Channel Assisted Cryptanalytic Attack Against QcBits Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Improved Blind Side-Channel Analysis by Exploitation of Joint Distributions of Leakages

verfasst von : Christophe Clavier, Léo Reynaud

Erschienen in: Cryptographic Hardware and Embedded Systems – CHES 2017

Verlag: Springer International Publishing

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Abstract

Classical side-channel analysis include statistical attacks which require the knowledge of either the plaintext or the ciphertext to predict some internal value to be correlated to the observed leakages.
In this paper we revisit a blind (i.e. leakage-only) attack from Linge et al. that exploits joint distributions of leakages. We show – both by simulations and concrete experiments on a real device – that the maximum likelihood (ML) approach is more efficient than Linge’s distance-based comparison of distributions, and demonstrate that this method can be easily adapted to deal with implementations protected by first-order Boolean masking. We give example applications of different variants of this approach, and propose countermeasures that could prevent them.
Interestingly, we also observe that, when the inputs are known, the ML criterion is more efficient than correlation power analysis.

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Vorheriges Kapitel A Side-Channel Assisted Cryptanalytic Attack Against QcBits
Nächstes Kapitel Convolutional Neural Networks with Data Augmentation Against Jitter-Based Countermeasures
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Fußnoten
1
The assumption that the distribution of the noise is Gaussian is not restrictive. If it is not, one uses the same equations given in this section, except that Eq. (3) must be consequently adapted to the actual (or supposed) distribution of the noise.
 
2
For sake of simplicity, we continue to use the notation \({{\mathrm{Pr}}}(\cdot )\) in the next equations while this actually denotes a term which is proportional to the actual probability.
 
3
While this can be viewed as a multiplication by 9 of the terms in the summation, it is worth to note that \(\Pr ((h_m^*,h_x^*,h_y^*)|k)\) is non null for at most 256 triplets.
 
4
This last observation can be explained by the fact that information brought by y and 2y are somewhat redundant. Indeed their Hamming weights are quite correlated since they are equal for all \(y<128\) values for which 2y is equal to \(y \ll 1\).
 
5
This comparison is either explicit (Linge’s distances) or implicit (ML).
 
6
Given two leakages \(\ell _1\) and \(\ell _2\) the centered product combining function computes \(f(\ell _1,\ell _2) = (\ell _1-{{\mathrm{E}}}(\ell _1)) \times (\ell _2-{{\mathrm{E}}}(\ell _2))\). The absolute value of centered difference combining function defined by \(g(\ell _1,\ell _2) = |(\ell _1-{{\mathrm{E}}}(\ell _1)) - (\ell _2-{{\mathrm{E}}}(\ell _2)) |\) has also been considered but shows to be less efficient than the centered product.
 
7
\(\sigma \) of the noise on the leakage and that on the Hamming weight are equal up to the factor \(|\alpha |\). It is thus expressed in leakage unit or in bit unit according to the context.
 
8
The Pearson \(\chi ^2\) distances were impossible to compute due to an insufficient number of traces.
 
9
EMV scheme also allows to use the Triple DES function.
 
10
A classical second-order CPA on the pair of leakages of \((P_{n+1} \oplus M_{n+1}, P_{n+1} \oplus M_{n+1} \oplus C_n)\) is not possible in this case as it would imply to correlate the combination of these leakages with the Hamming weight of \(C_n\) which does not vary.
 
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Metadaten
Titel
Improved Blind Side-Channel Analysis by Exploitation of Joint Distributions of Leakages
verfasst von
Christophe Clavier
Léo Reynaud
Copyright-Jahr
2017
Buch
Cryptographic Hardware and Embedded Systems – CHES 2017

Print ISBN: 978-3-319-66786-7

Electronic ISBN: 978-3-319-66787-4

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-66787-4_2