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2017 | OriginalPaper | Buchkapitel

Kernel Discriminant Analysis for Information Extraction in the Presence of Masking

verfasst von : Eleonora Cagli, Cécile Dumas, Emmanuel Prouff

Erschienen in: Smart Card Research and Advanced Applications

Verlag: Springer International Publishing

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Abstract

To reduce the memory and timing complexity of the Side-Channel Attacks (SCA), dimensionality reduction techniques are usually applied to the measurements. They aim to detect the so-called Points of Interest (PoIs), which are time samples which (jointly) depend on some sensitive information (e.g. secret key sub-parts), and exploit them to extract information. The extraction is done through the use of functions which combine the measurement time samples. Examples of combining functions are the linear combinations provided by the Principal Component Analysis or the Linear Discriminant Analysis. When a masking countermeasure is properly implemented to thwart SCAs, the selection of PoIs is known to be a hard task: almost all existing methods have a combinatorial complexity explosion, since they require an exhaustive search among all possible d-tuples of points. In this paper we propose an efficient method for informative feature extraction in presence of masking countermeasure. This method, called Kernel Discriminant Analysis, consists in completing the Linear Discriminant Analysis with a so-called kernel trick, in order to efficiently perform it over the set of all possible d-tuples of points without growing in complexity with d. We identify and analyse the issues related to the application of such a method. Afterwards, its performances are compared to those of the Projection Pursuit (PP) tool for PoI selection up to a 4th-order context. Experiments show that the Kernel Discriminant Analysis remains effective and efficient for high-order attacks, leading to a valuable alternative to the PP in constrained contexts where the increase of the order d does not imply a growth of the profiling datasets.

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Nächstes Kapitel Defeating Embedded Cryptographic Protocols by Combining Second-Order with Brute Force
Fußnoten
1
Even if the complexity is independent of d, the amount of information extracted is still decreasing exponentially with d, as expected when \((d-1)\)-th order masking is applied [9].
 
2
It has been shown to be optimal as preprocessing for a template attack under specific leakage models [4].
 
3
Whence the name dth-order attacks.
 
4
Not necessary distinct.
 
5
Other polynomial kernel functions may be more adapted if the acquisitions are not free from \(d^\prime \)th-order leakages, with \(d^\prime <d\). Among non-polynomial kernel functions, we effectuated some experimental trials with the most common Radial Basis Function (RBF), obtaining no interesting results. This might be caused by the infinite-dimensional size of the underlying feature space, that makes the discriminant components estimation less efficient.
 
6
This choice has been done to allow for reproducibility of the experiments.
 
7
For PCA and LDA methods, it is known that a good component selection is fundamental to obtain an efficient subspace [6], and that the first components not always represent the best choice. This is likely to be the case for the KDA as well, but in our experiments the choice of the two first components \(\varepsilon ^{\mathrm {KDA}}_1, \varepsilon ^{\mathrm {KDA}}_2\) turns out to be satisfying, and therefore to simplify our study we preferred to not investigate other choices.
 
8
A different approach is analysed in Sect. 4.5.
 
9
We think that is result is quite data-dependant, so the use of such an approach is not discouraged in general.
 
10
At the cost of adjust some parameters in a way that might affect the accuracy of the method, see [13] for a discussion.
 
11
A further validation is performed over such windows, using other two training sets to estimate \(\hat{\rho }\), in order to reduce the risk of false positives.
 
12
Interestingly, the threshold \(T_{det}\) depends on size of \(\mathcal {Z}\) and not on the size of the training sets of traces. This fact disables the classic strategy that consists in enlarging the sample, making \(T_{det}\) lower, in order to raise the statistical power of the test (i.e. \(\mathrm {Prob}[\hat{\rho }>T_{det}\vert \rho =1]\)). Some developments of this algorithm have been proposed [12], also including the substitution of the MMPC objective function with a Moments against Samples one, that would let \(T_{det}\) decrease when increasing the size of the training set.
 
13
It can be observed that the regions selected by \(\varepsilon ^{PP}\) correspond to those for which the \(\varepsilon ^{KDA}\) exhibits the highest magnitude implicit coefficients (Fig. 3, upper-triangular part on the right).
 
Literatur
1.
Archambeau, C., Peeters, E., Standaert, F.-X., Quisquater, J.-J.: Template attacks in principal subspaces. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 1–14. Springer, Heidelberg (2006). doi:10.​1007/​11894063_​1 CrossRef
2.
Bär, M., Drexler, H., Pulkus, J.: Improved template attacks. In: COSADE 2010 (2010)
3.
Batina, L., Hogenboom, J., van Woudenberg, J.G.J.: Getting more from PCA: first results of using principal component analysis for extensive power analysis. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 383–397. Springer, Heidelberg (2012). doi:10.​1007/​978-3-642-27954-6_​24 CrossRef
4.
Bruneau, N., Guilley, S., Heuser, A., Marion, D., Rioul, O.: Less is more: dimensionality reduction from a theoretical perspective. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 22–41. Springer, Heidelberg (2015). doi:10.​1007/​978-3-662-48324-4_​2 CrossRef
5.
Bruneau, N., Danger, J.-L., Guilley, S., Heuser, A., Teglia, Y.: Boosting higher-order correlation attacks by dimensionality reduction. In: Chakraborty, R.S., Matyas, V., Schaumont, P. (eds.) SPACE 2014. LNCS, vol. 8804, pp. 183–200. Springer, Heidelberg (2014). doi:10.​1007/​978-3-319-12060-7_​13
6.
Cagli, E., Dumas, C., Prouff, E.: Enhancing dimensionality reduction methods for side-channel attacks. In: Homma, N., Medwed, M. (eds.) CARDIS 2015. LNCS, vol. 9514, pp. 15–33. Springer, Heidelberg (2016). doi:10.​1007/​978-3-319-31271-2_​2 CrossRef
7.
Carlet, C., Danger, J.-L., Guilley, S., Maghrebi, H., Prouff, E.: Achieving side-channel high-order correlation immunity with leakage squeezing. J. Cryptographic Eng. 4(2), 107–121 (2014)CrossRef
8.
Centeno, T.P., Lawrence, N.D.: Optimising kernel parameters and regularisation coefficients for non-linear discriminant analysis. J. Mach. Learn. Res. 7, 455–491 (2006)MathSciNetMATH
9.
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999). doi:10.​1007/​3-540-48405-1_​26
10.
11.
12.
Durvaux, F., Standaert, F.-X.: From improved leakage detection to the detection of points of interests in leakage traces. IACR Cryptology ePrint Archive, p. 536 (2015)
13.
Durvaux, F., Standaert, F.-X., Veyrat-Charvillon, N., Mairy, J.-B., Deville, Y.: Efficient selection of time samples for higher-order DPA with projection pursuits. In: Mangard, S., Poschmann, A.Y. (eds.) COSADE 2014. LNCS, vol. 9064, pp. 34–50. Springer, Cham (2015). doi:10.​1007/​978-3-319-21476-4_​3 CrossRef
14.
Eisenbarth, T., Paar, C., Weghenkel, B.: Building a side channel based disassembler. In: Gavrilova, M.L., Tan, C.J.K., Moreno, E.D. (eds.) Trans. on Comput. Sci. X. LNCS, vol. 6340, pp. 78–99. Springer, Heidelberg (2010). doi:10.​1007/​978-3-642-17499-5_​4 CrossRef
15.
Gierlichs, B., Lemke-Rust, K., Paar, C.: Templates vs. stochastic methods. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 15–29. Springer, Heidelberg (2006). doi:10.​1007/​11894063_​2 CrossRef
16.
17.
Hospodar, G., Gierlichs, B., De Mulder, E., Verbauwhede, I., Vandewalle, J.: Machine learning in side-channel analysis: a first study. J. Cryptographic Eng. 1(4), 293–302 (2011)CrossRef
18.
Lemke-Rust, K., Paar, C.: Gaussian mixture models for higher-order side channel analysis. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 14–27. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-74735-2_​2 CrossRef
19.
Lerman, L., Poussier, R., Bontempi, G., Markowitch, O., Standaert, F.-X.: Template attacks vs. machine learning revisited (and the curse of dimensionality in side-channel analysis). In: Mangard, S., Poschmann, A.Y. (eds.) COSADE 2014. LNCS, vol. 9064, pp. 20–33. Springer, Cham (2015). doi:10.​1007/​978-3-319-21476-4_​2 CrossRef
20.
Li, T., Zhu, S., Ogihara, M.: Using discriminant analysis for multi-class classification: an experimental investigation. Knowl. Inf. Syst. 10(4), 453–472 (2006)CrossRef
21.
Lomné, V., Prouff, E., Rivain, M., Roche, T., Thillard, A.: How to estimate the success rate of higher-order side-channel attacks. In: Batina, L., Robshaw, M. (eds.) CHES 2014. LNCS, vol. 8731, pp. 35–54. Springer, Heidelberg (2014). doi:10.​1007/​978-3-662-44709-3_​3
22.
O’Flynn, C., Chen, Z.D.: ChipWhisperer: an open-source platform for hardware embedded security research. In: Prouff, E. (ed.) COSADE 2014. LNCS, vol. 8622, pp. 243–260. Springer, Cham (2014). doi:10.​1007/​978-3-319-10175-0_​17
23.
Prouff, E., Rivain, M., Bevan, R.: Statistical analysis of second order differential power analysis. IEEE Trans. Comput. 58(6), 799–811 (2009)MathSciNetCrossRef
24.
Reparaz, O., Gierlichs, B., Verbauwhede, I.: Selecting time samples for multivariate DPA attacks. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 155–174. Springer, Heidelberg (2012). doi:10.​1007/​978-3-642-33027-8_​10 CrossRef
25.
26.
Schölkopf, B., Müller, K.-R.: Fisher discriminant analysis with kernels. In: Neural Networks for Signal Processing IX, vol. 1, p. 1 (1999)
27.
Schölkopf, B., Smola, A., Müller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Comput. 10(5), 1299–1319 (1998)CrossRef
28.
Standaert, F.-X., Archambeau, C.: Using subspace-based template attacks to compare and combine power and electromagnetic information leakages. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 411–425. Springer, Heidelberg (2008). doi:10.​1007/​978-3-540-85053-3_​26 CrossRef
Metadaten
Titel
Kernel Discriminant Analysis for Information Extraction in the Presence of Masking
verfasst von
Eleonora Cagli
Cécile Dumas
Emmanuel Prouff
Copyright-Jahr
2017
Buch
Smart Card Research and Advanced Applications

Print ISBN: 978-3-319-54668-1

Electronic ISBN: 978-3-319-54669-8

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-54669-8_1