Abstract
Advanced Side-Channel Analyses make use of dimensionality reduction techniques to reduce both the memory and timing complexity of the attacks. The most popular methods to effectuate such a reduction are the Principal Component Analysis (PCA) and the Linear Discriminant Analysis (LDA). They indeed lead to remarkable efficiency gains but their use in side-channel context also raised some issues. The PCA provides a set of vectors (the principal components) onto which project the data. The open question is which of these principal components are the most suitable for side-channel attacks. The LDA has been valorized for its theoretical leaning toward the class-distinguishability, but discouraged for its constraining greed of data. In this paper we present an in-depth study of these two methods, and, to automatize and to ameliorate the principal components selection, we propose a new technique named cumulative Explained Local Variance (ELV) selection. Moreover we present some extensions of the LDA, available in less constrained situations than the classical version. We equip our study with a comprehensive comparison of the existing and new methods in real cases. It allows us to verify the soundness of the ELV selection, and the effectiveness of the methods proposed to extend the use of the LDA to side-channel contexts where the existing approaches are inapplicable.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
It can happen for example when attacking an RSA implementation, where the acquisitions are often huge (of the order of 1,000,000 points) and the number of measurements may be small when the SNR is good, implying that a good GE can be achieved with a small N.
- 2.
The name is due to the fact that it was proposed and tested for face recognition scopes.
- 3.
This study is let open for an extended version of this paper.
- 4.
This choice has been done to allow for reproducibility of the experiments.
- 5.
It consists in keeping the \(C\) first LDCs (the C last for the Direct LDA).
References
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)
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)
Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)
Bruneau, N., Guilley, S., Heuser, A., Marion, D., Rioul, O.: Less is more. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 22–41. Springer, Heidelberg (2015)
Chari, S., Rao, J.R., Rohatgi, P.: Template attacks. In: Kaliski Jr., B.S., Koç, Ç.K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 13–28. Springer, Heidelberg (2003)
Chen, L.-F., Liao, H.-Y.M., Ko, M.-T., Lin, J.-C., Yu, G.-J.: A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recogn. 33(10), 1713–1726 (2000)
Choudary, O., Kuhn, M.G.: Efficient stochastic methods: profiled attacks beyond 8 bits. IACR Cryptology ePrint Archive (2014)
Choudary, O., Kuhn, M.G.: Efficient template attacks. In: Francillon, A., Rohatgi, P. (eds.) CARDIS 2013. LNCS, vol. 8419, pp. 253–270. Springer, Heidelberg (2014)
Eisenbarth, T., Paar, C., Weghenkel, B.: Building a side channel based disassembler. In: Gavrilova, M.L., Tan, C.J.K., Moreno, E.D. (eds.) Transactions on Computational Science X. LNCS, vol. 6340, pp. 78–99. Springer, Heidelberg (2010)
Fisher, R.A.: The statistical utilization of multiple measurements. Ann. Eugenics 8(4), 376–386 (1938)
Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press Professional Inc, San Diego (1990)
Guhr, T., Müller-Groeling, A., Weidenmüller, H.A.: Random-matrix theories in quantum physics: common concepts. Phys. Rep. 299(4), 189–425 (1998)
Huang, R., Liu, Q., Lu, H., Ma, S.: Solving the small sample size problem of LDA. Pattern Recogn. 3, 29–32 (2002)
Karsmakers, P., Gierlichs, B., Pelckmans, K., De Cock, K., Suykens, J., Preneel, B., De Moor, B.: Side channel attacks on cryptographic devices as a classification problem. Technical report, COSIC technical report (2009)
Liu, K., Cheng, Y.-Q., Yang, J.-Y.: A generalized optimal set of discriminant vectors. Pattern Recogn. 25(7), 731–739 (1992)
Massey, J.L.: Guessing and entropy. In: 1994 Proceedings of the IEEE International Symposium on Information Theory, p. 204. IEEE (1994)
Mavroeidis, D., Batina, L., van Laarhoven, T., Marchiori, E.: PCA, Eigenvector localization and clustering for side-channel attacks on cryptographic hardware devices. In: Flach, P.A., De Bie, T., Cristianini, N. (eds.) ECML PKDD 2012, Part I. LNCS, vol. 7523, pp. 253–268. Springer, Heidelberg (2012)
Nisan, N., Zuckerman, D.: Randomness is linear in space. J. Comput. Syst. Sci. 52(1), 43–52 (1996)
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, Heidelberg (2014)
TELECOM ParisTech. DPA contest 4. http://www.DPAcontest.org/v4/
Specht, R., Heyszl, J., Kleinsteuber, M., Sigl, G.: Improving non-profiled attacks on exponentiations based on clustering and extracting leakage from multi-channel high-resolution EM measurements. In: Mangard, S., Poschmann, A.Y. (eds.) COSADE 2015. LNCS, vol. 9064, pp. 3–19. Springer, Heidelberg (2015)
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)
Standaert, F.-X., Malkin, T.G., Yung, M.: A unified framework for the analysis of side-channel key recovery attacks. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 443–461. Springer, Heidelberg (2009)
Yu, H., Yang, J.: A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recogn. 34, 2067–2070 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Cagli, E., Dumas, C., Prouff, E. (2016). Enhancing Dimensionality Reduction Methods for Side-Channel Attacks. In: Homma, N., Medwed, M. (eds) Smart Card Research and Advanced Applications. CARDIS 2015. Lecture Notes in Computer Science(), vol 9514. Springer, Cham. https://doi.org/10.1007/978-3-319-31271-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-31271-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-31270-5
Online ISBN: 978-3-319-31271-2
eBook Packages: Computer ScienceComputer Science (R0)