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Template attacks versus machine learning revisited and the curse of dimensionality in side-channel analysis: extended version

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Abstract

Template attacks and machine learning are two popular approaches to profiled side-channel analysis. In this paper, we aim to contribute to the understanding of their respective strengths and weaknesses, with a particular focus on their curse of dimensionality. For this purpose, we take advantage of a well-controlled simulated experimental setting in order to put forward two important aspects. First and from a theoretic point of view, the data complexity of template attacks is not sensitive to the dimension increase in side-channel traces given that their profiling is perfect. Second and from a practical point of view, concrete attacks are always affected by (estimation and assumption) errors during profiling. As these errors increase, machine learning gains interest compared to template attacks, especially when based on random forests. We then clarify these results thanks to the bias–variance decomposition of the error rate recently introduced in the context side-channel analysis.

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Notes

  1. Note that the gain of linear regression-based attacks over template attack is known and has been analyzed, e.g., in [14, 35]. Namely, it essentially depends on the size of the basis used in linear regression.

  2. In [32] the equation representing the perceived information has a minus sign, whereas the correct sign is positive.

  3. There are variants of SVM and RF that aim to remedy to this issue. Yet, the “probability-like” scores they output are not directly exploitable in the estimation of information theoretic metrics. For example, we could exhibit examples where probability-like scores of one do not correspond to a success rate of one. More recently, Choudary et al. [6] showed that key enumeration based on scores and based on probabilities provide different results, which highlights the difference between score-based and probability-based profiled attacks.

  4. By contrast, we do not discuss the impact on the bias and on the variance term of each meta-parameter of a random forest and a template attack. For the interested readers about this aspect, we refer to the document of Louppe [28] analyzing random forests and to the paper of Lerman et al. [25] analyzing template attack.

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Acknowledgements

F.-X. Standaert is a research associate of the Belgian Fund for Scientific Research (FNRS-F.R.S.). This work has been funded in parts by the European Commission through the ERC project 280141 (CRASH). L. Lerman is a postdoctoral researcher working on the SCAUT project and funded by the Brussels Institute for Research and Innovation (Innoviris).

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Authors and Affiliations

  1. Département d’informatique, Université Libre de Bruxelles, Brussels, Belgium

    Liran Lerman & Olivier Markowitch

  2. ICTEAM/INGI, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Romain Poussier & François-Xavier Standaert

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  1. Liran Lerman
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  2. Romain Poussier
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  4. François-Xavier Standaert
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Correspondence to Liran Lerman.

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Lerman, L., Poussier, R., Markowitch, O. et al. Template attacks versus machine learning revisited and the curse of dimensionality in side-channel analysis: extended version. J Cryptogr Eng 8, 301–313 (2018). https://doi.org/10.1007/s13389-017-0162-9

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