Romain Poussier

Simpler and More Efficient Rank Estimation for Side-Channel Security Assessment

Rank estimation algorithms allow analyzing the computational security of cryptographic keys for which adversaries have obtained partial information thanks to leakage or cryptanalysis. They are particularly useful in side-channel security evaluations, where the key is known by the evaluator but not reachable with exhaustive search. A first instance of such algorithms has been proposed at Eurocrypt 2013. In this paper, we propose a new tool for rank estimation that is conceptually simpler and much more efficient than this previous proposal. It allows approximating the key rank of (128-bit, 256-bit) symmetric keys with very tight bounds (i.e. with less than one bit of error), almost instantaneously and with limited memory. It also scales nicely to larger (e.g. 1024-bit) key sizes, for which the previous algorithm was hardly applicable.

Simple Key Enumeration (and Rank Estimation) Using Histograms: An Integrated Approach

The main contribution of this paper, is a new key enumeration algorithm that combines the conceptual simplicity of the rank estimation algorithm of Glowacz et al. (from FSE 2015) and the parallelizability of the enumeration algorithm of Bogdanov et al. (SAC 2015) and Martin et al. (from ASIACRYPT 2015). Our new algorithm is based on histograms. It allows obtaining simple bounds on the (small) rounding errors that it introduces and leads to straightforward parallelization. We further show that it can minimize the bandwidth of distributed key testing by selecting parameters that maximize the factorization of the lists of key candidates produced by the enumeration, which can be highly beneficial, e.g. if these tests are performed by a hardware coprocessor. We also put forward that the conceptual simplicity of our algorithm translates into efficient implementations (that slightly improve the state-of-the-art). As an additional consolidating effort, we finally describe an open source implementation of this new enumeration algorithm, combined with the FSE 2015 rank estimation one, that we make available with the paper.

Template Attacks vs. Machine Learning Revisited and the Curse of Dimensionality in Side-Channel Analysis

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 intuitions. First and from a theoretical 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 randomi¾?forests.

Score-Based vs. Probability-Based Enumeration – A Cautionary Note

The fair evaluation of leaking devices generally requires to come with the best possible distinguishers to extract and exploit side-channel information. While the need of a sound model for the leakages is a well known issue, the risks of additional errors in the post-processing of the attack results (with key enumeration/key rank estimation) are less investigated. Namely, optimal post-processing is known to be possible with distinguishers outputting probabilities (e.g. template attacks), but the impact of a deviation from this context has not been quantified so far. We therefore provide a consolidating experimental analysis in this direction, based on simulated and actual measurements. Our main conclusions are twofold. We first show that the concrete impact of heuristic scores such as produced with a correlation power analysis can lead to non-negligible post-processing errors. We then show that such errors can be mitigated in practice, with Bayesian extensions or specialized distinguishers (e.g. on-the-fly linear regression).

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

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.

A Systematic Approach to the Side-Channel Analysis of ECC Implementations with Worst-Case Horizontal Attacks

The wide number and variety of side-channel attacks against scalar multiplication algorithms makes their security evaluations complex, in particular in case of time constraints making exhaustive analyses impossible. In this paper, we present a systematic way to evaluate the security of such implementations against horizontal attacks. As horizontal attacks allow extracting most of the information in the leakage traces of scalar multiplications, they are suitable to avoid risks of overestimated security levels. For this purpose, we additionally propose to use linear regression in order to accurately characterize the leakage function and therefore approach worst-case security evaluations. We then show how to apply our tools in the contexts of ECDSA and ECDH implementations, and validate them against two targets: a Cortex-M4 and a Cortex-A8 micro-controllers.

Combining Leakage-Resilient PRFs and Shuffling

Combining countermeasures is usually assumed to be the best way to protect embedded devices against side-channel attacks. These combinations are at least expected to increase the number of measurements of successful attacks to some reasonable extent, and at best to guarantee a bounded time complexity independent of the number of measurements. This latter guarantee, only possible in the context of leakage resilient constructions, was only reached either for stateful (pseudo-random generator) constructions, or large parallel implementations so far. In this paper, we describe a first proposal of stateless (pseudo-random function) construction, for which we have strong hints that security bounded implementations are reachable under the constraints of small embedded devices. Our proposal essentially combines the well-known shuffling countermeasure with a tweaked pseudo-random function introduced at CHES 2012.We rst detail is performances. Then we analyze it against standard differential power analysis and discuss the different parameters influencing its security bounds. Finally, we put forward that its implementation in 8-bit microcontrollers can provide a better security vs. performance tradeo than state-of-the art (combinations of) countermeasures.