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Personne# Alexandre Raphaël Duc

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Cryptographie

thumb|La machine de Lorenz utilisée par les nazis durant la Seconde Guerre mondiale pour chiffrer les communications militaires de haut niveau entre Berlin et les quartiers-généraux des différentes ar

Cryptographie asymétrique

vignette|320x320px|Schéma du chiffrement asymétrique: une clé sert à chiffrer et une seconde à déchiffrer
La cryptographie asymétrique, ou cryptographie à clé publique est un domaine relativement réce

Sûreté

En politique, la sûreté est la protection contre le pouvoir ou la violence, le danger ou les menaces. Plus particulièrement, dans la déclaration des Droits de l'homme et du citoyen de 1789, la sûreté

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Alexandre Raphaël Duc, Sebastian Faust

We investigate the relationships between theoretical studies of leaking cryptographic devices and concrete security evaluations with standard side-channel attacks. Our contributions are in four parts. First, we connect the formal analysis of the masking countermeasure proposed by Duc et al. (Eurocrypt 2014) with the Eurocrypt 2009 evaluation framework for side-channel key recovery attacks. In particular, we re-state their main proof for the masking countermeasure based on a mutual information metric, which is frequently used in concrete physical security evaluations. Second, we discuss the tightness of the Eurocrypt 2014 bounds based on experimental case studies. This allows us to conjecture a simplified link between the mutual information metric and the success rate of a side-channel adversary, ignoring technical parameters and proof artifacts. Third, we introduce heuristic (yet well-motivated) tools for the evaluation of the masking countermeasure when its independent leakage assumption is not perfectly fulfilled, as it is frequently encountered in practice. Thanks to these tools, we argue that masking with non-independent leakages may provide improved security levels in certain scenarios. Eventually, we consider the tradeoff between measurement complexity and key enumeration in divide-and-conquer side-channel attacks, and show that it can be predicted based on the mutual information metric, by solving a non-linear integer programming problem for which efficient solutions exist. The combination of these observations enables significant reductions of the evaluation costs for certification bodies.

Alexandre Raphaël Duc, Florian Tramèr, Serge Vaudenay

The Learning With Error problem (LWE) is becoming more and more used in cryptography, for instance, in the design of some fully homomorphic encryption schemes. It is thus of primordial importance to find the best algorithms that might solve this problem so that concrete parameters can be proposed. The BKW algorithm was proposed by Blum et al. as an algorithm to solve the Learning Parity with Noise problem (LPN), a subproblem of LWE. This algorithm was then adapted to LWE by Albrecht et al. In this paper, we improve the algorithm proposed by Albrecht et al. by using multidimensional Fourier transforms. Our algorithm is, to the best of our knowledge, the fastest LWE solving algorithm. Compared to the work of Albrecht et al. we greatly simplify the analysis, getting rid of integrals which were hard to evaluate in the final complexity. We also remove some heuristics on rounded Gaussians. Some of our results on rounded Gaussians might be of independent interest. Moreover, we also analyze algorithms solving LWE with discrete Gaussian noise. Finally, we apply the same algorithm to the Learning With Rounding problem (LWR) for prime q, a deterministic counterpart to LWE. This problem is getting more and more attention and is used, for instance, to design pseudorandom functions. To the best of our knowledge, our algorithm is the first algorithm applied directly to LWR. Furthermore, the analysis of LWR contains some technical results of independent interest.

Modern cryptography pushed forward the need of having provable security. Whereas ancient cryptography was only relying on heuristic assumptions and the secrecy of the designs, nowadays researchers try to make the security of schemes to rely on mathematical problems which are believed hard to solve. When doing these proofs, the capabilities of potential adversaries are modeled formally. For instance, the black-box model assumes that an adversary does not learn anything from the inner-state of a construction. While this assumption makes sense in some practical scenarios, it was shown that one can sometimes learn some information by other means, e.g., by timing how long the computation take. In this thesis, we focus on two different areas of cryptography. In both parts, we take first a theoretical point of view to obtain a result. We try then to adapt our results so that they are easily usable for implementers and for researchers working in practical cryptography. In the first part of this thesis, we take a look at post-quantum cryptography, i.e., at cryptographic primitives that are believed secure even in the case (reasonably big) quantum computers are built. We introduce HELEN, a new public-key cryptosystem based on the hardness of the learning from parity with noise problem (LPN). To make our results more concrete, we suggest some practical instances which make the system easily implementable. As stated above, the design of cryptographic primitives usually relies on some well-studied hard problems. However, to suggest concrete parameters for these primitives, one needs to know the precise complexity of algorithms solving the underlying hard problem. In this thesis, we focus on two recent hard-problems that became very popular in post-quantum cryptography: the learning with error (LWE) and the learning with rounding problem (LWR). We introduce a new algorithm that solves both problems and provide a careful complexity analysis so that these problems can be used to construct practical cryptographic primitives. In the second part, we look at leakage-resilient cryptography which studies adversaries able to get some side-channel information from a cryptographic primitive. In the past, two main disjoint models were considered. The first one, the threshold probing model, assumes that the adversary can put a limited number of probes in a circuit. He then learns all the values going through these probes. This model was used mostly by theoreticians as it allows very elegant and convenient proofs. The second model, the noisy-leakage model, assumes that every component of the circuit leaks but that the observed signal is noisy. Typically, some Gaussian noise is added to it. According to experiments, this model depicts closely the real behaviour of circuits. Hence, this model is cherished by the practical cryptographic community. In this thesis, we show that making a proof in the first model implies a proof in the second model which unifies the two models and reconciles both communities. We then look at this result with a more practical point-of-view. We show how it can help in the process of evaluating the security of a chip based solely on the more standard mutual information metric.