Olivier Rioul

Clement Leroy, Tarak Arbi, Benoit Geller et al.

We study the secrecy of wireless channels in the presence of an eavesdropper, where the channels are random and the transmitter only has knowledge of the channel statistics. We investigate the optimal input distribution with respect to several secrecy metrics: the Secrecy Outage Probability (SOP), defined as the probability that the coding rate $r$ exceeds the instantaneous secrecy rate; the Ergodic Secrecy Rate (ESR), defined as the expected secrecy rate over channel realizations; and the Ergodic Positive Secrecy Rate (EPSR), defined as the expected value of the positive part of the secrecy rate. We introduce two partial orderings for random channels: the uniformly less noisy order and the less noisy on average order. We show that when the main channel is uniformly less noisy than the eavesdropper channel, the optimal input distribution is a non-precoded Gaussian input for both the SOP and the EPSR. Furthermore, we show that the same input distribution is optimal for the ESR when the less noisy on average order holds. In addition, similar optimality results for the SOP and the EPSR are obtained for single-transmit-antenna channels without requiring any channel ordering assumptions. Closed-form expressions of the secrecy metrics are derived for special cases of Rayleigh fading channels.

Wei Cheng, Yi Liu, Sylvain Guilley et al.

Measuring the information leakage is critical for evaluating the practical security of cryptographic devices against side-channel analysis. Information-theoretic measures can be used (along with Fano's inequality) to derive upper bounds on the success rate of any possible attack in terms of the number of side-channel measurements. Equivalently, this gives lower bounds on the number of queries for a given success probability of attack. In this paper, we consider cryptographic implementations protected by (first-order) masking schemes, and derive several information-theoretic bounds on the efficiency of any (second-order) attack. The obtained bounds are generic in that they do not depend on a specific attack but only on the leakage and masking models, through the mutual information between side-channel measurements and the secret key. Numerical evaluations confirm that our bounds reflect the practical performance of optimal maximum likelihood attacks.

Andrei Tănăsescu, Marios O. Choudary, Olivier Rioul et al.

A Massey-like inequality is any useful lower bound on guessing entropy in terms of the computationally scalable Shannon entropy. The asymptotically optimal Massey-like inequality is determined and further refined for finite-support distributions. The impact of these results are highlighted for side-channel attack evaluation where guessing entropy is a key metric. In this context, the obtained bounds are compared to the state of the art.

Quentin Roy, Yves Guiard, Gilles Bailly et al.

The usability of small devices such as smartphones or interactive watches is often hampered by the limited size of command vocabularies. This paper is an attempt at better understanding how finger identification may help users invoke commands on touch screens, even without recourse to multi-touch input. We describe how finger identification can increase the size of input vocabularies under the constraint of limited real estate, and we discuss some visual cues to communicate this novel modality to novice users. We report a controlled experiment that evaluated, over a large range of input-vocabulary sizes, the efficiency of single-touch command selections with vs. without finger identification. We analyzed the data not only in terms of traditional time and error metrics, but also in terms of a throughput measure based on Shannon's theory, which we show offers a synthetic and parsimonious account of users' performance. The results show that the larger the input vocabulary needed by the designer, the more promising the identification of individual fingers.

Julien Gori, Olivier Rioul

Trajectories in human aimed movements are inherently variable. Using the concept of positional variance profiles, such trajectories are shown to be decomposable into two phases: In a first phase, the variance of the limb position over many trajectories increases rapidly; in a second phase, it then decreases steadily. A new theoretical model, where the aiming task is seen as a Shannon-like communication problem, is developed to describe the second phase: Information is transmitted from a source (determined by the position at the end of the first phase), to a destination (the movement's end-point) over a channel perturbed by Gaussian noise, with the presence of a noiseless feedback link. Information-theoretic considerations show that the positional variance decreases exponentially with a rate equal to the channel capacity C. Two existing datasets for simple pointing tasks are re-analyzed and observations on real data confirm our model. The first phase has constant duration and C is found constant across instructions and task parameters, which thus characterizes the participant's performance. Our model provides a clear understanding of the speed-accuracy tradeoff in aimed movements: Since the participant's capacity is fixed, a higher prescribed accuracy necessarily requires a longer second phase resulting in an increased overall movement time. The well-known Fitts' law is also recovered using this approach.