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Olivier Rioul

Publications and source records attributed to Olivier Rioul.

At least 19 recordsLinked to original sources
arXiv2026

On the Optimum Secrecy Outage Probability and Ergodic Secrecy Rate over Wireless Channels

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.

cs.IT↗
arXiv2025

Data Processing Inequality for The Quantum Guesswork

Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state discrimination tasks. However, another criterion known as quantum guesswork has emerged as a crucial measure in assessing the distinguishability of non-orthogonal quantum states, when we are allowed to query a sequence of states. In this paper, we generalize well known properties in the classical setting that are relevant for the guessing problem. Specifically, we establish the pre and post Data Processing Inequalities. We also derive a more refined lower bound on quantum guesswork.

quant-ph↗
arXiv2025

From Classical to Quantum: Explicit Classical Distributions Achieving Maximal Quantum $f$-Divergence

Explicit classical states achieving maximal $f$-divergence are given, allowing for a simple proof of Matsumoto's Theorem, and the systematic extension of any inequality between classical $f$-divergences to quantum $f$-divergences. Our methodology is particularly simple as it does not require any elaborate matrix analysis machinery but only basic linear algebra. It is also effective, as illustrated by two examples improving existing bounds: (i)~an improved quantum Pinsker inequality is derived between $χ^2$ and trace norm, and leveraged to improve a bound in decoherence theory; (ii)~a new reverse quantum Pinsker inequality is derived for any quantum $f$-divergence, and compared to previous (Audenaert-Eisert and Hirche-Tomamichel) bounds.

quant-ph↗
arXiv2024

What can Information Guess? Guessing Advantage vs. Rényi Entropy for Small Leakages

We leverage the Gibbs inequality and its natural generalization to Rényi entropies to derive closed-form parametric expressions of the optimal lower bounds of $ρ$th-order guessing entropy (guessing moment) of a secret taking values on a finite set, in terms of the Rényi-Arimoto $α$-entropy. This is carried out in an non-asymptotic regime when side information may be available. The resulting bounds yield a theoretical solution to a fundamental problem in side-channel analysis: Ensure that an adversary will not gain much guessing advantage when the leakage information is sufficiently weakened by proper countermeasures in a given cryptographic implementation. Practical evaluation for classical leakage models show that the proposed bounds greatly improve previous ones for analyzing the capability of an adversary to perform side-channel attacks.

cs.IT↗
arXiv2023

Le Soleil se lèvera-t-il demain ?

Should we live every day as if it were our last? This question is legitimate when we know that Pierre-Simon de Laplace, in 1814, estimated the probability that the Sun would rise again the next day at 0.99999945. In this article, we explain in great detail the reasoning and calculations that lead to this surprising result.

math.HO↗
arXiv2023

An information theoretic necessary condition for perfect reconstruction

A new information theoretic condition is presented for reconstructing a discrete random variable $X$ based on the knowledge of a set of discrete functions of $X$. The reconstruction condition is derived from Shannon's 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common and complementary informations. Definitions and properties of the two entropic metrics are also fully detailed and shown compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated that leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable $X$ given a set $\{ X_1,\ldots,X_{n} \}$ of elements in the lattice generated by $X$. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, reconstruction of a word from a set of linear combinations, reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons.

cs.IT↗
arXiv2023

Maximal Leakage of Masked Implementations Using Mrs. Gerber's Lemma for Min-Entropy

A common countermeasure against side-channel attacks on secret key cryptographic implementations is $d$th-order masking, which splits each sensitive variable into $d+1$ random shares. In this paper, maximal leakage bounds on the probability of success of any side-channel attack are derived for any masking order. Maximal leakage (Sibson's information of order infinity) is evaluated between the sensitive variable and the noisy leakage, and is related to the conditional ``min-entropy'' (Arimoto's entropy of order infinity) of the sensitive variable given the leakage. The latter conditional entropy is then lower-bounded in terms of the conditional entropies for each share using majorization inequalities. This yields a generalization of Mrs. Gerber's lemma for min-entropy in finite Abelian groups.

cs.IT↗
arXiv2022

A Novel Mixture Model for Characterizing Human Aiming Performance Data

Fitts' law is often employed as a predictive model for human movement, especially in the field of human-computer interaction. Models with an assumed Gaussian error structure are usually adequate when applied to data collected from controlled studies. However, observational data (often referred to as data gathered "in the wild") typically display noticeable positive skewness relative to a mean trend as users do not routinely try to minimize their task completion time. As such, the exponentially-modified Gaussian (EMG) regression model has been applied to aimed movements data. However, it is also of interest to reasonably characterize those regions where a user likely was not trying to minimize their task completion time. In this paper, we propose a novel model with a two-component mixture structure -- one Gaussian and one exponential -- on the errors to identify such a region. An expectation-conditional-maximization (ECM) algorithm is developed for estimation of such a model and some properties of the algorithm are established. The efficacy of the proposed model, as well as its ability to inform model-based clustering, are addressed in this work through extensive simulations and an insightful analysis of a human aiming performance study.

stat.AP↗
arXiv2022

Attacking Masked Cryptographic Implementations: Information-Theoretic Bounds

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.

cs.IT↗
arXiv2022

Variations on a Theme by Massey

In 1994, Jim Massey proposed the guessing entropy as a measure of the difficulty that an attacker has to guess a secret used in a cryptographic system, and established a well-known inequality between entropy and guessing entropy. Over 15 years before, in an unpublished work, he also established a well-known inequality for the entropy of an integer-valued random variable of given variance. In this paper, we establish a link between the two works by Massey in the more general framework of the relationship between discrete (absolute) entropy and continuous (differential) entropy. Two approaches are given in which the discrete entropy (or Rényi entropy) of an integer-valued variable can be upper bounded using the differential (Rényi) entropy of some suitably chosen continuous random variable. As an application, lower bounds on guessing entropy and guessing moments are derived in terms of entropy or Rényi entropy (without side information) and conditional entropy or Arimoto conditional entropy (when side information is available).

cs.IT↗
arXiv2021

On Conditional $α$-Information and its Application to Side-Channel Analysis

A conditional version of Sibson's $α$-information is defined using a simple closed-form "log-expectation" expression, which satisfies important properties such as consistency, uniform expansion, and data processing inequalities. This definition is compared to previous ones, which in contrast do not satisfy all of these properties. Based on our proposal and on a generalized Fano inequality, we extend the case $α= 1$ of previous works to obtain sharp universal upper bounds for the probability of success of any type side-channel attack, particularly when $α= 2$.

cs.IT↗
arXiv2021

Asymptotically Optimal Massey-Like Inequality on Guessing Entropy With Application to Side-Channel Attack Evaluations

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.

cs.IT↗
arXiv2021

Designs in finite metric spaces: a probabilistic approach

A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in $Q$-polynomial distance-regular graphs. An approximation of their cumulative distribution function, based on the notion of Christoffel function in approximation theory is given. As an application we derive limit laws on the weight distributions of binary orthogonal arrays of strength going to infinity. An analogous result for combinatorial designs of strength going to infinity is given.

math.CO↗
arXiv2020

A Feedback Information-Theoretic Transmission Scheme (FITTS) for Modeling Trajectory Variability in Aimed Movements

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.

cs.HC↗
arXiv2020

Rényi Entropy Power and Normal Transport

A framework for deriving Rényi entropy-power inequalities (EPIs) is presented that uses linearization and an inequality of Dembo, Cover, and Thomas. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent $α$ of previous works. An information-theoretic proof of the Dembo-Cover-Thomas inequality---equivalent to Young's convolutional inequality with optimal constants---is provided, based on properties of Rényi conditional and relative entropies and using transportation arguments from Gaussian densities. For log-concave densities, a transportation proof of a sharp varentropy bound is presented.

cs.IT↗
arXiv2019

Entropy Estimation of Physically Unclonable Functions via Chow Parameters

A physically unclonable function (PUF) is an electronic circuit that produces an intrinsic identifier in response to a challenge. These identifiers depend on uncontrollable variations of the manufacturing process, which make them hard to predict or to replicate. Various security protocols leverage on such intrinsic randomness for authentification, cryptographic key generation, anti-counterfeiting, etc. Evaluating the entropy of PUFs (for all possible challenges) allows one to assess the security properties of such protocols. In this paper, we estimate the probability distribution of certain kinds of PUFs composed of $n$ delay elements. This is used to evaluate relevant Rényi entropies and determine how they increase with $n$. Such a problem was known to have extremely high complexity (in the order of $2^{2^n}$) and previous entropy estimations were carried out up to $n=7$. Making the link with the theory of Boolean threshold functions, we leverage on the representation by Chow parameters to estimate probability distributions up to $n=10$. The resulting Shannon entropy of the PUF is close to the max-entropy, which is asymptotically quadratic in $n$.

cs.IT↗