arXiv subjects

Paul-Marie Grollemund

Publications and source records attributed to Paul-Marie Grollemund.

8 recordsLinked to original sources

arXiv2026

Fleming-Viot Selection of the Yaglom Limit for Age-Structured Bellman-Harris Processes, with Application to Livestock Epidemic Surveillance

In this paper, we construct a Fleming-Viot particle system for a class of subcritical Bellman-Harris processes. We prove that it selects the Yaglom limit at a polynomial rate in the number of particles. Since lifetimes are non-exponential, the population size is not Markov, and the analysis must therefore be carried out on the space of age configurations. In this setting, the Lyapunov functions used for Galton-Watson processes are no longer norm-like. Nevertheless, we establish a Yaglom theorem that strengthens the classical result: the conditional laws converge in total variation at an exponential rate, with decay rate given by the Malthusian parameter. We also prove that the drift condition, which links the hazard rate to the offspring law, is necessary within a natural class of Lyapunov functions, showing that it is a feature of the measure-valued lift rather than a defect of the estimates. Finally, we illustrate the estimator through an application to livestock epidemic surveillance, where the Yaglom limit is the null distribution of a change-detection test.

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arXiv2024

Accuracy Limits as a Barrier to Biometric System Security

Biometric systems are widely used for identity verification and identification, including authentication (i.e., one-to-one matching to verify a claimed identity) and identification (i.e., one-to-many matching to find a subject in a database). The matching process relies on measuring similarities or dissimilarities between a fresh biometric template and enrolled templates. The False Match Rate FMR is a key metric for assessing the accuracy and reliability of such systems. This paper analyzes biometric systems based on their FMR, with two main contributions. First, we explore untargeted attacks, where an adversary aims to impersonate any user within a database. We determine the number of trials required for an attacker to successfully impersonate a user and derive the critical population size (i.e., the maximum number of users in the database) required to maintain a given level of security. Furthermore, we compute the critical FMR value needed to ensure resistance against untargeted attacks as the database size increases. Second, we revisit the biometric birthday problem to evaluate the approximate and exact probabilities that two users in a database collide (i.e., can impersonate each other). Based on this analysis, we derive both the approximate critical population size and the critical FMR value needed to bound the likelihood of such collisions occurring with a given probability. These thresholds offer insights for designing systems that mitigate the risk of impersonation and collisions, particularly in large-scale biometric databases. Our findings indicate that current biometric systems fail to deliver sufficient accuracy to achieve an adequate security level against untargeted attacks, even in small-scale databases. Moreover, state-of-the-art systems face significant challenges in addressing the biometric birthday problem, especially as database sizes grow.

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arXiv2024

Exploit the Leak: Understanding Risks in Biometric Matchers

In a biometric authentication or identification system, the matcher compares a stored and a fresh template to determine whether there is a match. This assessment is based on both a similarity score and a predefined threshold. For better compliance with privacy legislation, the matcher can be built upon a privacy-preserving distance. Beyond the binary output (`yes' or `no'), most schemes may perform more precise computations, e.g., the value of the distance. Such precise information is prone to leakage even when not returned by the system. This can occur due to a malware infection or the use of a weakly privacy-preserving distance, exemplified by side channel attacks or partially obfuscated designs. This paper provides an analysis of information leakage during distance evaluation. We provide a catalog of information leakage scenarios with their impacts on data privacy. Each scenario gives rise to unique attacks with impacts quantified in terms of computational costs, thereby providing a better understanding of the security level.

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arXiv2024

Sparse inference in Poisson Log-Normal model by approximating the L0-norm

Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in regression models, for instance in this article for the Poisson Log Normal model (PLN, Chiquet et al., 2021). This model aim to explain multivariate count data using dependent variables, and its utility was demonstrating in scientific fields such as ecology and agronomy. In the case of the PLN model, most recent papers focus on sparse networks inference through combination of the likelihood with a L1 -penalty on the precision matrix. In this paper, we propose to rely on a recent penalization method (SIC, O'Neill and Burke, 2023), which consists in smoothly approximating the L0-penalty, and that avoids the calibration of a tuning parameter with a cross-validation procedure. Moreover, this work focuses on the coefficient matrix of the PLN model and establishes an inference procedure ensuring effective variable selection performance, so that the resulting fitted model explaining multivariate count data using only relevant explanatory variables. Our proposal involves implementing a procedure that integrates the SIC penalization algorithm (epsilon-telescoping) and the PLN model fitting algorithm (a variational EM algorithm). To support our proposal, we provide theoretical results and insights about the penalization method, and we perform simulation studies to assess the method, which is also applied on real datasets.

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arXiv2024

Untargeted Near-collision Attacks on Biometrics: Real-world Bounds and Theoretical Limits

A biometric recognition system can operate in two distinct modes: identification or verification. In the first mode, the system recognizes an individual by searching the enrolled templates of all the users for a match. In the second mode, the system validates a user's identity claim by comparing the fresh provided template with the enrolled template. The biometric transformation schemes usually produce binary templates that are better handled by cryptographic schemes, and the comparison is based on a distance that leaks information about the similarities between two biometric templates. Both the experimentally determined false match rate and false non-match rate through recognition threshold adjustment define the recognition accuracy, and hence the security of the system. To our knowledge, few works provide a formal treatment of security in case of minimal information leakage, i.e., the binary outcome of a comparison with a threshold. In this paper, we focus on untargeted attacks that can be carried out both online and offline, and in both identification and verification modes. On the first hand, we focus our analysis on the accuracy metrics of biometric systems. We provide the complexity of untargeted attacks using the False Match Rate (FMR) and the False Positive Identification Rate (FPIR) to address the security of these systems. Studying near-collisions with these metrics allows us to estimate the maximum number of users in a database, given a chosen FMR, to preserve the security and the accuracy. These results are evaluated on systems from the literature. On the other hand, we rely on probabilistic modelling to assess the theoretical security limits of biometric systems. The study of this metric space, and system parameters (template size, threshold and database size), gives us the complexity of untargeted attacks and the probability of a near-collision.

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arXiv2022

Authentication Attacks on Projection-based Cancelable Biometric Schemes

Cancelable biometric schemes aim at generating secure biometric templates by combining user specific tokens, such as password, stored secret or salt, along with biometric data. This type of transformation is constructed as a composition of a biometric transformation with a feature extraction algorithm. The security requirements of cancelable biometric schemes concern the irreversibility, unlinkability and revocability of templates, without losing in accuracy of comparison. While several schemes were recently attacked regarding these requirements, full reversibility of such a composition in order to produce colliding biometric characteristics, and specifically presentation attacks, were never demonstrated to the best of our knowledge. In this paper, we formalize these attacks for a traditional cancelable scheme with the help of integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP). Solving these optimization problems allows an adversary to slightly alter its fingerprint image in order to impersonate any individual. Moreover, in an even more severe scenario, it is possible to simultaneously impersonate several individuals.

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arXiv2022

Near-collisions and their Impact on Biometric Security

Biometric recognition encompasses two operating modes. The first one is biometric identification which consists in determining the identity of an individual based on her biometrics and requires browsing the entire database (i.e., a 1:N search). The other one is biometric authentication which corresponds to verifying claimed biometrics of an individual (i.e., a 1:1 search) to authenticate her, or grant her access to some services. The matching process is based on the similarities between a fresh and an enrolled biometric template. Considering the case of binary templates, we investigate how a highly populated database yields near-collisions, impacting the security of both the operating modes. Insight into the security of binary templates is given by establishing a lower bound on the size of templates and an upper bound on the size of a template database depending on security parameters. We provide efficient algorithms for partitioning a leaked template database in order to improve the generation of a master-template-set that can impersonates any enrolled user and possibly some future users. Practical impacts of proposed algorithms are finally emphasized with experimental studies.

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arXiv2017

Bayesian functional linear regression with sparse step functions

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor seen as a function of time. This paper focuses on the Bayesian estimation of the support of the coefficient function. To this aim we propose a parsimonious and adaptive decomposition of the coefficient function as a step function, and a model including a prior distribution that we name Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to recover areas of time which influences the most the outcome. A Bayes estimator of the support is built with a specific loss function, as well as two Bayes estimators of the coefficient function, a first one which is smooth and a second one which is a step function. The performance of the proposed methodology is analysed on various synthetic datasets and is illustrated on a black Périgord truffle dataset to study the influence of rainfall on the production.

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