ED Mathématiques et Informatique
Efficient succinct zero-knowledge arguments in the CL encryption framework and applications
by Agathe BEAUGRAND (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 14h00 - Salle de conférences Institut de Mathématiques de Bordeaux Université de Bordeaux Bâtiment A33 351, Cours de la Libération 33400 TALENCE
in front of the jury composed of
- Guilhem CASTAGNOS - Maître de conférences - Université de Bordeaux - Directeur de these
- Adeline ROUX-LANGLOIS - Directrice de recherche - Laboratoire GREYC Caen - Rapporteur
- Philippe GABORIT - Professeur des universités - Université de Limoges - Rapporteur
- Damien VERGNAUD - Professeur des universités - Sorbonne Université - Examinateur
- Céline CHEVALIER - Maîtresse de conférences - Université Paris-Panthéon-Assas - Examinateur
- Ignacio CASCUDO - Associate Professor - IMDEA Software Institute - Examinateur
- Fabien LAGUILLAUMIE - Professeur des universités - Université de Montpellier - CoDirecteur de these
The CL encryption scheme is a linearly homomorphic public-key encryption system proposed in 2015 by Castagnos and Laguillaumie. It is built upon class groups of imaginary quadratic fields. These groups are well-studied and known to be finite, but their exact order is computationally hard to determine. This intractability is a valuable feature for cryptographic applications, and is central to the construction of the CL cryptosystem. However, it also introduces significant technical challenges in manipulating CL ciphertexts. One key difficulty lies in designing zero-knowledge arguments, and even more so, arguments of knowledge in groups of unknown order. Traditional techniques from the prime-order setting, particularly regarding knowledge soundness, cannot be easily adaptable, which often leads to inefficient protocols with high computational and communication overheads. In this thesis, we develop new zero-knowledge protocols tailored to the CL framework, with the goal of improving efficiency and shortening transcripts with respect to existing protocols. The proposed protocols leverage two main tools. The first is the C-rough assumption, introduced by Braun, Damgård and Orlandi in 2023. This assumption, specific to the CL setting, states that determining whether the order of a class group generated by the CL setup algorithm has prime factors below a threshold C is computationally hard. The second is a novel concept called partial extractability, that can be seen as a relaxed form of knowledge soundness. This notion is particularly well-suited to the CL context, as it allows to treat plaintexts and randomnesses somewhat separately in the arguments. In particular, this allows to exploit techniques from the prime order setting to retrieve information about plaintexts, even though the randomness is defined modulo a composite and, above all, unknown. Using these tools, we construct protocols to prove both classical statements, such as the well-formedness of a ciphertext, and more advanced ones, such as the correctness of a shuffle of ciphertexts. Zero-knowledge proofs are crucial for securing multiparty computation protocols against malicious adversaries, as they help ensuring that participants behave honestly with respect to the protocol. Improving the efficiency of such proofs in the CL framework is therefore a foundational step toward building secure and practical multiparty computation based on CL encryption. As an application of our techniques, we present a protocol that securely realizes the private set intersection-sum functionality - a variant of Private Set intersection - in the presence of a malicious adversary, illustrating the interest of CL encryption as a building block to achieve advanced MPC functionalities.
Random interpolation and related properties in spaces of holomorphic functions
by Giuseppe LAMBERTI (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 10h00 - Salle de conférence Institut de Mathématiques de Bordeaux, 351 Cours de la Libération, Bâtiment A33, 33405 Talence Cedex
in front of the jury composed of
- Andréas HARTMANN - Professeur - Université de Bordeaux - Directeur de these
- Joaquim ORTEGA-CERDA - Professeur - Universitat de Barcelona - Rapporteur
- Marco PELOSO - Professeur - Università degli Studi di Milano - Rapporteur
- Isabelle CHALENDAR - Professeure - Université Gustav Eiffel - Examinateur
- Anna KONONOVA - Chargée de recherche - Tel Aviv University - Examinateur
- Pascal THOMAS - Professeur émérite - Université de Toulouse - Examinateur
This thesis explores the interplay between complex analysis and probability theory by studying random interpolation and related properties, such as separation and Carleson measure conditions, in spaces of holomorphic functions. The aim of considering a random situation is two-fold. Firstly, in certain situations deterministic characterizations of certain properties are hard to check and the random setting then often gives simple conditions ensuring almost surely the properties under consideration. Secondly, even when a deterministic description is available and well understood, the random setting allows to see when a property is generic. We will consider here three types of so-called point processes: Steinhaus sequences, where the moduli of the points (in the unit or poly disc, the ball, or the complex plane) are fixed while their arguments are independent and uniformly distributed, Poisson point processes, where the number of points in a measurable set is given by a Poisson distribution whose parameter depends on the measure of the set, and determinantal point processes which induce a natural repulsion property between points. The first focus of the thesis concerns free interpolating sequences in the Nevanlinna class, which is the largest class containing Hardy spaces and sharing numerous properties with these. In the Nevanlinna class, interpolating sequences are deterministically characterized via harmonic majorants whose existence is generally difficult to verify. Using Steinhaus sequences, it is shown that the Blaschke condition, which actually characterizes zero sets in the Nevanlinna class, is in fact sufficient to ensure free interpolation with probability one. In Hardy spaces, interpolation is strongly related to Carleson measures. While these measures are well understood in one complex variable, the situation changes significantly in several variables. Therefore, the second focus of this thesis is the study of Carleson measures for Hardy spaces, both in the polydisc and in the unit ball. Using random matrix theory applied to the Gram matrix of normalized reproducing kernels, we obtain a 0-1 law for Carleson measures generated by Steinhaus sequences for the Hardy space, showing in particular that the characterizing condition is actually a one-box condition. The thesis further explores deterministic interpolation in de Branges-Rovnyak spaces defined by non-extreme rational functions, providing a full characterization of interpolating sequences in this more general setting thereby extending previously known results. While the deterministic situation is quite transparent, the Steinhaus setting allows to see that interpolation is driven by the highest multiplicity of the zeros on the unit circle of the Pythagorean mate of the function defining the de Branges-Rovnyak space. The last part of this thesis is devoted to the study of determinantal point processes associated to generalized Fock spaces. While it is known that the determinantal process associated with the classical Fock space is almost surely not separated with respect to the Euclidean distance, this work identifies sharp conditions under which the determinantal process associated with a smaller generalized Fock space is almost surely separated in the Euclidean distance, i.e. in the classical Fock space.
Sparse models and deep priors for image decomposition into structure-texture
by Antoine GUENNEC (IMB - Institut de Mathématiques de Bordeaux)
The defense will take place at 15h00 - Salle 2 Institut de Mathématiques de Bordeaux UMR 5251 Université de Bordeaux 351, Cours de la Libération F-33405 TALENCE
in front of the jury composed of
- Jean-François AUJOL - Professeur des universités - Université de Bordeaux - Directeur de these
- Julie DELON - Professeure des universités - Université Paris Cité - Rapporteur
- Bruno GALERNE - Professeur des universités - Institut Denis Poisson, Université d'Orléans - Rapporteur
- Yann TRAONMILIN - Chargé de recherche - Institut Mathématiques de Bordeaux - CoDirecteur de these
- Yannick BERTHOUMIEU - Professeur des universités - IMS, INP Bordeaux - Examinateur
- Jérome GILLES - Professeur des universités - San Diego State University - Examinateur
The problem of decomposing images into structure and texture aims to separate an image into two components: the structure, which contains the geometry of the content in the image, and the texture, which contains local oscillations and/or repetitive patterns present in the image. Initially, we focus on a sparse modeling in gradient (structure) + low-rank by patch (texture) (LPR model). Building on the theoretical work of the sparse + low-rank matrix decomposition problem, we construct an algorithm that automatically adjusts the regularization parameters in the LPR model. This involves estimating the gradient sparsity and the patch-rank of the structure and texture respectively, during the descent iterations, to approximate the parameters that guarantee recovery. Additionally, we perform the algorithm locally across the image. The resulting algorithm is a localized version of the LPR model with automatic tuning of regularization parameters and is easily scalable as each operation can be parallelized efficiently. Secondly, we present a joint modeling of structure-texture. For this, we learn a regularization function $R_{sotimes t}$ that takes the structure and texture components jointly as input. The learning of the regularization function $R_{sotimes t}$ is done using a database of synthetic structure-texture pairs generated from random variables. Numerically, we show that the joint modeling provides a gain in recovery performances compared to a classical modeling $R_s(u) + lambda R_t(v)$ (with $f=u+v$), while eliminating the need to adjust the parameter $lambda$ for each image. Finally, we are interested in the recovery of low-dimensional models. Under the conditions of a restricted isometry property on the observation operator $mathcal{A}$ and a $eta$-restricted Lipschitz property on the projection, we find that we have a linear rate of convergence of recovery for the projected gradient algorithm. Based on this observation, we investigate the convergence speed of plug-and-play algorithms (PnP-PGM), in which a denoiser replaces the projection. Experiments on both synthetic and real data show that if the reference image is approximately a fixed point of the denoiser, then we obtain a linear rate of convergence of recovery.
ED Sociétés, Politique, Santé Publique
A Translocal Political Space. Diaspora Associative Organisations and Political Transfers between France, the Comoros, and Mali
by Camille TRAORE (Les Afriques dans le Monde)
The defense will take place at 14h00 - Salle Merle Sciences Po Bordeaux 11 Allée Ausone 33607 Pessac Cedex
in front of the jury composed of
- Etienne SMITH - Maître de conférences - Sciences Po Bordeaux - CoDirecteur de these
- Patrick HASSENTEUFEL - Professeur des universités - Université Versailles Saint-Quentin-en-Yvelines - Rapporteur
- Élise PALOMARES - Professeure des universités - Université de Rouen - Rapporteur
- Cécile VIGOUR - Directrice de recherche - CNRS - Sciences Po Bordeaux - CoDirecteur de these
- Camille HAMIDI - Professeure des universités - Université Lumière Lyon-2 - Examinateur
- Thomas LACROIX - Directeur de recherche - CNRS - Sciences Po - Examinateur
- Philippe LAVIGNE-DELVILLE - Directeur de recherche - IRD - Examinateur
Anchored in a translocal approach to public policy analysis, this dissertation sheds light on the unexpected effects of diaspora associative mobilizations on transnational policies and local institutional transformations—often preceding national legislative frameworks. It also reveals how local and national authorities, as well as international aid institutions, instrumentalise categories of migrants and diaspora, thereby enabling a minority of diaspora actors to position themselves within strategic spaces of political change in migration-related territories: the translocal political space. In three national contexts, elected officials from both origin and destination territories adjust their practices in response to diaspora associations, which are simultaneously perceived as valuable resources and potential political threats. Over time, local development initiatives led by diaspora associations—supported by their local governments in France—have fostered the emergence of inter-municipal cooperation frameworks in Mali and the Comoros. These developments exemplify political transfer dynamics tied to diaspora engagement and highlight the growing interconnection of local policies across Comorian, French, and Malian migration spaces. The geographical, social, and cultural mobility of diaspora leaders reveals their capacity to navigate multiple political systems and to strategically mobilize resources available in both settings. In doing so, they shape a translocal political arena, and with it, a form of translocal power. By tracing their transnational circulations, this dissertation shows how migrant associative networks foster the diffusion and adoption of new local political practices and institutions. The dissertation draws on a wide range of academic literature, intersecting development studies on Mali and the Comoros, the sociology of transnational migration, local policy analysis, decentralisation studies, and public policy transfer. This comparative and transnational approach enables a productive dialogue between these various theoretical frameworks. The empirical investigation is based on several months of fieldwork combining interviews, participant observation, and archival research, conducted across three sites: the eastern suburbs of Paris (Seine-Saint-Denis and Val-de-Marne), the cercle of Yélimané in Mali (Kayes region), and the northern region of Grande Comore (Union of the Comoros). The analysis of biographical trajectories identifies recurrent patterns among members of diaspora associations and elected officials in French, Malian, and Comorian local governments. A comparative approach provides a framework for embedding these trajectories within the broader political and social contexts of migratory territories.