The research activities of the ECO group covers a large spectrum at the interface of computer algebra, coding theory and cryptography, with motivations ranging from the theoretical foundations to the practical applications of these domains. The originality of our approach is to combine various aspects of computer science and mathematics. In particular, we are interested in:
- Algebra to understand and to describe the underlying structure of the objectsÂ
- Combinatorics to analyse their properties
- Arithmetic to efficiently solve computational problemsÂ
- Softwares to turn our theoretical results into effective solutions
- Complexity theory, to assess the efficiency of the algorithms and the security of cryptosystems
More precisely, our current works include the following problems:
- Computer Algebra:Â efficient algorithms in linear algebra, sparse or in-place polynomial arithmetic, finite field arithmetic, verified computingÂ
- Cryptography:Â public-key cryptography, elliptic curves, side-channel attacks and countermeasures, design and proofs of protocols, advanced cryptography, multi-party computation, post-quantum crypto
- Error Correcting Codes:Â algebraic decoding algorithms, bounds on parameters, fault tolerant linear algebra
Staff
Pascal Giorgi, Professeur des universités, UM
Katharina Boudgoust, Chargé de recherche, CNRS
Rocco Mora, Maître de conférences, UM
Laurent Imbert, Directeur de recherche, CNRS
Fabien Laguillaumie, Professeur des universités, UM
Romain Lebreton, Maître de conférences, UM
Andrei Romashchenko, Chargé de recherche, CNRS
Eleonora Guerrini, Professeur des universités, UM
Associates and Students
Nicole Franzoi, UM
Lucas Ottow, UM
Laz Panard, CNRS
Regular Co-workers
Quentin Combal, CDD Ingénieur-Technicien, CNRS
Haetham Al Aswad, CDD Chercheur, CNRS
Federico Savasta, CDD Chercheur, CNRS
Gabrielle Beck, CDD Chercheur, CNRS
Title: Étude des gadgets masqués dans Kyber
PhD defendant: Camille Mutschler
Defense date: 2024-12-17
Thesis director:
Laurent Imbert
Title: Algorithmes pour les polynômes creux: interpolation, arithmétique, test d’identité
PhD defendant: Armelle Perret Du Cray
Defense date: 2023-03-29
Thesis director:
Pascal Giorgi
Title: Reconstruction Rationnelle Simultanée et applications à la Théorie des Codes Correcteurs d’Erreurs
PhD defendant: Ilaria Zappatore
Defense date: 2020-10-16
Thesis director:
Laurent Imbert
Title: Détection de comportements à risque dans les applications en utilisant l’analyse statique
PhD defendant: Denis Martinez
Defense date: 2016-02-02
Thesis directors:
Roland Ducournau,
Laurent Imbert