J'ai le plaisir de vous inviter à ma soutenance d'Habilitation à Diriger des Recherches (HDR) intitulée :

Contributions to Fully Homomorphic Encryption: Constructions on the Torus and Techniques for Functional Evaluation

qui se tiendra le 17 avril 2026 à 16h à Sorbonne Université, Tour 25-26, salle 105. Lien visio : à venir.

Le jury sera composé de :

• Jean-Sébastien Coron, Professeur des universités, Université du Luxembourg, Luxembourg (rapporteur).
• Sihem Mesnager, Professeure des universités, Université Paris 8 (rapporteure).
• Damien Stehlé, Directeur scientifique, CryptoLab, France (rapporteur).
• Iryna Andriyanova, Professeure des universités, ETIS UMR 8051, CY Cergy Paris Université, ENSEA, CNRS (examinatrice).
• Caroline Fontaine, Directrice de recherche CNRS, Université Paris-Saclay, CNRS, ENS Paris-Saclay, LMF (examinatrice).
• Daniele Micciancio, Full Professor, University of California San Diego, USA (examinateur).
• Damien Vergnaud, Professeur des universités, Sorbonne Université (examinateur).

La soutenance sera suivie d'un pot, auquel vous êtes chaleureusement conviés.

Manuscrit : pdf

Title: Contributions to Fully Homomorphic Encryption: Constructions on the Torus and Techniques for Functional Evaluation

Abstract: Since the seminal construction of a Fully Homomorphic Encryption (FHE) schemes proposed by Gentry in 2009, numerous FHE schemes have been proposed to improve efficiency and practicality. The first part of my HDR thesis contributes to this evolution by concentrating on low-latency, gate-by-gate homomorphic computation with the TFHE scheme, I co-authored with Chillotti, Gama, and Georgieva. It first revisits the TFHE framework and its main building blocks, and show how bootstrapping efficiency can be improved by expressing the decryption circuit as a composition of homomorphic multiplexers and by replacing costly homomorphic internal products with more efficient external products. We further detail the circuit bootstrapping technique enabling conversions between ciphertext types with reduced noise, as well as functional bootstrapping, which allows the homomorphic evaluation of arbitrary functions through their encoding into the bootstrapping procedure.
Building on these foundations, the second part of the manuscript reviews the range of computations efficiently supported by TFHE, covering homomorphic function evaluation in disjunctive normal form as well as homomorphic evaluation in computational models such binary decision diagrams and deterministic automata. We also review packing methods, which transform multiple LWE ciphertexts into a single Ring LWE ciphertext, as well as a novel packing algorithm with low memory overhead, we proposed with Bossuat,
Finally, the third part addresses the problem of circuit privacy in TFHE and sanitisation, a related property that has been introduced by Ducas and Stehlé in 2016. With Bourse, we introduced a modified single-bootstrapping technique that ensures circuit confidentiality more efficiently than prior multi-step approaches, significantly reducing overhead and making this property practically achievable.