My Ph.D. dissertation is entitled Design and Implementation of Lattice-Based Cryptography contains most of my works on lattice-based cryptography, fully homomorphic encryption and multilinear maps.
— my Ph.D. dissertation received the 2014 Gilles Kahn Prize by the Informatics Society of France.
abstract: Today, lattice-based cryptography is a thriving scientific field. Its swift expansion is due, among others, to the attractiveness of fully homomorphic encryption and cryptographic multilinear maps. Lattice-based cryptography has also been recognized for its thrilling properties: a security that can be reduced to worstcase instances of problems over lattices, a quasi-optimal asymptotic efficiency and an alleged resistance to quantum computers. However, its practical use in real-world products leaves a lot to be desired. This thesis accomplishes a step towards this goal by narrowing the gap between theoretical research and practical implementation of recent public key cryptosystems.
In this thesis, we design and implement a lattice-based digital signature, two fully homomorphic encryption schemes and cryptographic multilinear maps. Our highly efficient signature scheme, BLISS, opened the way to implementing lattice-based cryptography on constrained devices and remains as of today a promising primitive for post-quantum cryptography. Our fully homomorphic encryption schemes enjoy competitive homomorphic evaluations of nontrivial circuits. Finally, we describe the first implementation of cryptographic multilinear maps. Based on our implementation, a non interactive key exchange between more than three parties has been realized for the first time, and amounts to a few seconds per party.