Implementation of Lattice Trapdoors on Modules and Applications

International audienceWe develop and implement efficient Gaussian preimage sampling techniques on module lattices, which rely on the works of Micciancio and Peikert in 2012, and Micciancio and Genise in 2018. The main advantage of our implementation is its modularity, which makes it practical to use for signature schemes, but also for more advanced constructions using trapdoors such as identity-based encryption. In particular, it is easy to use in the ring or module setting, and to modify the arithmetic on Rq (as different schemes have different conditions on q). Relying on these tools, we also present two instantiations and implementations of proven trapdoor-based signature schemes in the module setting: GPV in the random oracle model and a variant of it in the standard model presented in Bert et al. in 2018. For that last scheme, we address a security issue and correct obsolescence problems in their implementation by building ours from scratch. To the best of our knowledge, this is the first efficient implementation of a lattice-based signature scheme in the standard model. Relying on that last signature, we also present the implementation of a standard model IBE in the module setting. We show that while the resulting schemes may not be competitive with the most efficient NIST candidates, they are practical and run on a standard laptop in acceptable time, which paves the way for practical advanced trapdoor-based constructions