Abstract : Asymmetric cryptographic constructions used today could be attacked given a powerful enough quantum computer. Even if such a computer does not exist yet, it is important to anticipate its possible construction and to prepare a transition to cryptographic tools having a security resistant against attacks from quantum computers. I will introduce lattice-based cryptography, which is the most promising candidate to build post-quantum cryptographic constructions, and in particular, how we build efficient constructions based on structured lattice problems.

Keywords : lattice-based cryptography; lattice; learning with errors