Lattice-Based Cryptography

Post-quantum cryptography refers to cryptographic schemes that would not be vulnerable following the construction of a sufficiently powerful quantum computer. In this article, we focus on so-called asymmetric cryptographic constructions, enabling users to communicate or authenticate securely without first possessing a common secret. It is this branch of cryptography that will be most affected by the arrival of a quantum computer. Indeed, the security of the constructions we use today relies on two families of problems that are classically difficult, but which will become quantum easy.

Cryptography based on Euclidean lattices is one of the post-quantum solutions identified in recent years. It seems to be the most promising and has many advantages. In particular, it enables us to design a multitude of cryptographic constructions, from the simplest to the most advanced, which are increasingly efficient while basing their security on well-studied algorithmic problems. In this article, we will explain how to build an encryption scheme and two signature schemes that are secure even against quantum computers, and what are the hard problems on which the security of these constructions is based.