The goal of this course is to describe recent progresses (last 5 years or so) in lattice-based cryptology. Using lattices allows one to build public-key primitives with asymptotic efficiency superior to other existing systems, while providing much more precise security guarantees.
- Euclidean lattices : definitions, properties, algorithmic problems, lattice basis reduction, approximate algorithms
- Classical lattice-based crypto : GGH, NTRU.
- Modern techniques : discrete gaussians, smoothing parameter, statistical distance, sampling
- Algorithmic problems underlying the new cryptographic functions : SIS, LWE
- Lattice-based cryptographic functions : Hash functions, digital signatures, encryption, Identity-Based Encryption, Homomorphic Encryption.