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.

Course outline

  • 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.

Web page for the course