March 21, 2022

Lectures: Monday / Wednesday 10 – 11:20 am

Point Lattices over the reals are remarkably useful in cryptography. Among many others, the Learning With Errors (LWE) assumption has changed the landscape of cryptography in recent years. Nearly every known cryptographic objective, from signatures, non-interactive zero-knowledge, fully homomorphic encryption, to attribute-based encryption, can be based on LWE. Lattices are also one of the most widely used bases for developing post-quantum and quantum cryptography, and it is a unique source of computational hardness with worst-case to average-case connections. In this course, we will delve into lattices and lattice-based cryptography. 

Topics covered, depending on time and interests, may include:

  • basic properties of lattices,
  • basic algorithms for attacking lattice problems and LWE,
  • worst-case to average-case, decision to search, reduction,
  • basic cryptographic constructions: pseudo-random functions, signatures, chosen-ciphertext secure encryption, etc,
  • powerful cryptographic constructions: fully homomorphic encryption, attribute-based encryption, constraint pseudo-random function etc,
  • lattices and quantum computation.