Lectures

  • Introduction and Minkowski’s theorem. (notes)
  • The Gram-Schmidt orthogonalization and the LLL algorithm. (notes)
  • Crypto interlude 1: Using LLL to break knapsack-based cryptography.
  • Crypto interlude 2: Ajtai’s worst-case to average-case reduction.
  • Babai’s nearest plane algorithm. (notes)
  • GPV’s lattice-based signatures and discrete Gaussian sampling.