Cryptographic Functions from Worst-Case Complexity Assumptions

Lattice problems have been suggested as a potential source of computational hardness to be used in the construction of cryptographic functions that are provably hard to break. A remarkable feature of lattice-based cryptographic functions is that they can be proved secure (that is, hard to break on the average) based on the assumption that the underlying lattice problems are computationally hard in the worst-case. In this paper we give a survey of the constructions and proof techniques used in this area, explain the importance of basing cryptographic functions on the worst-case complexity of lattice problems, and discuss how this affects the traditional approach to cryptanalysis based on random challenges.