Collision-free hashing from lattice problems

Abstract

In 1995, Ajtai described a construction of one-way functions whose security is equivalent to the difficulty of some well known approximation problems in lattices. We show that essentially the same construction can also be used to obtain collision-free hashing. This paper contains a self-contained proof sketch of Ajtai's result. © 2011 Springer-Verlag Berlin Heidelberg.