Smooth projective hashing and password-based authenticated key exchange from lattices

Abstract

We describe a public-key encryption scheme based on lattices - specifically, based on the hardness of the learning with error (LWE) problem - that is secure against chosen-ciphertext attacks while admitting (a variant of) smooth projective hashing. This encryption scheme suffices to construct a protocol for password-based authenticated key exchange (PAKE) that can be proven secure based on the LWE assumption in the standard model. We thus obtain the first PAKE protocol whose security relies on a lattice-based assumption. © 2009 Springer-Verlag.