Smooth Projective Hashing and Password-Based Authenticated Key Exchange from Lattices

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.

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