New Password Authenticated Key Exchange Based on the Ring Learning with Errors

New Password Authenticated Key Exchange Based on the Ring Learning with Errors

Abstract

Authenticated Key Exchange (AKE) is a cryptographic scheme with the aim to establish a high-entropy and secret session key over an insecure communications network. PasswordAuthenticated Key Exchange (PAKE) assumes that the parties in communication share a simple password, which is human-memorable and is used to achieve the authentication. These features are appealing in an age when most people access sensitive personal data remotely from pervasive hand-held devices. Theoretically PAKEs allow secure computation and authentication of a high-entropy piece of data using a low-entropy string as a starting point. In this thesis, we apply the proposed technique in [JD12] to construct two lattice-based PAKE protocols that have simple and elegant designs that extend the class of Random Oracle Model (ROM)-based protocols PAK and PPK [BMP00; Mac02] protocols to a lattice-based setting. The new protocol following the structure of PAK is three-pass and provides mutual explicit authentication; the protocol following the structure of PPK is two-pass and provides implicit authentication. Our protocols rely on the Ring Learning with Errors (RLWE) assumption and exploit the additive structure of the underlying RLWE ring, which allows the protocols to achieve provable security. Our protocols have a comparable level of efficiency to PAK and PPK, which makes them highly attractive. We present a preliminary implementation of our protocols to demonstrate that these protocols are efficient and practical, and, therefore, that our two protocols are suitable quantum safe replacements for PAK and PPK.

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