Achieving One-Round Password-Based Authenticated Key Exchange over Lattices

Password-based authenticated key exchange (PAKE) protocol, a widely used authentication mechanism to realize secure communication, allows protocol participants to establish a high-entropy session key by pre-sharing a low-entropy password. An open challenge in PAKE is how to design a quantum-resistant round-optimal PAKE. To solve this challenge, lattice-based cryptography is a promising candidate for post-quantum cryptography. In addition, Katz and Vaikuntanathan (ASIACRYPT'09) design the first three-round PAKE protocol by leveraging the smooth projective hash function (SPHF) over lattices. Subsequently, Zhang and Yu (AISACRYPT'17) optimized Katz-Vaikuntanathan's approximate SPHF via a splittable public key encryption. They then constructed a two-round PAKE by using the simulation-sound non-interactive zero-knowledge (NIZK) proofs, but how to construct a lattice-based simulation-sound NIZK remains an open research question. In other words, how to design a one-round PAKE via an efficient lattice-based SPHF still remains a challenge. In this work, we attempt to fill this gap by proposing a lattice-based SPHF with adaptive smoothness. We then obtain a one-round PAKE protocol over lattices with rigorous security analysis by integrating the proposed SPHF into the one-round framework proposed by Katz and Vaikuntananthan (TCC'11). Furthermore, we explore the possibilities of achieving two-round PAKE and universal composable (UC) security from our SPHF, and show the potential application of our PAKE in Internet of Things (IoTs) where communication cost is the main consideration.

Automated summary

In this research, we propose a lattice-based one-round PAKE protocol with adaptive smoothness by introducing a lattice-based SPHF. We integrate the proposed SPHF into an existing one-round framework and provide rigorous security analysis. Furthermore, we explore the possibilities of achieving two-round PAKE and universal composable security, and demonstrate the potential application in the Internet of Things.