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

Abstract

Password-based authenticated key exchange($\mathsf {PAKE}$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$\mathsf {PAKE}$PAKEis how to design a quantum-resistant round-optimal$\mathsf {PAKE}$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 firstthree-round$\mathsf {PAKE}$PAKEprotocol by leveraging the smooth projective hash function ($\mathsf {SPHF}$SPHF) over lattices. Subsequently, Zhang and Yu (AISACRYPT’17) optimized Katz-Vaikuntanathan’s approximate$\mathsf {SPHF}$SPHFvia a splittable public key encryption. They then constructed atwo-round$\mathsf {PAKE}$PAKEby 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$\mathsf {PAKE}$PAKEvia an efficient lattice-based$\mathsf {SPHF}$SPHFstill remains a challenge. In this work, we attempt to fill this gap by proposing a lattice-based$\mathsf {SPHF}$SPHFwith adaptive smoothness. We then obtain aone-round$\mathsf {PAKE}$PAKEprotocol over lattices with rigorous security analysis by integrating the proposed$\mathsf {SPHF}$SPHFinto the one-round framework proposed by Katz and Vaikuntananthan (TCC’11). Furthermore, we explore the possibilities of achieving two-round$\mathsf {PAKE}$PAKEand universal composable (UC) security from our$\mathsf {SPHF}$SPHF, and show the potential application of our$\mathsf {PAKE}$PAKEin Internet of Things (IoTs) where communication cost is the main consideration.