Quantum-safe multi-server password-based authenticated key exchange protocol

Password-based authentication is one of the most prevailing access control mechanism. Typical password-authenticated key exchange (PAKE) protocols are single-server settings and are therefore vulnerable to server compromise attack. To defend against such attack, multi-server PAKE schemes have been advanced, but most of which are built on non-quantum-secure hardness assumptions. Lattice-based cryptosystems are regarded as the most promising one for post-quantum eara by NIST, while the known multi-server password-based authentication solution over lattices achieves merely key transport and is public key infrastructure (PKI)-based, resulting in low efficiency and poor deployability. In this work, we resort to distributed smooth projective hash function (SPHF) to bridge the gap between multi-server PAKE protocol and quantum-security. We first design an exact SPHF and derive the first distributed SPHF over lattices by leveraging the additive homomorphic property of the strong learning with errors (LWE) problem. In particular, the relevant parameters of the public key encryption (PKE) scheme it predicates on are identified, thus eliminating the influence of incomplete lattice homomorphism on the correctness of our SPHFs. Pertinent lattice-based multi-server PAKE protocols are further proposed on both transparent and non-transparent transmission modes by integrating our distributed SPHF into the multi-server framework of Raimondo and Gennaro (EUROCRYPT'03). Our PAKE constructions are able to resist both quantum and sever compromise attacks as well as avoid the expensive cryptographic primitives, including non-interactive zero knowledge (NIZK) proofs, signature/verification, secret sharing and fully homomorphic encryption. Experimental results demonstrate that our SPHFs and PAKE protocols offer better efficiency.