Two-server Password authenticated Key Exchange Protocol Based on MLWE

Currently, PAKE (Password Authenticated Key Exchange) protocols on lattice using a single-server architecture are widely applied. However, such protocols are vulnerable to server leakage attacks, dictionary attacks, and other threats. To address these issues, researchers have proposed multi-server and two-server architecture-based PAKE protocols. However, PAKE protocols in a multi-server architecture require the use of complex cryptographic primitives such as signatures, and zero-knowledge proofs to ensure security, which reduces the execution efficiency of the protocol. To solve these problems, we propose a two-server PAKE protocol on the lattice based on the MLWE (Module learning with errors) problem. The protocol is built using instances of the MLWE problem and utilizes the Peikert error coordination technique, which ensures both parties with similar values arrive at the same result through computation. Additionally, we introduce the error pairing hypothesis and demonstrates its security within the random oracle model. The protocol securely stores different shares of password information across various servers. This approach protects user password data, even if one of the servers is compromised. Compared to similar protocols, we avoid the use of numerous cryptographic primitives, and can better resist quantum computing attacks and server leakage. And we reduce computational and communication costs, and can better meet practical application needs.