Provably Quantum Secure Three-Party Mutual Authentication and Key Exchange Protocol Based on Modular Learning with Error

With the rapid development of quantum computers, post-quantum cryptography (PQC) has become critical technology in the security field. PQC includes cryptographic techniques that are secure against quantum-computer-based attacks, utilizing methods such as code-based, isogeny-based, and lattice-based approaches. Among these, lattice-based cryptography is the most extensively studied due to its ease of implementation and efficiency. As quantum computing advances, the need for secure communication protocols that can withstand quantum computer-based threats becomes increasingly important. Traditional two-party AKE protocols have a significant limitation: the security of the entire system can be compromised if either of the communicating parties behaves maliciously. To overcome this limitation, researchers have proposed three-party AKE protocols, where a third party acts as an arbiter or verifier. However, we found that a recently proposed three-party AKE protocol is vulnerable to quantum-computer-based attacks. To address this issue, we propose a provably quantum secure three-party AKE protocol based on MLWE. The proposed scheme leverages the user’s biometric information and the server’s master key to prevent the exposure of critical parameters. We analyzed the security of the protocol using simulation tools such as the Burrows–Abadi–Needham (BAN) logic, Real-or-Random (RoR) model, and Automated Validation of Internet Security Protocols and Applications (AVISPA). Furthermore, comparative analysis with similar protocols demonstrates that our protocol is efficient and suitable.