Anonymous Three-Party Quantum-Safe Authenticated Key Agreement with Forward Secrecy: Ring Learning with Errors

Objective: To design a secure and efficient three-party post-quantum authenticated key agreement (AKE) protocol that ensures mutual authentication, user anonymity, and forward secrecy, while resisting both classical and quantum adversaries. Methods: The proposed protocol is constructed using the Ring Learning with Errors (Ring-LWE) assumption, which is widely regarded as quantum-resistant. The scheme enables two users to establish a shared session key through a trusted server over an insecure channel. Cryptographic hash functions, lattice-based operations, and masking techniques are employed to achieve authentication, anonymity, and key confidentiality. Formal correctness proofs, informal security analysis, and comparative performance evaluations are conducted to validate the protocol. Findings: The study describes qualitative benefits like "outperforms current protocols" but lacks specific metrics, such as exact computation costs (e.g., 4913 ns total execution) or communication rounds, and "reduces user-side cost to 2438 ns vs. 5395 ns in Islam et al.". Also, substantially more efficient than pairing- or chaotic-map-based protocols, which incur costs exceeding 12000 ns. Communication overhead is reduced by limiting the exchange to two RLWE-based messages and one server response, avoiding expensive bilinear pairing or biometric hash transmissions. These results demonstrate that the proposed scheme provides stronger security guarantees at a lower computational and communication cost, making it suitable for resource-constrained mobile and IoT environments. Novelty: Unlike existing approaches, the proposed protocol simultaneously guarantees user anonymity, forward secrecy, and quantum resistance in a three-party setting based on Ring-LWE. It overcomes known vulnerabilities in prior schemes and achieves improved efficiency without compromising security, making it a practical and robust solution for post-quantum secure communications. Keywords: Key Establishment, Authentication, Ring Learning with Errors, Anonymous Key Exchange, Post Quantum Forward Secrecy