What question did this study set out to answer?

This research aims to design a secure, efficient three-party authenticated key agreement scheme suitable for resource-constrained mobile devices in the face of quantum computing threats.

June 13, 2026

A Secure and Efficient Ring Learning With Error Based Three‐Party Authenticated Key Agreement Scheme for Wireless Mobile Communication Systems

Key Points

This research aims to design a secure, efficient three-party authenticated key agreement scheme suitable for resource-constrained mobile devices in the face of quantum computing threats.
Conducted a cryptanalysis of existing schemes identifying vulnerabilities.
Developed a new three-party mutual authentication and key agreement scheme using Ring-LWE.
Secured the communication with four messages while ensuring user anonymity and unlinkability.
Uncovered four vulnerabilities in existing schemes leading to major security flaws.
Proposed scheme improves communication cost significantly, yielding better results than previous methods.
Formal security analysis shows tight reduction to the Decision-RLWE assumption.

Abstract

ABSTRACT Quantum computing poses a mounting and concrete threat to the cryptographi protocols underpinning mobile communication systems, where both security and computational efficiency are critical constraints. Existing three‐party authenticated key agreement (3PAKA) schemes either rely on classically hard problems broken by Shor's algorithm or, among postquantum proposals, fail to simultaneously achieve user anonymity, unlinkability, and perfect forward secrecy at acceptable cost for resource‐constrained mobile devices. We first conduct a rigorous cryptanalysis of the recent lattice‐based scheme of Singh et al. and uncover four concrete vulnerabilities: an identity recovery vulnerability and scalability failure arising from XOR masking with a static server key, which forces an exhaustive identity search and opens a denial‐of‐service vector; blind acceptance by the responder , as User forwards the initiator's message without verifying the sender's identity; authentication blindness at the initiator , since the response received by User carries no cryptographic proof of User 's identity; and server‐side incomplete verification caused by a missing session parameter , which the server requires but never receives. To remedy these deficiencies, we propose a Three‐Party Post‐Quantum Mutual Authentication and Key Agreement (MAKA) scheme for mobile devices, built on the Ideal‐Lattice Ring Learning With Errors (Ring‐LWE) assumption with parameters and Gaussian width . The proposed four‐message protocol employs biometric‐bound fuzzy extractors, dynamic masked identities , and fresh per‐session Ring‐LWE samples to achieve mutual authentication, user anonymity, unlinkability, and perfect forward secrecy. Security is formally analyzed in the Bellare–Rogaway (BR) model under the Random Oracle Model (ROM), yielding a tight reduction to the Decision‐RLWE assumption. Our message structure yields a total communication cost of bits, representing approximately improvement over Singh et al. It also demonstrates a favourable communicationcost relative to those of Islam and Basu, Rewal et al., Kumar et al., Dabra et al., and Park et al. across both metrics.

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