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.
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.
ABSTRACT A three‐party post‐quantum key agreement protocol involves server with two communicating parties securely agreeing on a shared secret key in a way that is resistant to quantum attacks. Once the shared secret key is shared using authenticated key agreement protocol, then user (A), and user (B) can use it for securing communication channel using symmetric‐key encryption AES‐256 algorithm. Although there are few third‐party post‐quantum authenticated and key agreement schemes exist, but the recent studies in this paper illustrates that they are not satisfying properties like unlinkability, anonymity, perfect forward secrecy, and signal leakage attacks. Therefore, the proposed protocol ensures anonymity, unlinkablity, perfect forward secrecy, and resistant against signal leakage attacks. The proposed protocol uses different random numbers for each of sessions and ensures freshness of the session key to maintain forward secrecy. In this protocol, the user (A) only communicates with server, and establish an authenticated session key with user (B) which avoids server overheads. The use of ring learning with errors (RLWE) instead of the simpler learning with errors (LWE) is primarily motivated by the need for efficiency, compactness, and scalability in cryptographic applications. A comparative study, including both performance and security assessments, demonstrates that the proposed design is more secure and efficient.
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
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server over public channel. Shor’s algorithm is a big threat for existing authenticated key exchange protocols. Lattice based cryptography plays a very important role in designing authentication and key agreement secure against the threat of quantum attacks. However, it is not easy job to design quantum resistant password based three party protocol due to the high demand for security requirements and the limited resources nature of mobile devices. In this article, we have proposed a new post quantum three party key exchange based on ring learning with errors assumption. This protocol is motivated from Islam et al.’s authenticated key exchange protocol. Their protocol is not secure against stolen smartcard attack, password guessing attack, and can’t provide user anonymity. The anonymous communication is a big requirement for practical applications like e-healthcare services/smart vehicular communication. This paper also contains the performance analysis of the proposed protocol along with other relevant protocols.
In recent years, the rapid growth of wireless technologies and the widespread use of mobile devices have drawn people toward diverse web applications. Today, users can conveniently access a variety of online services anytime and anywhere through their mobile devices. With wireless communication becoming the dominant medium, security has emerged as a major challenge, since networks are widely exposed. To address this, numerous authentication protocols have been proposed. However, most existing protocols rely on integer factorization or discrete logarithm problems, which are vulnerable to polynomial-time quantum algorithms. This makes them unsuitable for a post-quantum era. To ensure secure wireless communications for mobile devices, there is a critical need for authenticated key agreement (AKA) protocols that withstand quantum attacks. In this work, we propose a two-party AKA protocol for mobile devices built upon the ring learning with errors (RLWE) problem, whose security is grounded in hard lattice assumptions. We analyze the security of our protocol using formal and informal security methods and assess its performance through comparative evaluation of computational and communication costs against related schemes. Our findings demonstrate that the proposed protocol achieves the necessary security requirements while providing efficient and reliable communication.
In this paper, we have proposed a two-party authenticated key establishment (AKE), and authenticated key transport protocols based on lattice-based cryptography, aiming to provide security against quantum attacks for secure communication. This protocol enables two parties, who may share long-term public keys, to securely establish a shared session key, and transportation of the session key from the server while achieving mutual authentication. Our construction leverages the hardness of lattice problems Ring Learning With Errors (Ring-LWE), ensuring robustness against quantum and classical adversaries. Unlike traditional schemes whose security depends upon number-theoretic assumptions being vulnerable to quantum attacks, our protocol ensures security in the post-quantum era. The proposed protocol ensures forward secrecy, and provides security even if the long-term key is compromised. This protocol also provides essential property key freshness and resistance against man-in-the-middle attacks, impersonation attacks, replay attacks, and key mismatch attacks. On the other hand, the proposed key transport protocol provides essential property key freshness, anonymity, and resistance against man-in-the-middle attacks, impersonation attacks, replay attacks, and key mismatch attacks. A two-party key transport protocol is a cryptographic protocol in which one party (typically a trusted key distribution center or sender) securely generates and sends a session key to another party. Unlike key exchange protocols (where both parties contribute to key generation), key transport protocols rely on one party to generate the key and deliver it securely. The protocol possesses a minimum number of exchanged messages and can reduce the number of communication rounds to help minimize the communication overhead.
The Ring Learning with Errors (RLWE) problem has emerged as a foundational hardness assumption for post-quantum authenticated key exchange (AKE) protocols. In this paper, we propose a post-quantum and efficient RLWE-Based AKE protocol for mobile devices. We provide formal security reduction in the random oracle model under the decisional RLWE and PRF assumptions. We also show that our scheme is safe against key mismatch attack, signal leakage attack, and provide informal analysis of all standard AKE security properties. Further, we showcase that our scheme also provides perfect forward secrecy and replay attack resistance. Finally, we compare our scheme with several other existing schemes in terms of various security attributes along with computational efficiency to demonstrate its practicality and advantages over the other schemes.