An authenticated mobile key exchange is necessary for post quantum secure communication over a public channel. It allows two entities to create a secure and unique session key for every communication session. We feel a need to design two party efficient and secure authenticated key agreement. We have also observed all the protocols given above are based on learning with error assumption over a finite ring. The ”Module Learning with Errors” assumption is the more appropriate choice among ”Learning with Errors” and ”Ring Learning with Errors” for designing practical password-authenticated key exchange protocols. With the help of ”Module Learning with Errors” assumption, and by lowering the number of ring polynomials, several implementations of the protocols can be realized. Therefore, this paper contains quantum safe, efficient, and practical ”Module Learning with Errors” assumption based authenticated key agreement protocol. The protocol’s security analysis is presented within the framework of the random oracle model.
An authenticated mobile key exchange is necessary for post quantum secure communication over a public channel. It allows two entities to create a secure and unique session key for every communication session. We feel a need to design two party efficient and secure authenticated key agreement. We have also observed all the protocols given above are based on learning with error assumption over a finite ring. The ”Module Learning with Errors” assumption is the more appropriate choice among ”Learning with Errors” and ”Ring Learning with Errors” for designing practical password-authenticated key exchange protocols. With the help of ”Module Learning with Errors” assumption, and by lowering the number of ring polynomials, several implementations of the protocols can be realized. Therefore, this paper contains quantum safe, efficient, and practical ”Module Learning with Errors” assumption based authenticated key agreement protocol. The protocol’s security analysis is presented within the framework of the random oracle model.
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.
A three-party authenticated key exchange protocol enables two entities to agree on a session key with the help of a dedicated server through an insecure channel. Lattice based cryptography plays a very important role in authentication and key exchanges that protects against the threat of quantum attacks. However, it is not easy 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 a variant of lattice assumption, the ring learning errors. The protocol ensures security against impersonation attack, stolen smartcard attack, password guessing attack, and other existing attacks. In authentication phase, the protocol have used lattice based cryptography that plays a very important role in authentication and key exchanges that protects against the threat of quantum attacks. The proposed protocol ensures both securities against quantum attacks and efficiency due to simple algebraic operations that are polynomial addition and multiplications.
Abstract Password‐authenticated key exchange ( PAKE ) is a cryptographic primitive that can establish secure remote communications between the client and the server, especially with the advantage of amplifying memorable passwords into strong session keys. However, the arrival of the quantum computing era has brought new challenges to traditional PAKE protocols. Thus, designing an efficient post‐quantum PAKE scheme becomes an open research question. In this paper, the authors construct a quantum‐safe PAKE protocol, which is a horizontal extension of the password‐authenticated key (PAK) protocol in the field of module lattices. Subsequently, the authors accompany the proposed protocol with a rigorous security proof in the random oracle model with two adaptions: applying the CDF‐Zipf model to characterise the ability of the adversary and using the pairing with errors assumption to simplify the proof. Taking the flexibility of the module learning with errors ( MLWE ) problem, the authors elaborately select three parameter sets to meet different application scenarios. Specifically, the authors’ Recommended‐PAKE implementation achieves 177‐bit post‐quantum security with a generous margin to cope with later improvement in cryptanalysis. The performance results indicate that the authors’ MLWE‐PAKE is quite practical: compared with the latest Yang‐PAK , the authors’ Recommended‐PAK reduces the communication cost and the running time by 36.8% and 13.8%, respectively.
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
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.