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Symmetry

Three-Party Password Authentication and Key Exchange Protocol Based on MLWE

Songhui Guo, Yun Song, Song Guo, Yeming Yang, Shuaichao Song

Published Sep 13, 2023• 13 citations
Publisher

Abstract

With the rapid development of quantum theory, the discrete logarithm problem and significant integer factorization problem have polynomial solution algorithms under quantum computing, and their security is seriously threatened. Therefore, a three-party password-authenticated key agreement scheme based on module learning with errors problem was proposed, and its security was proved in the BPR model. Compared with other password-authenticated key agreement protocols, the proposed protocol has higher efficiency and a shorter key length, which can resist quantum attacks. Therefore, the protocol is efficient and secure and suitable for large-scale network communication.

DOI
10.3390/sym15091750

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With the rapid development of quantum theory, the discrete logarithm problem and significant integer factorization problem have polynomial solution algorithms under quantum computing, and their security is seriously threatened. Therefore, a three-party password-authenticated key agreement scheme based on module learning with errors problem was proposed, and its security was proved in the BPR model. Compared with other password-authenticated key agreement protocols, the proposed protocol has higher efficiency and a shorter key length, which can resist quantum attacks. Therefore, the protocol is efficient and secure and suitable for large-scale network communication.
The rapid development of quantum computers poses a significant threat to the majority of current authenticated key exchang protocols, designed on the hardness of large integer factorization and discrete logarithm problems. Therefore, it is imperative to develop secure and efficient quantum-resistant authenticated key exchang protocols. This paper designs a new public-key cryptographic scheme for identity authentication based on Ring Learning With Errors (RLWE) problem and error reconciliation mechanism. Based on the scheme, we further design a quantum-resistant authenticated key exchange protocol (AKE). This protocol is provably secure under the standard eCK model and achieves forward secrecy. Compared with other classic key exchange protocols based on the RLWE problem, our protocol shows comprehensive advantages in terms of security, computational complexity, and communication complexity.
As the security of password authenticated key exchange protocols based on traditional public key cryptosystems is threatened by quantum computing, the research on password authenticated key exchange protocols that can resist quantum computing attacks has become a hot spot of current research. At present, the anonymity of anonymous PAKE protocol is generally linkable, and cannot completely protect the user’s identity privacy information. This paper proposes a two-party password authenticated key exchange protocol with anonymity based on SPHF from ideal lattice, and gives a strict security proofunder the BPR model. The security and performance analysis proves that the proposed protocol has good advantages in communication costs and security.
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.
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.
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.