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IEEE Transactions on Consumer Electronics

QT-PAKE: Secure Messaging via Quantum-Safe Threshold PAKE

Zengpeng Li, Hao Zhu, Guangyu Liao, Mei Wang, Peiran Li, Prosanta Gope

Published Sep 18, 2025• 0 citations
Publisher

Abstract

Password authentication is a prevalent method of user verification across the Internet, and its use extends to scenarios where resources are limited. However, current password authentication protocols primarily rely on traditional password authenticated key exchange (PAKE) protocols (e.g., SRP, OPAQUE), which are vulnerable to attacks by quantum adversaries. To date, no efficient quantum algorithm has been found to solve the common challenges in lattice-based cryptography. Therefore, quantum-resistant PAKE protocols are generally built upon lattice-based cryptography. In this work, we propose a threshold verifiable oblivious pseudorandom function () protocol based on secret sharing. We then integrate it into a PAKE protocol and present an instantiation of a quantum-safe threshold PAKE protocol () based on the Ring Learning with Errors (RLWE) assumption. This integration gives our PAKE protocol resistance to precomputation attacks, similar to OPAQUE. Furthermore, by incorporating thresholding techniques into the PAKE protocol, we mitigate the risk of single points of failure on the server side. Our protocol not only preserves the security guarantees of traditional PAKE schemes but also resists attacks from quantum adversaries. We also provide a comprehensive security analysis and evaluation of, providing valuable insights for its practical implementation.

DOI
10.1109/tce.2025.3611598

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Password authentication is a prevalent method of user verification across the Internet, and its use extends to scenarios where resources are limited. However, current password authentication protocols primarily rely on traditional password authenticated key exchange (PAKE) protocols (e.g., SRP, OPAQUE), which are vulnerable to attacks by quantum adversaries. To date, no efficient quantum algorithm has been found to solve the common challenges in lattice-based cryptography. Therefore, quantum-resistant PAKE protocols are generally built upon lattice-based cryptography. In this work, we propose a threshold verifiable oblivious pseudorandom function () protocol based on secret sharing. We then integrate it into a PAKE protocol and present an instantiation of a quantum-safe threshold PAKE protocol () based on the Ring Learning with Errors (RLWE) assumption. This integration gives our PAKE protocol resistance to precomputation attacks, similar to OPAQUE. Furthermore, by incorporating thresholding techniques into the PAKE protocol, we mitigate the risk of single points of failure on the server side. Our protocol not only preserves the security guarantees of traditional PAKE schemes but also resists attacks from quantum adversaries. We also provide a comprehensive security analysis and evaluation of, providing valuable insights for its practical implementation.
The Password-Authenticated Key Exchange (PAKE) protocol is a useful tool for establishing secure remote communication between users, especially given the prevalence of amplifying a human-memorable password into a strong session key in the age of hand-held devices. Recent advances in quantum computing have stimulated interest in quantum-safe cryptographic schemes. Therefore, we propose QSPAK and QSPPK, two post-quantum and efficient PAKE protocols which are parallel extensions of PAK and PPK, but based on the hardness assumption over module lattices. Specifically, we make a comprehensive trade-off among multiple significant performance indicators such as the post-quantum security, the failure rate, the communication cost and the running time to guide optimal parameter choices. This rigorous instantiation has never been seen in previous PAKE papers. Additionally, utilizing the flexibility of module lattices, we provide three parameter sets (#1, #2, and #3) matching different security scenarios. We implement and benchmark QSPAK and QSPPK against other competitive proposals. The performance results indicate that our QSPAK and QSPPK, besides being more efficient, exhibit the flexibility and security advantages over the latter schemes. Furthermore, we construct a post-quantum password-authenticated TLS 1.3 framework, aimed towards provide a further suggestion for IETF standardization of quantum-safe PAKE.
Stronger anonymity password authentication key exchange protocols based on traditional cryptography are not resistant to quantum computing attacks, and there is no lattice-only anonymous password authentication key exchange protocol protocol that satisfies the strong anonymity requirement. Therefore, this paper constructs stronger anonymity PAKE protocol based on the ring learning with errors (RLWE) and smooth projective hash function (SPHF) based on ideal lattice. The proposed protocol can achieve stronger anonymity and resists to desynchronization attacks and quantum attack. The security of the protocol is proved under the BPR model. The security and performance analysis shows that the proposed PAKE protocol has better advantages in security and efficiency.
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.
Secure Remote Password (SRP) protocol is an essential password-authenticated key exchange (PAKE) protocol based on the discrete logarithm problem (DLP). The protocol is specifically designed to obtain a session key and it has been widely used in various scenarios due to its attractive security features. In the SRP protocol, the server is not required to save any data directly associated with passwords. And this makes attackers who manage to corrupt the server fail to impersonate the client unless performing a brute-force search for the password. However, the development of quantum computing has potentially made classic DLP-based public-key cryptography schemes not secure, including the SRP protocol. So it is significant to design a quantum-resistant SRP protocol. In this paper, based on the original scheme, we propose a post-quantum SRP protocol from the learning with errors (LWE) problem. And we give rigorous proof and analyses on the correctness and security of the scheme. Besides being resistant to known quantum attacks, it maintains the various secure qualities of the original protocol.
Password Authenticated Key Exchange (PAKE) establishes secure communication channels using passwords for authentication. Currently, standardized PAKEs rely on classical asymmetric cryptography. However, these PAKEs may become insecure should the expected quantum threat become a reality. Despite the growing interest in realizing quantum-safe PAKEs, they did not receive much attention from the ongoing Post-Quantum Cryptography (PQC) integration efforts. Hence, there is a significant awareness gap compared to PQC primitives subject to the official standardization processes. We provide a comprehensive overview of existing PQC PAKEs, classify their design rationales and authentication methods, and address aspects related to their security and performance. We identify PAKE designs that are still unexplored in the PQC realm and discuss the possibility of their adaptation. Thus, we offer a detailed reference for future work on PQC PAKEs.
Transport Layer Security (TLS) protocols are essential for ensuring the confidentiality, integrity, and authentication of data communications. Mutual authentication between client and server is crucial in high-security scenarios such as finance and government. However, existing TLS protocols typically rely on certificate-based public key infrastructures (PKI) for client authentication, which increases deployment complexity and introduces risks associated with third-party trust. In contrast, password-authenticated TLS protocols use memorable passwords for client authentication, offering advantages in simplicity and usability. Nonetheless, such protocols remain vulnerable to server compromise and fail to provide sufficient security against quantum adversaries.To address these challenges, we propose a novel TLS protocol based on asymmetric password-authenticated key exchange (PAKE). The protocol employs an asymmetric PAKE mechanism wherein only password-derived information is stored on the server, while the client derives its private key from the password. This design effectively mitigates the risk of server leakage attacks. The protocol further integrates two types of post-quantum secure key encapsulation mechanisms (KEMs): an OW-ChCCA (One-Way Checkable against Chosen-Ciphertext Attacks) secure KEM for server key exchange and authentication, and an OW-PCA (One-Way Plaintext-Checkable Attacks) secure KEM for binding the client’s password-derived private key to enable client authentication. Both KEMs support multi-user, multi-challenge settings and admit tight, post-quantum secure instantiations.Furthermore, this paper provides a formal security analysis of the proposed protocol within an optimized multi-stage key exchange model. By combining the random oracle and ideal cipher models with a game-based proof methodology, we demonstrate that the protocol achieves mutual authentication and forward secrecy, while also providing tight security bounds and post-quantum resilience. This work thus presents a promising solution for constructing post-quantum password-authenticated TLS protocols.