There is an intuitive connection between quantum technology and chaos theory which may lead to a novel way to construct password-authenticated key exchange (PAKE) protocols to resist quantum attacks efficiently. This paper designs an optimal-round semi-honest-quantum PAKE protocol with chaotic maps. In which the clients act as classical users while the server acts as a quantum user with the ability to prepare entangled quantum, this semi-quantum environment makes the application process more efficient and convenient and reduces the cost of deploying the environment. In addition, the protocol takes full advantage of the true randomness of multiple GHZ-like states, as well as the ergodicity of chaotic maps and the sensitivity of initial conditions to realise the key exchange and the session key generation process, and guarantees the security, randomness and unpredictability of the session keys. Our protocol is an optimal-round design, i.e., only one communication is needed to complete the key exchange process, which greatly reduces the number of communications and the possibility of key information being intercepted. Finally, the content of security proof and efficiency analysis also demonstrate our protocol is suitable for efficiently protecting authentication keys and feasible to implement.
There is an intuitive connection between quantum technology and chaos theory which may lead to a novel way to construct password-authenticated key exchange (PAKE) protocols to resist quantum attacks efficiently. This paper designs an optimal-round semi-honest-quantum PAKE protocol with chaotic maps. In which the clients act as classical users while the server acts as a quantum user with the ability to prepare entangled quantum, this semi-quantum environment makes the application process more efficient and convenient and reduces the cost of deploying the environment. In addition, the protocol takes full advantage of the true randomness of multiple GHZ-like states, as well as the ergodicity of chaotic maps and the sensitivity of initial conditions to realise the key exchange and the session key generation process, and guarantees the security, randomness and unpredictability of the session keys. Our protocol is an optimal-round design, i.e., only one communication is needed to complete the key exchange process, which greatly reduces the number of communications and the possibility of key information being intercepted. Finally, the content of security proof and efficiency analysis also demonstrate our protocol is suitable for efficiently protecting authentication keys and feasible to implement.
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.
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.
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.
Password-based authenticated key exchange (PAKE) allows participants sharing low-entropy passwords to agree on cryptographically strong session keys over insecure networks. In this paper, we present two PAKE protocols from lattices in the two-party and three-party settings, respectively, which can resist quantum attacks and achieve mutual authentication. The protocols in this paper achieve two rounds of communication by carefully utilizing the splittable properties of the underlying primitive, a CCA (Chosen-Ciphertext Attack)-secure public key encryption (PKE) scheme with associated nonadaptive approximate smooth projection hash (NA-ASPH) system. Compared with other related protocols, the proposed two-round PAKE protocols have relatively less communication and computation overhead. In particular, the two-round 3PAKE is more practical in large-scale communication systems.
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.
Abstract As quantum communication networks approach practical deployment, mediated semi-quantum key distribution (MSQKD) has attracted attention for enabling classical users to share keys via semi-honest servers. This paper proposes a cross-domain MSQKD protocol based on four-particle GHZ-like states. Two semi-honest servers prepare and transmit quantum sequences with decoy states, while users perform only Bell and single-photon measurements to derive shared keys. The protocol eliminates additional unitary operations, significantly reducing user-side quantum requirements, hardware costs, and implementation complexity. By exploiting entanglement correlations, it achieves a qubit efficiency of 42.86% and resists both external and internal attacks. The feasibility of the protocol is verified through simulations on Qiskit and the IBM quantum platform, demonstrating its practicality under current quantum technology.