This article presents a formal specification and verification of the PQ OpenPGP protocol using the algebraic specification language CafeOBJ and successfully verify that the PQ OpenPGP protocol satisfies three essential security properties: secrecy of the session key, forward secrecy, and authenticity.
Abstract
With the rapid advancement of quantum computing, classical cryptographic protocols face an increasing risk of being broken. The Post-Quantum OpenPGP (PQ OpenPGP) protocol is an extension of the OpenPGP standard that incorporates hybrid cryptography by combining a classical key exchange and a post-quantum key encapsulation mechanism. This design aims to provide long-term security even in the presence of adversaries equipped with quantum computational capabilities and ensures backward compatibility while transitioning safely to the quantum era. This article presents a formal specification and verification of the PQ OpenPGP protocol using the algebraic specification language CafeOBJ. Our specification captures key aspects of the protocol, including hybrid key encapsulation using post-quantum Module-Lattice Key Encapsulation Mechanism (ML-KEM) and classical Elliptic Curve Diffie–Hellman (ECDH)-KEM, dual digital signatures using post-quantum Module-Lattice Digital Signature Algorithm (ML-DSA) and classical Edwards-curve Digital Signature Algorithm (EdDSA). To model adversarial behavior, we extend the standard Dolev-Yao intruder model, widely used in the analysis of security protocols, by incorporating quantum-enabled capabilities. Under our threat model, the intruder not only has full control over the network, as in the traditional Dolev-Yao setting, but is also capable of breaking classical public-key cryptographic primitives and compromising sensitive information, reflecting the realistic power of large-scale quantum computers. We successfully verify that the PQ OpenPGP protocol satisfies three essential security properties: secrecy of the session key, forward secrecy, and authenticity. The proofs are supported by ten auxiliary lemmas. Given the formal specification, security properties, and conjecture lemmas, the Invariant Proof Score Generator (IPSG) tool automatically generates proof scores to facilitate verification. This work contributes to the growing research on formal verification in post-quantum cryptographic protocols.
The advent of quantum computing poses a significant threat to conventional public-key cryptographic systems, particularly resource-constrained mobile and cyber-physical environments. To address this challenge, this study proposes an implementation-oriented unified hybrid key derivation framework that integrates the Elliptic Curve Diffie–Hellman Ephemeral (ECDHE-P256) and post-quantum ML-KEM-768 algorithm for quantum-resilient secure communication. The proposed approach combines independently generated classical and post-quantum shared secrets through a lightweight mixing step followed by HKDF-SHA256 extraction and expansion to derive a unified 256-bit session key. This design preserves forward secrecy while enhancing resilience against quantum adversaries without requiring substantial modifications to the existing communication infrastructures. The framework was implemented on a heterogeneous testbed consisting of an x86_64 client and ARM64-based Android device. Experimental evaluations were conducted across 27 test configurations under three network latency conditions (50, 150, and 500 ms) using payload sizes of 64, 1024, and 10240 KB. Each configuration was executed for 1000 iterations to ensure statistically reliable measurements. The results demonstrate that, compared with standalone ECDHE-P256 and standalone ML-KEM-768, the proposed hybrid framework introduces only minimal computational overhead while maintaining stable resource utilization. Furthermore, network latency contributes more significantly to end-to-end communication delay than cryptographic processing overhead, indicating that the integration of classical and post-quantum cryptographic mechanisms does not constitute a major performance bottleneck. Overall, the proposed implementation-oriented framework provides a practical and lightweight transition strategy to quantum-resilient secure communication in heterogeneous mobile, IoT, and cyber-physical environments.
W. Maya, Teuku Yuliar Arif, Hammam Riza et al.· IEEE Access· 0 citations
The Internet Key Exchange Protocol Version 2 (IKEv2) underpins Internet Protocol Security (IPsec) by establishing secure associations and negotiating cryptographic keys. Its reliance on classical public-key primitives such as Elliptic Curve Diffie–Hellman (ECDH) renders it vulnerable to quantum attacks, as Shor’s algorithm can break these schemes once large-scale quantum computers become available. To address this challenge, we integrate post-quantum cryptography into IKEv2 using a hybrid key exchange combining ECDH over P-384 with the ML-KEM-768 parameter set of the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM), following Request for Comments (RFC) 9370 and RFC 9242. We present a Fragmentation Boundary Model that identifies when post-quantum payloads approach or exceed the non-fragmenting IKE_SA_INIT payload budget across ML-KEM parameter sets, Internet Protocol (IP) versions, and effective path maximum transmission units (PMTUs). We implemented the hybrid design on a Texas Instruments TM4C1294 microcontroller running FreeRTOS and CycloneTCP, and measured its execution time, memory footprint, and network overhead. Across 150 successful handshakes per configuration, mean Security Association establishment time increased from 3390.4 to 3488.6 ms, an overhead of 98.2 ms (2.9%). Flash use increased by 8%, random-access memory (RAM) use by 5%, and total IKEv2 traffic size by 42%, while no IP fragmentation was observed under the evaluated Internet Protocol version 4 (IPv4) conditions. These findings establish the feasibility of the evaluated hybrid configuration on the TM4C1294 platform and provide a platform-specific baseline for further evaluation of quantum-resilient IPsec on embedded automotive architectures.
A. Bahaaeldin, M. W. El-Kharashi, B. Abdullah· Electronics· 0 citations
The necessity of a secure key exchange protocol arises from the critical need to establish encrypted communication over an untrusted network. Over time, a multitude of key exchange mechanisms have been developed to counteract adversarial threats. The Diffie-Hellman key exchange protocol (DHKE) is one of the most widely used protocols for symmetric key sharing. However, this protocol exhibits certain inherent limitations that attackers may exploit. It lacks authentication mechanism and is susceptible to Man-in-the-Middle (MITM) attacks and quantum attacks. To mitigate these vulnerabilities, we have designed a hybrid key exchange protocol combining DHKE with Learning With Errors (LWE), a lattice-based post-quantum primitive. This proposed protocol provides authentication via a Public Key Infrastructure (PKI) together with CRYSTALS-Dilithium digital signature, resilience against MITM attacks, and robustness against classical and quantum threats. We have done a security analysis using the Dolev-Yao threat model, extended to quantum-equipped attackers, and showed that the protocol achieves mutual authentication, session key secrecy, and forward secrecy under the hardness of LWE and DHKE. Lastly, we provided detailed parameter recommendations based on NIST standards and shed light on side-channel attacks.
A. K. M. Fakhrul Hossain· SUST Journal of Science and...· 0 citations
This paper proposes a secure and quantum-resistant key exchange scheme leveraging the FrodoKEM algorithm, a lattice-based post-quantum key encapsulation mechanism designed to resist attacks from quantum adversaries, and compares the performance and security against traditional key exchange mechanisms.
P. V. Krishna, Meeravali Shaik· International journal of com...· 0 citations
The threat of quantum computers to classical public-key cryptography has created an urgent need to evolve secure communication protocols with post-quantum cryptographic (PQC) primitives. The Noise Protocol Framework, widely used in systems such as WireGuard and WhatsApp, traditionally relies on the Elliptic Curve Diffie-Hellman (ECDH) public-key exchange scheme, which is vulnerable to quantum threats. In this paper, we present NoisePQC++, a unified C++23 implementation of the Noise Protocol framework augmented with post-quantum Key Encapsulation Mechanisms and Hybrid Forward Secrecy. Our design integrates the National Institute of Standards and Technology (NIST) standardized ML-KEM algorithm alongside classical ECDH, enabling full PQC, hybrid ECDH+PQC handshakes, and unified support for all 57 classical Noise handshake pattern variants, 13 post-quantum Noise handshakes, and their hybrid variants. Compared with prior work, NoisePQC++ offers broader protocol coverage, more complete implementation support, and greater flexibility. Our evaluation shows minimal overhead under normal network conditions and acceptable overhead in adverse cases, while significantly improving resistance against quantum adversaries. These results indicate that NIST-standardized post-quantum and hybrid Noise handshakes are practical and provide a credible basis for future deployment.
Nadeem Ahmed, A. Gangopadhyay, Lei Zhang· 0 citations
The migration of remote-access and industrial communication systems from classical public-key cryptography to post-quantum cryptography (PQC) requires careful evaluation at both the protocol and system levels. This paper presents PQC-E2E-CA, a system-level evaluation framework for reviewing post-quantum and hybrid cryptographic configurations in Secure Shell (SSH). The framework integrates OQS-enabled OpenSSH and OpenSSL with Linux netem network emulation, automated experiment execution, SCP integrity verification, and statistical post-processing. The evaluation separates key exchange behavior from host key authentication. Specifically, it measures ML-KEM and hybrid ML-KEM as SSH key exchange mechanisms, and ML-DSA as a host-key signature mechanism. Experiments are conducted under controlled RTT and packet-loss conditions using a gateway virtualised client-server testbed. The results show that ML-KEM and hybrid ML-KEM can be integrated into SSH without prohibitive application-level session setup overhead in the evaluated environment. Among the evaluated configurations, ML-KEM-768 demonstrates comparatively lower SSH session establishment latency at 50 ms RTT with 0% packet loss. ML-DSA-44 achieves the lowest host-key authentication latency under the same conditions and maintains relatively stable performance at 150 ms RTT with 5% packet loss. SCP throughput results for 100 MB and 200 MB transfers indicate that sustained transfer performance is mainly influenced by RTT and transport-layer dynamics using a single dominant key exchange configuration. These findings support migration toward standardized post-quantum mechanisms in SSH-based gateway and remote-access environments, provided that algorithm choice and system configuration are validated under representative workloads and network conditions.
Shahid Allah Bakhsh, Inam ul Haq, Tarek Helmy et al.· Frontiers of Computer Scienc...· 0 citations
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