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IEEE Journal on Selected Areas in Communications

On Mixing of Quantum Key Distribution and Post-Quantum Cryptographic Keys: Min-Entropy Bounds, Provisioning Policies, and Network-Oriented Trade-Offs

Miralem Mehić, Stefan Raß, Sergej Jakovlev, Marcin Niemiec, Peppino Fazio, Miroslav Vozn̆ák

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1109/jsac.2026.3722598

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The looming threat of large-scale quantum computers necessitates a paradigm shift in cryptographic design, giving rise to the field of Post-Quantum Cryptography (PQC). While the computational hardness assumptions underpinning PQC schemes are well-studied, their fundamental security limits from an information-theoretic perspective remain an area requiring deeper exploration. This paper introduces and systematically investigates the concept of "entropic resilience," defined as the inherent ability of a cryptographic system to maintain its security guarantees even under an adversary possessing unbounded computational power, provided only limited information about the secret components is revealed. We present a comprehensive framework for analyzing the information-theoretic security of prominent PQC families, including lattice-based, code-based, and hash-based schemes. Our methodology leverages various entropy measures, such as min-entropy and conditional entropy, to quantify the information leakage and the irreducible uncertainty preserved in cryptographic secrets. We derive theoretical bounds on the information-theoretic security for representative PQC constructions and discuss the implications of these bounds for parameter selection, key generation, and resistance against information-theoretic attacks and side channels. The findings highlight critical trade-offs between entropy requirements, efficiency, and the achievable level of provable security in a post-quantum world. Ultimately, this work provides a foundational understanding of the ultimate security boundaries for PQC, guiding the design of more robust and provably secure schemes against both classical and quantum adversaries.
Quantum key distribution (QKD) provides future-proofed security based on the quantum physics. The end-to-end security services in the fields such as finance, government, and military are mainly carried by optical networks. Limited by technical and economical obstacles of QKD deployment, partially-QKD-deployed optical networks (pQKD-ONs) are much more practical. Key pooling is a technique to decouple keys from the underlying infrastructure for timely key provisioning. However, traditional QKD key provisioning (QKPR) methods are specific to QKD-deployed nodes. In this paper, we propose the pQKD-ON architecture and design the multi-level key pool slicing scheme for key management in pQKD-ONs. Then, we propose a general auxiliary-graph-based QKPR algorithm for key supply in pQKD-ONs. Based on the algorithm, we design four dynamic QKPR policies by adjusting edge weights of the auxiliary graphs including Quantum-Key-Pool-First (QKP-First), Key-Pool-Slice-First (KPS-First), Key-Availability-First (KA-First), and Quantum-Key-Pool-All (QKP-All) policies. We evaluate the performances of the QKPR policies in terms of key consumption, security level, and QKPR latency under two network topologies. Simulation results show that the KA-First policy can achieve 9.9% lower key consumption ratio than the KPS-First policy; the KPS-First policy sacrifices the security level but can achieve lower QKPR latency than the QKP-First and QKP-All policies.
Quantum computing advances pose a serious threat to conventional public-key cryptographic systems such as RSA and elliptic curve cryptography as quantum algorithms may undermine the computational assumptions that guaranty their security. This challenge has driven the development of quantumsafe security approaches among which Quantum Key Distribution (QKD) represents a fundamentally different paradigm based on quantum mechanical principles rather than mathematical complexity. This paper presents a structured review of recent progress in QKD based on a systematic analysis of literature between 2020 and 2025, we examine core protocols including discrete-variable, continuous-variable, measurement-deviceindependent, and twin-field approaches, while also discussing their relationship with post-quantum cryptography as a complementary strategy for future secure communication systems. We provide a unified comparison framework to support practical design and policy decisions by organizing protocols and implementations along deployment dimensions. The study analyze theoretical foundations, implementation technologies across fiber, free-space, satellite, and integrated photonic platforms, and key performance trade-offs involving scalability, security robustness, and deployment feasibility. Findings indicate substantial progress in transitioning QKD from laboratory research toward practical implementations, supported by advances in network architectures, integrated hardware and hybrid cryptographic designs. The comparative analysis will highlight distinct strengths and limitations among protocol families and emphasize the potential of combining QKD with post-quantum cryptographic methods to enhance resilience. Remaining challenges including scalability constraints, implementation-level vulnerabilities, performance limitations over long distances, and integration with existing communication infrastructures are critically discussed. Finally, emerging research directions such as quantum repeaters, hybrid quantum-classical security models, and exploratory directions such as artificial intelligence-assisted optimizations are identified as key factors in enabling the evolution of QKD toward largescale quantum-secure networking.