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Journal of Optical Communications and Networking

On offline scheduling for time-division multiplexing QKD networks

Juan Carlos Hernandez-Hernandez, David Larrabeiti, María Calderón, Ignacio Soto, Farhad Arpanaei

Published Jul 24, 2025• 0 citations
Publisher

Abstract

Quantum key distribution (QKD) combined with quantum-safe encryption algorithms offers a practical path to future-proof communication security. Currently, the BB84 QKD protocol is mature and can be deployed over legacy optical fiber infrastructure using commercial products, with trusted key relaying as a workaround for its distance limitations. However, designing cost-effective QKD networks is essential for widespread adoption by end users and telecom operators (Telcos). To address this challenge, we propose and study a novel, to our knowledge, strategy: periodic time sharing of QKD transceivers. This strategy, especially cost saving at low and medium workloads, allows for generating keys for pairs of nodes at deterministic rates decided a priori. This work presents an offline solution for allocating and scheduling QKD transceivers that are shared by the aforementioned time-division multiplexing (TDM) scheme in a QKD network. We propose a mixed-integer linear programming (MILP)-based scheduling (MBS) method to solve this problem, which is computationally expensive, even for small network topologies. As an alternative, we introduce allocation-driven scheduling (ADS), an algorithm that internally breaks the problem into two steps: allocate first and schedule later. The scheduling can be handled by either a relaxed-MBS (rMBS) or a round-robin scheduling (RRS) approach (ADS-rMBS and ADS-RRS, respectively). Both methods yield results comparable to MBS for small networks. Furthermore, simulations illustrate that both ADS-rMBS and ADS-RRS enable a pay-as-you-grow model, reducing the initial capital expenditure in low-load scenarios. Compared with the non-TDM baseline (i.e., QKD transceivers are non-shared), the cost savings range from 30% to 50%, making QKD deployment more economically viable. Moreover, ADS-rMBS generally outperforms ADS-RRS, but requires a higher runtime, reaching up to 2500 s in large networks. Conversely, ADS-RRS maintains a stable 1 ms runtime across all conditions, making both approaches viable depending on the traffic matrix update interval.

DOI
10.1364/jocn.566174

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Quantum key distribution (QKD) combined with quantum-safe encryption algorithms offers a practical path to future-proof communication security. Currently, the BB84 QKD protocol is mature and can be deployed over legacy optical fiber infrastructure using commercial products, with trusted key relaying as a workaround for its distance limitations. However, designing cost-effective QKD networks is essential for widespread adoption by end users and telecom operators (Telcos). To address this challenge, we propose and study a novel, to our knowledge, strategy: periodic time sharing of QKD transceivers. This strategy, especially cost saving at low and medium workloads, allows for generating keys for pairs of nodes at deterministic rates decided a priori. This work presents an offline solution for allocating and scheduling QKD transceivers that are shared by the aforementioned time-division multiplexing (TDM) scheme in a QKD network. We propose a mixed-integer linear programming (MILP)-based scheduling (MBS) method to solve this problem, which is computationally expensive, even for small network topologies. As an alternative, we introduce allocation-driven scheduling (ADS), an algorithm that internally breaks the problem into two steps: allocate first and schedule later. The scheduling can be handled by either a relaxed-MBS (rMBS) or a round-robin scheduling (RRS) approach (ADS-rMBS and ADS-RRS, respectively). Both methods yield results comparable to MBS for small networks. Furthermore, simulations illustrate that both ADS-rMBS and ADS-RRS enable a pay-as-you-grow model, reducing the initial capital expenditure in low-load scenarios. Compared with the non-TDM baseline (i.e., QKD transceivers are non-shared), the cost savings range from 30% to 50%, making QKD deployment more economically viable. Moreover, ADS-rMBS generally outperforms ADS-RRS, but requires a higher runtime, reaching up to 2500 s in large networks. Conversely, ADS-RRS maintains a stable 1 ms runtime across all conditions, making both approaches viable depending on the traffic matrix update interval.
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Time-sharing of Quantum Key Distribution (QKD) transceivers with the help of optical switches and a central Software-Defined Networking (SDN) controller is a promising technique to better amortize the large investments required to build a Quantum Key Distribution Network (QKDN). In this work, we investigate the implications of introducing Time-Division Multiplexing (TDM) in trusted-relay QKDNs at the wide-area network scale in terms of performance and cost-saving. To this end, we developed both a Mixed Integer Linear Programming (qTDM-MILP) model and a Heuristic Algorithm (qTDM-HA) to solve the allocation of QKD transceivers and network resources for a novel switched QKDN operating scheme: qTDM-QKDN. Our heuristic method provides a close-to-optimal resource planning for the offline problem that computes the minimum number of QKD transceivers and optical switch ports at each node, as well as the number of quantum channels on each link required to satisfy a target set of end-to-end secret-keyrate demands. Moreover, both the model and the heuristic provide the time fractions that each QKD transceiver needs to peer with each neighbor QKD transceiver. We compared our proposed model and heuristic algorithm for cost minimization with non-time sharing QKD transceivers (nTDM) as baseline. The results show that qTDM can achieve substantial cost-savings in the range of 10%-40% compared to nTDM. Furthermore, this work sheds light on the selection of the value for the working cycle T and its influence on network performance.
It is well known that optical access networks are able to provide high data rates over long distances and to a reasonable number of users. Security and privacy are always a challenge for public accessible network infrastructures. Especially in time-division multiplexing passive optical networks (TDM-PONs), in which the downstream signal is broadcasted to all users connected via the same wavelength channel in a shared fiber link, privacy can be a critical concern. Although encryption at the application layer can provide a high level of security, this can be achieved only if the encryption key distribution is perfectly save. On the other hand, encryption on the physical layer such as quantum cryptography or, more precisely, quantum key distribution (QKD) is a very promising approach to achieve secure communication. However, there remain several issues that have to be solved before the quantum cryptography reaches the maturity level needed for a cost effective implementation in practical networks. In this paper, we address quantum key distribution (QKD) over passive optical access networks, which is an enabling technology required to cost efficiently deploy practical quantum encrypted data communication in the access area. We study different methods to integrate QKD systems in conventional optical access networks and quantitatively evaluate their suitability for a potential implementation.
Quantum key distribution (QKD) uses the laws of quantum mechanics to distribute secret keys with information-theoretic security. To realize QKD for secure communications among multiple distant users, fiber-based QKD networks can be deployed with today's available technologies. Incorporating QKD into existing wavelength-division multiplexing (WDM) network infrastructure provides a practical way to reduce the difficulty and cost of QKD networking. Nonetheless, the costs of QKD nodes and QKD links are still considered as the major barriers to long-distance QKD network deployment in practice. In this work, we study how to minimize the cost of deploying QKD-over-WDM backbone networks. We introduce a general architecture of QKD-over-WDM backbone networks. A novel cost-oriented model is defined to elaborate the cost-minimized problem, in which various QKD network components including QKD transceivers, QKD auxiliary equipment for QKD backbone nodes and trusted repeater nodes (TRNs), and QKD links are considered. The physical-layer parameters such as secret-key rate, physical distance, and the layout of TRNs are also incorporated in our defined model. We develop an integer linear programming (ILP) model and a novel cost-efficient QKD networking (CEQN) heuristic algorithm to address the cost-minimized problem. The extensive simulations indicate that our proposed approaches are effective in reducing the cost of deploying QKD-over-WDM backbone networks, where the designed CEQN algorithm is efficient to demonstrate similar to the ILP model. Finally, some open issues in future work are discussed, given that this work only presents an early highlevel analysis as opposed to a definitive detailed model.
Quantum Key Distribution (QKD) is currently being explored as a solution to the threats posed to current cryptographic protocols by the evolution of quantum computers and algorithms. However, single-photon quantum signals used for QKD permit to achieve key rates strongly limited by link performance (e.g., loss and noise) and propagation distance, especially in multi-node QKD networks, making it necessary to design a scheme to efficiently and timely distribute keys to the various nodes. In this work, we introduce the new problem of joint Routing, Channel, Key-rate and Time-slot Assignment (RCKTA), which is addressed with four different network settings, i.e., allowing or not the use of optical bypass (OB) and trusted relay (TR). We first prove the NP-hardness of the RCKTA problem for all network settings and formulate it using a Mixed Integer Linear Programming (MILP) model that combines both quantum channels and quantum key pool (QKP) to provide an optimized solution in terms of number of accepted key rate requests and key storing rate. To deal with problem complexity, we also propose a heuristic algorithm based on an auxiliary graph, and show that it is able to obtain near-optimal solutions in polynomial time. Results show that allowing OB and TR achieves an acceptance ratio of 39% and 14% higher than that of OB and TR, respectively. Remarkably, these acceptance ratios are obtained with up to 46% less QKD modules (transceivers) compared to TR and only few (less than 1 per path) additional QKD modules than OB.
Quantum key distribution (QKD) networking over wavelength-division multiplexing (WDM) network infrastructure provides a new paradigm for secure communications across the networks. With limited wavelength resources in existing WDM networks, how to efficiently schedule QKD to provision sufficient secret keys over WDM networks becomes a new challenge. This study proposes a new time-scheduled scheme in combination with quantum key pool (QKP) technique to overcome this challenge. A new architecture of QKD-over-WDM networks is presented, in which QKPs are constructed to decouple secret-key resources from the underlying infrastructure for timely secret-key provisioning. In the time-scheduled scheme, routing, wavelength, and time-slot allocation (RWTA) problem is proposed for efficient QKP construction (QKPC) over WDM networks, in which three sub-problems (i.e., secret-key consumption, time-slot allocation, and time-slot continuity) are discussed, respectively. An integer linear programming (ILP) model and a novel joint path-and-link-based RWTA (JPL-RWTA) heuristic algorithm are designed to solve the RWTA problem, in which the three sub-problems are addressed together. Simulation results indicate that the ILP model and JPL-RWTA algorithm are effective approaches to obtain the positive balance between resource utilization of QKPC and successful probability of QKPC (SPQKPC). Moreover, the SPQKPC can be increased at the cost of reducing the flexibility of secret-key consumption, the uniformity of time-slot allocation, and the proportion of time-slot continuous QKPC to time-slot discrete QKPC requests.