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IEEE Transactions on Industrial Informatics

Secret Key Rate Over Multiple Relays in Quantum Key Distribution for Cyber–Physical Systems

Peng‐Yong Kong

Published Apr 23, 2024• 13 citations
Publisher

Abstract

In a cyber–physical system, quantum key distribution (QKD) protocols can provide a continuous supply of common secret key bits for secure communications between the control center and a remote device. QKD protocols operate on a peer-to-peer basis between two adjacent nodes and are distance-limited. Hence, trusted nodes are installed between two communicating end nodes for a better QKD range and key rate. These trusted nodes relay in a hop-by-hop manner, key bits generated in the first hop to the other end node. At each trusted node, the first hop key bits are encrypted by other locally generated key bits before being relayed. Since QKD process is stochastic, secret key bits are generated at different rates at different hops. Thus, buffer is needed at a trusted node to temporally hold some key bits while waiting for other key bits. There is no existing work that accounts for such a realistic relaying operation in deriving the key rate. This article contributes to developing a key rate model to determine accurately the end-to-end rates across multiple trusted nodes. We have evaluated accuracy of the proposed model through extensive simulations. The results show that there exist an optimal number of trusted nodes for a given distance between two end nodes. For example, the optimal number of relays increases from four for 100 km to six for 200 km.

DOI
10.1109/tii.2024.3385535

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In a cyber–physical system, quantum key distribution (QKD) protocols can provide a continuous supply of common secret key bits for secure communications between the control center and a remote device. QKD protocols operate on a peer-to-peer basis between two adjacent nodes and are distance-limited. Hence, trusted nodes are installed between two communicating end nodes for a better QKD range and key rate. These trusted nodes relay in a hop-by-hop manner, key bits generated in the first hop to the other end node. At each trusted node, the first hop key bits are encrypted by other locally generated key bits before being relayed. Since QKD process is stochastic, secret key bits are generated at different rates at different hops. Thus, buffer is needed at a trusted node to temporally hold some key bits while waiting for other key bits. There is no existing work that accounts for such a realistic relaying operation in deriving the key rate. This article contributes to developing a key rate model to determine accurately the end-to-end rates across multiple trusted nodes. We have evaluated accuracy of the proposed model through extensive simulations. The results show that there exist an optimal number of trusted nodes for a given distance between two end nodes. For example, the optimal number of relays increases from four for 100 km to six for 200 km.
Original quantum key distribution (QKD) protocols operate on a peer-to-peer basis between two adjacent nodes, which are directly connected through a quantum channel. Such protocols are severely distance limited. To extend the range, existing schemes use trusted nodes to relay in a hop-by-hop manner, secret key generated at one end node to the other end node. It is difficult to ensure node trustworthiness and more trusted nodes will lead to an enlarged attack surface. This paper proposes a scheme called honest relay key distribution (HRKD) that does not require relays be trusted. Specifically, HRKD removes the trusted node requirement by distilling a secret key directly between end nodes which are separated by multiple hops and imposing strict timing requirements on quantum state bases announcement and key usage. We have analyzed HRKD to show that its key secrecy protection can be as good as BB84 in some cases and is better than trusted node key relaying. We have derived its secret key rate as a function of distance between two end nodes. We have verified the key rate accuracy through extensive simulations. Evaluation results have also confirmed that with an increase in the distance between two end nodes, HRKD requires a maximum of two physical honest relays regardless of the distance while trusted node key relaying requires an increasing number of relays.
There is a need to ensure unconditionally secure communications between different sites of an organization. We use quantum key distribution (QKD) protocol to provide a continuous stream of secret key bits to each communicating pair for message encryption through one-time-pad (OTP) cryptography. Due to long distance between different sites, trusted nodes are used to relay each service key in a hop-by-hop manner from one end node to another end node of a communicating pair. In a QKD network, routes for key relaying can be affected by availability of relay key bits at trusted nodes. Also, relay key allocation among different routes can impact security. We consider the scenario of supporting multiple communicating pairs, where each pair demands delivery of a certain service key rate across the QKD network, and trusted nodes may not have sufficient relay key rates to perform bitwise encryption to protect the service key. Hence, there is a need to allocate the limited relay key bits to meet all service key delivery demands while considering its effects on security. We propose to perform jointly routing and relay key allocation to minimize attack success probability. We have formulated the joint problem as an optimization and further proposed an efficient algorithm to find the optimal solutions. We have evaluated the proposed algorithm to confirm its ability and efficiency in finding optimal routes and relay key allocations. For the specific network topology that we have adopted, results show that the minimum number of required trusted nodes increases linearly when end nodes are added to the system. Furthermore, we can achieve a higher security level by adding more trusted nodes in a QKD network. But increasing the number of trusted nodes beyond the minimum requirement may not continue to reduce significantly the attack success probability.
Quantum key distribution (QKD) protocols generate a same secret key at two nodes which are at different locations. Such key is used to encrypt and decrypt messages for unconditionally secure communications through a classical channel. Originally, QKD protocols are designed to work between two nodes which are directly connected through a point-to-point quantum channel. Currently, commercial QKD systems have limited range and key rate. To increase key rate and extend range, the key generated by QKD at one end node is relayed hop-by-hop to the other end node through multiple trusted nodes. In a QKD network with multiple pairs of communicating nodes, routing deals with the issue of deciding for each pair, which trusted nodes are used to form a path connecting the end nodes. This paper presents an overview of QKD and highlights the differences between QKD routing as compared to classical routing. The challenges of QKD routing are presented. Existing works dealing with the challenges are surveyed. This paper ends with a discussion on remaining research issues.
Quantum key distribution (QKD) allows the distribution of secret keys for quantum-secure communication between two distant parties, vital in the quantum computing era in order to protect against quantum-enabled attackers. However, overcoming rate-distance limits in QKD and the establishment of quantum key distribution networks necessitate key relaying over trusted nodes. This process may be resource-intensive, consuming a substantial share of the scarce QKD key material to establish end-to-end secret keys. Hence, an efficient scheme for key relaying and the establishment of end-to-end key pools is essential for practical and extended quantum-secured networking. In this paper, we propose and compare two protocols for managing, storing, and distributing secret key material in QKD networks, addressing challenges such as the success rate of key requests, key consumption, and overhead resulting from relaying. We present an innovative, fully decentralized key distribution strategy as an alternative to the traditional hop-by-hop relaying via trusted nodes, where three experiments are considered to evaluate performance metrics under varying key demand. Our results show that the decentralized pre-flooding approach achieves higher success rates as application demands increase. This analysis highlights the strengths of each approach in enhancing QKD network performance, offering valuable insights for developing robust key distribution strategies in different scenarios.
Cyber–physical systems rely heavily on communication networks for remote monitoring and control. It is crucial to protect the communication networks from cyberattacks because an attack on the physical subsystem can be indirectly launched from a compromised cyber subsystem. Since remote control devices have limited computational power, we ensure communication confidentiality and integrity using one-time-pad (OTP) symmetric cryptography, which despite simple is unconditionally secure. To provide OTP with secret keys, we use quantum key distribution (QKD) across multiple hops, where each intermediate relay is a trusted node. These nodes can be weak points in cyberattacks. Hence, this article focuses on routing in multihop QKD networks that reduces the required number of trusted nodes. We formulate and solve an optimization problem to find the set of QKD routes that minimizes the number of activated trusted nodes while satisfying the secret key rate requirements of multiple communicating pairs. Extensive evaluation results confirm that the proposed scheme can indeed has fewer activated trusted nodes as compared to a benchmark scheme that finds only the shortest paths for communicating pairs.
Quantum key distribution (QKD) protocols are designed to distribute secure keys between two remote parties. Current QKD systems require the presence of a trusted relay to distribute the keys over intercontinental distances, due to technological limitations. When the trusted relay is intermittently available to the end parties, as in the case of low Earth orbit (LEO) satellites, the QKD system undergoes a severe reduction in the amount of exchangeable secret bits. This paper proposes a new way to analyze the performance of QKD systems under these premises. It is shown that the secret key rate is not the most important figure of merit in the design of QKD protocols with intermittent relays, despite its importance for standard QKD links.