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

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.