Routing, Channel, Key-Rate, and Time-Slot Assignment for QKD in Optical Networks

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.