Covert Secret Key Agreement Scheme Based on the Underwater Acoustic Dynamic Hypergraph

In order to cope with the problem of how to agree on a covert secret key with high reliability and strong secrecy among an arbitrary number of legitimate nodes in underwater acoustic channel (UAC), a Covert Secret key agreement scheme based on underwater acoustics dynamic hypergraph called CSDH is proposed. The CSDH scheme is novel in three aspects. First, we utilize attention mechanism for extracting the feature of node in UAC and construct a dynamic hypergraph model by its characteristics, which has less storage space and lower computational complexity. Second, we design a spatio-temporal hypergraph convolution method based on the spatial and temporal variation characteristics of UAC in which the number of the nodes is arbitrary, the hyperedge is dynamic, and each hyperedge can encompass an arbitrary number of nodes. Third, we utilize covert communication and polar coding to construct high-entropy bit indices set and very high-entropy bit indices set to generate a common covert key among arbitrary number of legitimate nodes to ensure that not only the key is secret but the entire key agreement process remains covert to eavesdroppers. The reliability, uniformity, secrecy, covertness and secrecy capacity of the CSDH scheme are proved by the information theory and hypergraph theory. The simulation results demonstrate the performance of the CSDH scheme is better than that of existing schemes.