In this paper, we consider an eavesdropping attack on a multi-hop, UnderWater Acoustic Sensor Network (UWASN) that consists of $M+1$ underwater sensors which report their sensed data via Orthogonal Frequency Division Multiplexing (OFDM) scheme to a sink node on the water surface. Furthermore, due to the presence of a passive malicious node in nearby vicinity, the multi-hop UnderWater Acoustic (UWA) channel between a sensor node and the sink node is prone to eavesdropping attack on each hop. Therefore, the problem at hand is to do (helper/relay) node selection (for data forwarding onto the next hop) as well as power allocation (across the OFDM sub-carriers) in a way that the secrecy rate is maximized at each hop. To this end, this problem of Node Selection and Power Allocation (NSPA) is formulated as a mixed binary-integer optimization program, which is then optimally solved via decomposition approach, and by exploiting duality theory along with the Karush-Kuhn-Tucker conditions. We also provide a computationally-efficient, sub-optimal solution to the NSPA problem, where we reformulate it as a mixed-integer linear program and solve it via decomposition and geometric approach. Moreover, when the UWA channel is multipath (and not just line-of-sight), we investigate an additional, machine learning-based approach to solve the NSPA problem. Finally, we compute the computational complexity of all the three proposed schemes (optimal, sub-optimal, and learning-based), and do extensive simulations to compare their performance against each other and against the baseline schemes (which allocate equal power to all the sub-carriers and do depth-based node selection). In a nutshell, this work proposes various (optimal and sub-optimal) methods for providing information-theoretic security at the physical layer of the protocol stack through resource allocation.
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