Combinatorial Watermarking Under Limited SCER Adversarial Models

<h3>Abstract</h3> Combinatorial watermarking can help establish trust in global navigation satellite system (GNSS) signals. In combinatorial watermarking, the GNSS provider elects to secretly invert a subset of ranging code chips and then later distributes those inversions to receivers. From these ranging code perturbations, receivers can use signal statistics to determine the authenticity of the signal. In previous work, we demonstrated how one can design combinatorial watermarking schemes and derive the distributions of receiver statistics to ensure low probabilities of missed detection and false alarm, assuming that an adversary does not attempt to estimate the watermarked chips and replay. In this work, we extend the analysis of combinatorial watermarking to adversaries capable of engaging in security code estimation and replay (SCER) attacks. We derive the distributions of our statistics for defense against SCER-capable adversaries. Provided a bound on the estimation capability of the SCER-capable adversary, one can use this work to design a combinatorial watermarking scheme that meets security requirements.