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We have validated above the multi-watermark detector using a static function, (mathcal {I}), to define the multi-watermark and different performance loss between single- and multi-watermarks.

We next present the results and validations obtained for a system with the same performance loss between single- and multi-watermark detectors and where the multi-watermark is generated from a non-static function, (mathcal {I}_{d}).

Fig. 12 Numeric simulation results using the single- and multi-watermark detection schemes with the same performance loss, and different adversary window size for eavesdropping the data channel before the attack.

Fig. 10 Numeric simulation results using the single- and multi-watermark detection schemes with the same performance loss, different adversary system order, and a window size equal to 200. a Detection ratio regarding single-watermark for systems of order ten.

In this simulation, single- and multi-watermark detectors have 30% performance loss, Δ J, with respect to the optimal cost.

Fig. 8 Numeric simulation results using the single- and multi-watermark detection schemes with the same performance loss.

In Fig. 8 a, we show the result of using both single- and multi-watermark for a system of order four.

Figure 8 shows the result obtained after running 200 Monte Carlo simulations of a system with single- and multi-watermark detectors against a non-parametric cyber-physical adversary.