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298 CHAPTER 11 Node Compromise Detection in Wireless Sensor Networks In the case of mobile replicas, we investigate how replica mobility affects the detection capability of our scheme. In the case of static (immobile) replicas, the attacker keeps his replica nodes close together while fixing them to a certain positions to lessen the chance of speed-based detection. An exploration of the static replica case is use- ful since this case represents the worst case for detection, and thus we can see how our scheme works in the worst case. In our simulation, 500 mobile sensor nodes are placed within a square area of 500 m × 500 m. We use the Random Waypoint Mobility (RWM) model to determine mobile sensor node move- ment patterns. In particular, to accurately eval- uate the performance of the scheme, we use the RWM model with the steady-state distribution provided by the Random Trip Mobility (RTM) model. All simulations were performed for 1000 simulation seconds. We fixed a pause time of 20 simulation seconds and a minimum moving speed of 1.0 m/s of each node. Each node uses IEEE 802.11 as the medium access control protocol in which the transmission range is 50 m. To emu- late the speed errors caused by the inaccuracy of time synchronization and localization proto- cols, we modify the measured speeds with max- imum speed error rate . Specifically, we take speed s measured using perfect time synchro- nization and localization protocols and generate speed s selected uniformly at random from the range [s - s , s + s ]. We evaluated the scheme with values of 0.01, 0.1, and 0.2. We conducted the evaluation with low (V max = 10 m/s), mod- erate (V max = 20, 40 m/s), high (V max = 60 m/s), and very high (V max = 80, 100 m/s) mobility rates. When we consider robotic vehicular platforms, low (no more than 36 km/h) and moderate (no more than 72 or 144 km/h) mobility rates may be suitable. High (no more than 216 km/h) and very high (no more than 288 or 360 km/h) mobility rates may be suitable for modeling autonomous aircraft. The simulation results of both cases show that this scheme very quickly detects mobile (resp. static) replicas with at most five (resp. ten) samples while restricting both false-positive and false-negative rates below 0.013. 11.6. CONCLUSION AND FUTURE WORK In this chapter, we first proposed SPRT-based node compromise detection schemes against the limited node compromise strategy in static sen- sor networks. We analytically showed that our proposed schemes achieve high detection accu- racy while exhibiting robust resilience against a variety of attacks. The simulation results indi- cate that the proposed schemes quickly detect the static and mobile compromised nodes with at most ten samples in static sensor networks while restraining the false-positive and false-negative rates below 1%. We then proposed replica node detection schemes against wide-spread node com- promise strategy. Static replica detection schemes utilize group deployment knowledge to achieve efficient and robust replica detection capability with zero false positive. The analytical and sim- ulation results represent that static replicas are detected with much less communication, com- putation, and storage overhead than the prior work in the literature. Mobile replica detection schemes use the SPRT to accomplish fast detec- tion of mobile replicas with at most ten sam- ples while limiting the false-positive rates below 1.3%. We would like to extend this chapter to implement the proposed schemes into sensor motes and investigate their performances when limited and wide-spread node compromise strate- gies are used. Since a sensor mote is a resource- constrained device, it will be a challenging issue to implement efficiently and effectively all com- ponents into a sensor mote. To tackle this issue, it will be imperative to optimize each component in terms of resource usage. EXERCISES 1. In static replica detection schemes, two-dimen- sional Gaussian distribution is used for group deployment model in a two-dimensional sta- tic sensor network. If we use static replica detection schemes in a three-dimensional static sensor network, three-dimensional