## 5 Performance and Security Analysis
### Security Analysis
We can know from [23] that when telosB motes [27] are used, the energy for receiving one bit requires \(0.2707\mu\)J and the energy for transmitting one bit requires \(0.2505\mu\)J. In ExCo, the energy \(E_{ExCo}\) wasted by the forwarding of one single bogus message in the PDoS attack is therefore \(0.5212\cdot(\sqrt{n}-1)\cdot L_{ExCo}=0.5212\cdot(\sqrt{n}-1)\cdot(128+2\sqrt {n})\mu\)J. In AAD, the energy \(E_{AAD}\) wasted by the forwarding of one single bogus message in the PDoS attack is therefore \(0.5212\cdot(\lambda-1)\cdot L_{AAD}=0.5212\cdot(\lambda-1)\cdot(328+2\sqrt{n })\mu\)J. Hence, the ratio of energy saving of our AAD method to ExCo can be expressed as \(\frac{0.5212\cdot(\lambda-1)\cdot(328+2\sqrt{n})}{0.5212\cdot(\sqrt{n}-1)\cdot(12 8+2\sqrt{n})}\) and is depicted in Figure 10. Since the ratio less than one means that the energy consumed by AAD is lower than that consumed by ExCo, we can observe in Figure 10 that in most cases the energy consumption of AAD is lower than that of ExCo. Note that the energy calculation is based on the energy consumed by the message transmission from the source to the destination. Since the adversary can always launch PDoS attacks, the calculation is independent of the parameter \(t\). The energy saving of AAD is due to the use of \(\lambda\) in restricting the number of hops used to relay the messages. **Resilience Against FEDoS attacks. ** Recall that FEDoS attacks aim to deceive the sink into rejecting the genuine sensor readings by providing false authentication tags. FEDoS attacks easily work because what the sink can trust is only the authentication tag the co-authenticators provide. Therefore, if one of co-authenticators is compromised, the false authentication tag generated by it makes FEDoS attack successful. Nevertheless, in AAD, for a compromised sensor that happens to be a co-authenticator of the data of the sink's interest, it cannot simply generate and then provide a random bit string acting as the authentication tag to the sink. Instead, together with the claimed authentication tag, some additional information should be accompanied so that before accepting the received bit string as the genuine authentication tag, the sink can check the legitimacy of the claimed authentication tag. Specifically, \(P\) and \(E\) serve for this purpose. From the algorithm of the verification phase summarized in Figure 7, it can be observed that for the route to a specific co-authenticator, unless the keys of all the sensors on the route are known by the adversary and the corresponding co-authenticator is compromised prior to the round \(\bar{r}\), the authentication tag cannot be counterfeited. We have an interesting observation that, in the case where \(\overline{t_{j}^{r}}=1\), successfully launching FEDoS attacks is as difficult as successfully replacing the data on the target sensor at the target round because they all need to compromise the sensors in \(\bar{S_{j}^{r}}\) and the sensors on the route from the target sensor to the sensor in \(\bar{S_{j}^{r}}\). Here, we also employ FEDoS ratio to evaluate the resilience of AAD against FEDoS attacks. When the average number \(|N_{1}|\) of the one-hop  
Figure 10: The ratio of energy saving of our AAD method over ExCo in different settings. number of the sensor in a network is \(5\), \(R_{0.5}\)'s of AAD in different settings are shown in Figure 11. When the average number \(|N_{1}|\) of the one-hop number of the sensor in a network is \(10\), \(R_{0.5}\)'s of AAD in different settings are shown in Figure 12. It can be known from Figures 11 and 12 that the resilience of AAD against FEDoS attacks is independent of the network topology such as the sensor density and the number of sensors. In addition, it can be observed that, as \(\bar{t}_{j}^{r}\) increases, \(R_{0.5}\) will be decreased.