## 9 Performance Evaluation
### Processing and Computational Evaluation  
Hash functions are used to calculate the pseudonyms and symmetric cryptography is used to encrypt the messages. Because we need to calculate three pseudonyms and one acknowledgement pseudonym after each transmission, using encryption to create pseudonyms was avoided since it requires more processing power compared to hash functions. When a SN senses data, it needs to calculate four OWH for PID, OHPID, and APID at the sender and OHPID at the receiver. If the system opts for data authentication, then another hash function is needed. The source node needs only one encryption for the data if \(\mathrm{O_{h}}=0\), however, it needs \(\mathrm{O_{h}}\) more encryptions if onion fashion is used. Each intermediary node needs one decryption operation and then another encryption to issue the new message. [PERSON] _et al._[16] indicates that SAS does not use hashing or encryption to create pseudonyms because it uses already created pseudonyms from a space. The other scheme by [PERSON] _et al._[16], CAS, uses two hashing operations and two encryption operations. APR uses at least six hashing functions. DCARPS uses constant IDs, so no hashing functions or encryptions for creating IDs. EAC has four hashing operations. It is clear that our framework needs a bit extra processing power due to the higher privacy and security we have achieved. None of the other schemes can achieve privacy against global threats and active adversary attacks. The power consumption due to the additional encryption operations is marginal compared to the power consumption caused by data transmission. Figure 29 exhibits different storage  
\begin{table}
\begin{tabular}{c c c c} \hline No. & **Scheme** & **Storage Cost (bits)** & **Computation Cost** \\ \hline
1 & SAS & \(2\mathrm{nN}+4\mathrm{nN_{ave}}+16\) & No hashing operations \\
2 & CAS & \(6\mathrm{n}+7\mathrm{nN_{ave}}+16\) & Two hashing operations and two encryptions \\
3 & HIR & \(2\mathrm{n}+2\mathrm{nN_{ave}}\) & One hashing function \\
4 & RHIR & \(2\mathrm{n}+2\mathrm{nN_{ave}}+\mathrm{nkN_{ave}}\) & No hashing functions \\
5 & APR & \(9\mathrm{n}+7\mathrm{nN_{ave}}+2\mathrm{N}-2\mathrm{N_{ave}}-2\) & Six hashing functions \\
6 & DCARPS & \(3\mathrm{n}\) & No hashing functions \\
7 & ACS & \(5\mathrm{nN_{ave}}\) & Two hashing functions \\
8 & PhID & \((3\mathrm{n}+2)\times\mathrm{N_{ave}}\) & Four hashing function \\
9 & EAC & \(6\mathrm{n}+6\mathrm{nN_{ave}}+2\) & Four hashing operations \\
10 & FAC & \(10\mathrm{n}+(7\mathrm{n}+16)\times\mathrm{N_{ave}}\) & Four hashing operations \& O\({}_{h}\) encryptions \\ \hline \end{tabular}
\end{table}
Table 4: Performance Comparison. \(N\) is the total number of sensors; \(N_{ave}\) is the average number of neighbors; \(k\) (only for RHIR) is number of stored hash values where the SN stores \(k\) hash values per one neighbor which are calculated in advance at setup phase.  
size for different privacy schemes, which are discussed throughout this work. It shows that the increase in storage is _linear_ and relatively comparable to the other protocols. The size of the storage would increase when the number of neighbors increases. Each SN has limited flash memory size, which could confine the maximum number of neighbors that a sensor can fit. As an example, _TelosB_ more [16, 20] has 1 MB external flash memory. Thus, if one neighbor node requires 1.2 k bits of storage memory, then TelosB could fit more than 800 neighbors, which is very much more than what is needed in practical networks. Although FAC shows a bit of increase in the storage required to store the pseudonyms but it is the only one, among the discussed protocols in this work, provides a steady and functional anonymity and location privacy under strong global and active attack. In addition, the current technology provides sensors with sizable storage memory, which makes it not an issue at all.