## 3 Proposed Anonymization Method, Iterative _k_-Anonymous Clustering Method (I\(k\)-ACM)
### Multicasting and Energy Saving  
Main aim of \(k\)-Anonymity solutions is providing the required privacy level with minimum information loss. However another factor, minimization of energy consumption, is an important criteria in WSNs. A sensor node consumes energy for different processes like event sensing, CPU processing, or transmitting/receiving data packets. Among these processes, transmission/reception operations consumes much of the energy. Table 3 shows energy consumption rates for transmission/reception which are published in technical report written by [PERSON] _et al._[12]. It is stated that energy consumption ratio of transmission/reception of one byte data to energy consumption of encryption of one byte data is 2333.34. Since each sensor node acts as a router for the messages of other nodes and one message goes over many hops in the network, energy saving for transmission/reception operations becomes a crucial design criterion. Shortening the length of messages and decreasing the number of travelled hops would help to reduce energy enormously.  
In a WSN topology where there are multiple sinks and each sink has different privacy criteria, the basic solution of anonymization is that group head sensor anonymizes the data, produces different outputs for each requirement of sink and sends each output to related sink in different paths as shown in Figure 7 (in this figure, there are two sinks in WSN). This sending method is called as _multipath_. However, I\(k\)-ACM produces unique output which is ready for multicasting. One anonymized output that guarantees all the privacy requirements, is sent to a multicast point. After reaching to multicast point, one copy of data is sent to sink1 and the other copy is sent to sink2 as presented in Figure 8. Multicasting schema decreases the number of travelled hops for some group head nodes.  
Assume that there are two sinks named \(Sink1\), \(Sink2\). \(Sink1\) requires \(k1\)-anonymized data and \(Sink2\) requires \(k2\)-anonymized data. The lengths of anonymized outputs are \(l_{k1}\) and \(l_{k2}\), which are obtained by \(k\)-anonymization with only generalization operation for having \(k1\)-anonymized and \(k2\)-anonymized data, respectively. Data length of anonymous data generated by I\(k\)-ACM is labelled as \(l_{IkACM}\). The number of hops in the shortest route from group head sensor, \(G\), to Sink1 and Sink2 is represented as \(h_{G,Sink1}\), \(h_{G,Sink2}\) respectively. Also assume that the hop distance between \(G\) and multicast point, \(M\), is \(h_{G,M}\), distances from \(M\) to Sink1 and Sink2 are \(h_{M,Sink1}\) and \(h_{M,Sink2}\), respectively. Unique anonymized data is sent to, \(M\), if an appropriate node exists in the network which holds the Inequality 5.  
\begin{table}
\begin{tabular}{|c|c|} \hline
**Energy Consumption Ratios** & **Ratio Value** \\ \hline Transmission/Reception & 1.5 \\ Transmission/Encryption & 2333.34 \\ Encryption/Decryption & 1 \\ \hline \end{tabular}
\end{table}
Table 3: Energy consumption ratios.  
Among the possible node candidates, the one which minimizes the value of \(h_{G,M}+h_{M,Sink1}+h_{M,Sink2}\) is chosen.  
\[(h_{G,Sink1}.l_{k1})+(h_{G,Sink2}.l_{k2})>(h_{G,M}+h_{M,Sink1}+h_{M,Sink2}).l_{IkACM} \tag{5}\]