## 4 Security and Performance Analysis
### Performance Analysis  
Table 3 shows a comparison of the time complexity between our proposed protocol and [PERSON] and [PERSON]'s scheme. Table 4 shows a comparison of the communication cost between our scheme and [PERSON] and [PERSON]'s scheme. Table 5 shows a simulation which we developed based on NS2 (Network Simulation 2).  
\begin{table}
\begin{tabular}{l l l} \hline Nodes Relationship & [PERSON] and [PERSON]’s scheme[23] & Our scheme \\ \hline Sensor node and Cluster node & _2T’\({}_{R}\)_ +2T’\({}_{h}\)_+2T'\({}_{EECC}\) & _2T’\({}_{E}\)_ +1T’\({}_{MSG}\)_+1T’\({}_{h}\)_ \\ (or H-node) & & N/A & _3T’\({}_{E}\)_ +2T’\({}_{MSG}\)_+3T’\({}_{h}\)_ \\ Cluster node (or H-node) and & N/A & _3T’\({}_{E}\)_ +2T’\({}_{MSG}\)_+3T’\({}_{h}\)_ \\ Base station & H-node and H-node & _T’\({}_{EECC}\)_ +4T'\({}_{R}\)_+2T’\({}_{h}\)_ & N/A \\ \hline \end{tabular} Notes:  
\(T\)’\({}_{E}\): the transmission time for a symmetric encryption message (For example AES-128 bits)  
\(T\)’\({}_{MSG}\): the transmission time for a message (16 bits, for example _ID’\({}_{si}\), ID’\({}_{ci}\)_)  
\(T\)’\({}_{h}\): the transmission time for a hash message (for example, hash message of 168 bits)  
\(T\)’\({}_{EECC}\): the transmission time for an ECC ciphertext (for example, a ciphertext of 256 bits)  
\(T\)’\({}_{R}\): the transmission time for a random number (for example, random number of 16 bits)  
\end{table}
Table 3: Comparison of time complexity between our scheme and [PERSON]’s scheme.  
The [PERSON]'s scheme is based on ECC public key encryption and the random number challenge response mechanism. By contrast our scheme is based on the symmetric cryptosystem and hash function mechanism. From Table 3 and Table 4, we can see that the operation time of our scheme is faster than that of [PERSON]'s scheme for a large number of sensors. But the H-node end of [PERSON] and [PERSON]'s scheme is superior to ours for one transaction. However, the detailed analyses are presented in our scheme. Otherwise, the [PERSON] and [PERSON]'s scheme should process a key agreement procedure in advance, our scheme only uses the dynamic parameters to complete the same function without specific communication during transaction. Our scheme is simpler. Two mechanisms are different; but the differences in communication cost are not significant.  
In the following section, we compare the energy consumed in our proposed scheme to the energy consumed in other schemes. A comparison of the total energy consumption in other schemes for various different numbers of nodes is shown in Figure 13. As can be seen, the total energy consumed  
\begin{table}
\begin{tabular}{l l} \hline
**Parameter** & **Values** \\ \hline Simulation tool & NS2 \\ Simulation area & 2,000 m \(\times\) 2,000 m \\ Number of nodes & 100–400 nodes \\ Base station mobility model & Random waypoint model \\ Radio transmission range & 100 m \\ Data packet size & 64 bytes \\ Data transmission rate & 1 Mbps \\ \hline \end{tabular}
\end{table}
Table 5: Parameters used in the simulation environment.  
Figure 13: Comparison of energy consumption _versus_ number of grids for different schemes.  
in the proposed scheme and in the DARQ, CODE and TTDD schemes increased when the number of grids increased. However, the total energy consumed in our scheme is less than the energy consumed in the CODE and TTDD schemes, but is more than the DARQ scheme. Since our scheme uses a grid-based mechanism to restrict the possibility of packet flooding, such a result meets our expectations. However, although our scheme is based on the DARQ scheme, more energy is consumed in encryption computation.