# Efficient Key Exchange Using Identity-Based Encryption in Multipath TCP Environment
## 5 Experimental Evaluation of Proposed Model
### Performance Evaluation  
In the proposed model of SKEXMTCP, the session keys, which are used for the authentication of entities during the establishment of new subflows and advertisement of new addresses, are encrypted by using IBE. In order to retrieve the public parameters of IBE and private key from the PKG, extra packets are required to be exchanged between communicating nodes and the PKG, but it does not add any overhead on communication through MPTCP. Moreover, in order to encrypt the packet using IBE, the host does not require a public key, as any arbitrary string can be used to encrypt the messages using IBE, whereas if any of the public key cryptosystems such as ECC are used, the hosts need to generate the session keys before encryption. Figure 14 shows the comparison between the time required for the key generation and encryption using ECC and IBE. The graph shows that ECC requires more time, as it needs to generate session keys for encryption, while IBE can use any arbitrary string for the encryption. In [31], the authors used ECC for the session key generation, and the keys will be used for authentication, which decreases the overall performance.  
The cost of the proposed model in terms of implementation can be calculated by considering: (i) the cost of key generation, (ii) the cost of communication between hosts and PKG, and (iii) the cost of the three-way handshake.  
* Let us assume that the cost of key generation is \(n\).
* To obtain the cost of communication between the hosts and PKG, one needs to consider the cost of a request for a private key from a host to PKG and the cost of a reply from PKG to a host with a private key.
* Assume that the cost of a request for a private key from a host to PKG is \(n1\) and the cost of a reply from PKG to a host with a private key is \(n2\).
* Thus, the cost of communication between [PERSON] and PKG to deliver a private key to [PERSON] is \(n1+n2\), and the cost of communication between [PERSON] and PKG to deliver a private key to [PERSON] is also \(n1+n2\).
* Thus, the total cost for communication between PKG and hosts is \(2(n1+n2)\).
* Now, let us calculate the cost of a three-way handshake SYN, SYN+ACK, and ACK is \(n3,\ n4\), and \(n5\) respectively.
* Thus, the overall cost is \[N1=2\ (n1+n2)+n3+n4+n5\]
* If we consider that the overall cost of the model is \(\text{O}(N)=\ \text{O}(N1)\), then \[N1\ \ll N1\times N1\]  
Table 6 shows the comparative analysis in terms of the number of bytes required for key exchange and delay for packet exchanges [23; 24] of various solutions to enhance the security of MPTCP. It also shows the comparison of various proposed solutions to enhance the security of MPTCP in terms of bytes required for key exchange and no delays [22]. Here, the delay shows the number of extra packets required, which is a one-way delay. The graphical representation in Figure 15 shows that the proposed solution behaves the same in terms of required bytes in the key exchange and delay as MPTCP.  
Figure 14: Comparison between times required for the key generation and encryption using ECC and IBE.  
Figure 15: Comparative study of bytes required in key exchange with various MPTCP options in security solutions [17; 20; 23; 24; 33; 46; 47].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Proposed Solution** & **SCMTCP** & **Lightweight Subflow** & **SMPTCP** & **MPTLS** & **Hash Chain** [20] & **MPTCP** [17] \\ \hline
**MP\_CAPABLE** & & & & & & & \\  & & & & & & & \\  & & & & & & & \\  & & & & & &