## 6 Experimental Analysis and Results
### Experimental Set-Up  
The experimental environment was built using the Solidity language. All the participants' smart gateways were defined during our implementation as mappings from the Ethereum addresses of the participating smart homes. In addition, the Ethereum address of the SmGW was also initialized. Twenty different authorized participants and their trading transactions were considered in the SMP to measure the success of \(\mathcal{A}\) in the game against \(\mathcal{A}^{\tau}\). Furthermore, we evaluated the success of \(\mathcal{A}\) in recovering the public IDs of the participants in the proposed approach and the other base approaches in [6; 7; 30]. We also analyzed the trading transaction messages to investigate the effectiveness of the proposed approach at achieving transactional data privacy. The messages were encrypted and decrypted using both the traditional RSA and the sped up RSA, each of which was enabled in the approach for separate scenarios. Across our tests, we replicated a simulation scenario to consider both the limited information and no information situations. In the limited information situation, we assumed that \(\mathcal{A}\) was aware of the position or delivery of all SMP participants and, as such, could determine if a transaction was rendered in return for traded resources. In this scenario, we had both the IDs of the provider and requester in the prior knowledge of \(\mathcal{A}\) while processing \(\mathit{Success}_{\mathcal{A}}\). In the no information situation, we assumed a situation where \(\mathcal{A}\) did not know the position or operation of all participants and, as such, did not have any previous information but believed that some trading transactions took place between some participants in the network. Evaluating the Success of \(\mathcal{A}\) at Discovering Participant's Anonymity and Untracability in the SMP  
We analyzed the metrics \(\mathit{Success}_{\mathcal{A}}\) for the benchmark approaches [6; 7; 30] to check for the performance of \(\mathcal{A}\) in exposing the participant's session ID with respect to our E-Bitmessage-based approach. The results in Figure 3 show that the probability of \(\mathcal{A}\)'s failure in our approach was more pronounced compared with that in [6; 7; 30]. This shows that the degree of achievement of \(\mathcal{P}\)'s anonymity and untraceability could be observed with high probability (0.848 on average) in our approach. Hence, the results confirm the claim made in Proposition 1 and Theorem 1. Furthermore, it can be observed that there was no definite trend in Figure 3 with respect to the increasing number of participants. This was due to the fact that the system at a given time instance \(\Delta\) was composed of multiple participants, each carrying a different number of trading transactions with a different number of parties (trading activities). Thus, the computational complexities applied to each participant during the trading activities depends on the number of activities carried out by that participant at the given time instance. For instance, participant 9, which had fewer trading activities (having two trading sessions) at given time instance \(\Delta\), would have a lower computational overhead as well as the lowest probability of \(\mathcal{A}\)'s success compared with participant 16 with the most trading activities (having eight trading sessions) at a given time instance \(\Delta\). In a nutshell, the findings show that the fewer trading activities a participant \(\mathcal{P}\) has, the lower the computational complexity applied to it, and the lower the probability of \(\mathcal{A}\)'s success is with it. To have a better understanding of the trend in the results, they are further summarized in Table 3, which is based on the sample of 20 participants categorized in an increasing order of five groups. The table shows that \(\mathcal{A}\) had a negligible effect on the participants when using our approach, with an average efficiency of around 15% in terms of linking IDs to their correct owners.