## 7 Experiment and Analysis
### Evaluation of PoAP
#### 7.3.3 Security Evaluation  
To test whether a rapid content publication attack could yield additional profits in the NexoNet, assume four groups of users publish content under different rates. With parameter setting \(\omega_{1}=1\), the interval between content publications must satisfy \(\Delta T\geq 3\) s to gain the full publication PV: \(\alpha_{gcp}\) for each content. These four groups of users employ publication intervals of 1.000 s, 0.500 s, 0.250 s, and 0.125 s, respectively; the resulting transaction fee accumulation is illustrated in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **PoAP** & **PBFT** & **PoW** & **PoS** \\ \hline TPS & High & Low & Low & High \\ Scalability & Good & Bad & Good & Good \\ Fork & Hard & Hard & Easy & Easy \\ Incentive & Multiple incentive & None & Token & Token \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of consensus mechanism.  
Figure 8: Comparison of consensus delay.  
Figure 9: Comparison of TPS.  
The observations from Figure 10 indicate that due to the characteristic of the hyperbolic tangent function used in Formula (1), increasing the rate of content publication from 1.000 s leads to diminishing increments in transaction fee rewards, even resulting in a decrease when accelerating from 0.250 s to 0.125 s. Given the transaction fee associated with publishing content, users cannot gain additional profits by rapid content publication in a short period. This demonstrates that the introduction of the hyperbolic tangent function in the user participation assessment algorithm successfully prevents rapid content publication attacks.  
In the PoAP consensus mechanism, the foundation for a maintainer to become a committee member or a proposer is predicated upon securing a substantial number of votes from users. Thus, there exists a potential vulnerability wherein malicious maintainers could conspire with users to amass a greater volume of votes than their counterparts. To counteract this threat, a cryptographic sortition algorithm is introduced during the committee election, significantly mitigating the risk associated with this type of attack. In the experimental setup, malicious maintainers collude with certain users within the NexoNet, where these conspiring users exclusively cast their votes for the target maintainer. To test the frequency with which the malicious maintainer is elected as a proposer, over 1000 rounds of consensus were conducted. For these tests, an election period length \(T_{election}=10\) is set.  
The test results are shown in Figure 11. Given that each maintainer can only be elected as a proposer once within each election period, this constrains the maximum number of times a committee member can be elected as a proposer to 100 over 1000 rounds of consensus. We contrast the scenario of electing the committee member with the highest votes as the proposer directly, without the use of cryptographic sortition algorithms, against the scenario where such algorithms are employed for elections. Theoretically, each maintainer should have an average opportunity to act as the proposer 50 times. When colluding with users with 15% total PV, a malicious maintainer elected directly as the proposer could be elected as a proposer approximately 70 times. This number could rise to approximately 90 when colluding with users with 35% total PV, nearing the theoretical maximum of 100 times. However, by using a cryptographic sortition algorithm into the committee election process, even collusion with users with 75% total PV would only allow an additional 30 chances to propose block, significantly mitigating the risk of collusion attacks against the PoAP consensus mechanism.  
Figure 10: The accumulation of transaction fee for launching rapid content publication attack.