# Reputation Consensus Mechanism for Blockchain Based on Information-Centric Networking
## 4 Design
### Reputation Model
#### 4.1.2 Reputation Processing  
Reputation Value Correction  
To effectively manage new nodes and the dynamic changes in their reputation values, we introduce a correction mechanism based on the Logistic Growth Model [40]. This mechanism ensures that new nodes experience slower reputation growth initially, preventing them or potential malicious nodes from quickly gaining disproportionately high reputation through minimal normal behavior, thereby increasing the cost of Sybil attacks. Over time, nodes with consistent good performance will see accelerated reputation growth, encouraging sustained high-quality behavior. Once a node's reputation reaches a high level, the growth rate stabilizes, ensuring only consistently high-performing nodes maintain elevated reputation, contributing to network stability and trustworthiness.  
The reputation correction uses the logistic growth function:  
\[f(t)=\frac{L}{1+e^{-k(t-t_{0})}},\]  
And its discrete form becomes:  
\[f(n)=\frac{L}{1+e^{-k(n-n_{0})}},\]  
where:  
* \(L\) : The theoretical upper limit of the reputation value, set to 1.
* \(e\) : The base of the natural logarithm.
* \(k\) : Parameter determining the growth rate.
* \(t\) : Time or another cumulative behavior-related metric; \(n\) is the number of completed reputation update cycles by time \(t\).
* \(t_{0}\) : The inflection point where the reputation value reaches half of its maximum; \(n_{0}\) is the number of completed reputation update cycles by time \(t_{0}\).  
This correction ensures that reputation growth aligns with actual performance, promoting a fair and stable network environment.  
Reputation Value Update  
To better reflect recent behaviors' impact on reputation, we introduce a decay mechanism based on the Ebbinghaus forgetting curve [41].  
This mechanism adjusts the influence of historical behavior on reputation, emphasizing recent performance. The forgetting curve is expressed as:  
\[\sigma=e^{-\lambda T_{R}},\]  
where:  
* \(\sigma\) is the memory retention rate.
* \(\lambda\) is the forgetting rate controlling decay speed; the larger \(\lambda\), the faster the decay.
* \(T_{R}\) is the reputation update period.  
This ensures that reputation dynamically reflects behavioral changes over time. The update mechanism is:  
\[\begin{split} R(n)&=\sigma\cdot R(n-1)+f(n)\cdot \Delta R(n)\\ &=e^{-\lambda T_{R}}\cdot R(n-1)+\frac{L}{1+e^{-k(n-n_{0})}}\cdot \Delta R(n).\end{split} \tag{6}\]  
Equation (6) represents the complete reputation update formula for a node. It is formulated by summing the decayed historical reputation \(R(n-1)\) and the reputation increment \(\Delta R(n)\) accrued during the update period, where the increment is adjusted by a logistic correction. If we assume constant increments \(\Delta R(n)=\Delta R\) and no behavioral deterioration, as \(n\rightarrow\infty\), the reputation correction function \(f(n)\to L=1\), and the reputation \(R(n)\) converges to:  
\[\begin{split} R_{\infty}&=\lim_{n\rightarrow\infty }R(n)=e^{-\lambda T_{R}}\cdot R_{\infty}+\Delta R\\ &=\frac{\Delta R}{1-e^{-\lambda T_{R}}}.\end{split} \tag{7}\]  
This formula provides the steady-state convergence value, where \(\Delta R\) controls the increment per cycle, and \(\lambda\) and \(T_{R}\) control the decay speed. Adjusting these parameters affects the equilibrium point and convergence speed, influencing the final reputation score.  
This decay mechanism ensures the system considers both recent and historical behaviors, encouraging continuous good conduct and improving fairness and timeliness.