# Reputation Consensus Mechanism for Blockchain Based on Information-Centric Networking
## 4 Design
### Hybrid Consensus Mechanism
#### 4.2.1 Reputation Consensus Mechanism
To balance these trade-offs and enhance system security and stability, we employ a reputation threshold based on principles from BFT consensus mechanisms [24]. Specifically, we set a threshold \(\theta\) (commonly \(\theta=\frac{2}{3}\)) to ensure that the cumulative reputation of the selected nodes represents a supermajority of the total reputation, thereby maintaining robustness even if up to one-third of the nodes are faulty or malicious. Figure 9: Temporal intervals in blockchain: block generation (\(T_{B}\)), checkpoint interval (\(T_{E}\)), and reputation update period (\(T_{R}\)). The threshold condition is expressed as:

\[\frac{R_{s}}{R_{\text{total}}}=\frac{\sum_{i=1}^{N_{\text{s}}}R_{i}}{\sum_{j=1}^{N _{\text{R}}}R_{j}}\geq\theta, \tag{10}\]

where:

* \(R_{s}\) is the total reputation of the \(N_{\text{s}}\) selected nodes;
* \(R_{\text{total}}\) is the total reputation of all \(N_{R}\) candidate nodes;
* \(N_{R}\) is the total number of candidate reputation nodes competing for selection as checkpoint proposers;
* \(R_{i}\) and \(R_{j}\) are the reputation scores of the selected nodes and candidate nodes, respectively. Equation (10) specifies that, to ensure network fairness, the cumulative reputation of the nodes selected during each reputation consensus period \(T_{R}\) must constitute at least a fraction \(\theta\) of the total reputation. Assuming the average reputation of the selected nodes is \(\overline{R}_{s}=\frac{R_{s}}{N_{\text{c}}}\), we can rearrange Equation (10) to solve for the minimum number of selected nodes \(N_{\text{s}}\):

\[\frac{N_{\text{s}}\times\overline{R}_{\text{s}}}{R_{\text{total}}} \geq\theta,\] \[N_{\text{s}} \geq\frac{\theta\times R_{\text{total}}}{\overline{R}_{s}}. \tag{11}\]

Since \(T_{R}=N_{\text{s}}\times T_{E}\) from Equation (9), we can express the minimum reputation update period \(T_{R_{\text{min}}}\) as:

\[T_{R_{\text{min}}}=N_{\text{s}}\times T_{E}\geq\frac{\theta\times R_{\text{ total}}}{\overline{R}_{s}}\times T_{E}. \tag{12}\]

Substituting \(T_{E}=N_{\text{c}}\times T_{B}\):

\[T_{R_{\text{min}}}\geq\frac{\theta\times R_{\text{total}}}{\overline{R}_{s}} \times N_{\text{C}}\times T_{B}. \tag{13}\]

For \(\theta=\frac{2}{3}\), \(N_{\text{C}}=32\), and \(T_{B}=12\) s, the minimum reputation update period becomes:

\[T_{R_{\text{min}}}\geq\frac{2}{3}\times\frac{R_{\text{total}}}{\overline{R}_{ s}}\times 32\times 12\text{ s}. \tag{14}\]

By ensuring that \(T_{R}\) meets or exceeds \(T_{R_{\text{min}}}\), we maintain a high level of trust and security in the system, even in the presence of faulty or malicious nodes. This approach balances the trade-offs between network efficiency, fairness, and security, aligning with the principles of BFT consensus mechanisms. #### 4.2.3 Fork Choice and Finality

This study adopts the LMD GHOST protocol for fork choice. Ordinary validators verify the legitimacy of checkpoint proposers' reputation values by combining on-chain staking data and verification from trusted third-party institutions and subsequently validate checkpoint blocks. When a checkpoint block receives support and approval from more than two-thirds of validators, the checkpoint is considered justified. According to the Casper FFG protocol, if a justified checkpoint \(A\) is followed by another justified checkpoint \(B\) in subsequent epochs, then checkpoint \(A\) is finalized. ## 5 Security and Incentive Analysis

### Security Analysis

In this study, we propose a multidimensional reputation evaluation model that integrates both on-chain stake and network contribution, aiming to mitigate potential malicious behaviors by reputation nodes. When a reputation node exhibits dishonest behavior, its reputation score is reset to zero, the node is blacklisted, and all funds staked by the node in the blockchain are confiscated. This rigorous punitive mechanism effectively deters malicious activities and safeguards the security and stability of the network.