## 3 Trust-Optimized 6G-IoT Framework
### Trust Management System  
The TEO-IoT introduces a new trust management system where the trust score is calculated based on a combination of traditional metrics, such as historical behavior, data integrity, and security compliance, with contextual reliability, interaction consistency, and predictive stability. These integrated parameters show the development of a flow in the trust evaluation mechanism as shown in Algorithm 1. ```
Input: Historical data \(\mathbf{X}_{i}(t)\), Data integrity \(\mathbf{D}_{i}(t)\), Security compliance \(\mathbf{S}_{i}(t)\), Context vector \(\mathbf{Z}_{i}(t)\), Device interaction \(\mathbf{y}_{i}(t)\), Predicted state \(\hat{\mathbf{X}}_{i}(t+\Delta t)\), Actual state \(\mathbf{X}_{i}(t+\Delta t)\) Output: Trust score \(\tau_{i}(t)\), Resilience \(\mathbf{R}(t)\), Security level \(\mathbf{S}(t)\)
1 Initialize parameters \(\alpha_{1}\), \(\alpha_{2}\), \(\alpha_{3}\), \(\alpha_{4}\), \(\alpha_{5}\), \(\alpha_{6}\), and weighting factors \(\alpha_{7}\), \(\alpha_{8}\), \(\alpha_{9}\);
2 Step 1: Trust Score Calculation
3 Calculate trust score \(\tau_{i}(t)\) using (13);
4 Calculate contextual reliability \(\mathbf{C}_{i}(t)\) using (14);
5 Calculate interaction consistency \(\mathbf{I}_{i}(t)\) using (15);
6 Calculate predictive stability \(\mathbf{P}_{i}(t)\) using (16);
7 Step 2: Maintaining Resilience and Robustness
8 Update resilience state \(\mathbf{R}(t)\) using (17);
9 Update predictive failure model \(\mathbf{F}_{i}(t)\) using (18);
10 Step 3: Security Protocols
11 Calculate integrity score \(\mathbf{D}_{i}(t)\) using (19);
12 Update compliance score \(\mathbf{S}_{i}(t)\) using (20);
13 Compute overall security level \(\mathbf{S}(t)\) using (21);

#### 3.2.1 Trust Score Calculation

The trust score \(\tau_{i}(t)\) for the \(i\)-th device is computed by aggregating multiple components, each reflecting different aspects of the device's behavior and network interactions. The fundamental equation is

\[\tau_{i}(t) =\alpha_{1}\mathbb{E}\Big{[}\mathbf{w}^{\top}\mathbf{X}_{i}(t) \Big{]}\] \[\quad+\alpha_{2}\mathbf{D}_{i}(t)+\alpha_{3}\mathbf{S}_{i}(t)\] \[\quad+\alpha_{4}\mathbf{C}_{i}(t)+\alpha_{5}\mathbf{I}_{i}(t)+ \alpha_{6}\mathbf{P}_{i}(t), \tag{13}\]

where \(\mathbf{C}_{i}(t)\) denotes contextual reliability, \(\mathbf{I}_{i}(t)\) represents interaction consistency, and \(\mathbf{P}_{i}(t)\) captures predictive stability. The weighting factors \(\alpha_{1}\) to \(\alpha_{6}\) in Equation (13) define the relative significance of components contributing to the trust score, including historical behavior, data integrity, security compliance, contextual reliability, interaction consistency, and predictive stability. These values are determined empirically using techniques such as optimization algorithms (e.g., grid search) or sensitivity analysis to ensure balanced contributions. Initial values are guided by domain expertise and refined through iterative validation to align with specific application requirements. Contextual reliability \(\mathbf{C}_{i}(t)\) is evaluated using the conditional probability:

\[\mathbf{C}_{i}(t)=\mathbb{P}(\mathbf{X}_{i}(t)\mid\mathbf{Z}_{i}(t)), \tag{14}\]

where \(\mathbf{Z}_{i}(t)\) is the context vector, including environmental factors and device-specific attributes. The interaction consistency \(\mathbf{I}_{i}(t)\) is modeled by a temporal correlation function:

\[\mathbf{I}_{i}(t)=\int_{0}^{t}\rho(\mathbf{y}_{i}(\tau),\mathbf{y}_{i}(\tau- \Delta t))e^{-\beta(t-\tau)}d\tau, \tag{15}\]

where \(\rho(\cdot,\cdot)\) measures the correlation between interactions over a time lag \(\Delta t\), and \(\beta\) is a decay factor. Predictive stability \(\mathbf{P}_{i}(t)\) is assessed using a machine learning prediction model:

\[\mathbf{P}_{i}(t)=\mathbb{E}\Big{[}\big{(}\hat{\mathbf{X}}_{i}(t+\Delta t)- \mathbf{X}_{i}(t+\Delta t)\big{)}^{2}\Big{]}, \tag{16}\]

where \(\hat{\mathbf{X}}_{i}(t+\Delta t)\) is the predicted state vector, and \(\mathbf{X}_{i}(t+\Delta t)\) is the actual state vector.