# Secure Cryptographic Key Encapsulation and Recovery Scheme in Noisy Network Conditions
## 6 Experimental Results  
This section presents the outcomes of our experiments conducted on a 12 th Generation Intel(r) Core(tm) i7-12700K processor operating at 3600 MHz featuring 12 cores and 20 threads. The system is equipped with 32 GB of RAM and runs on Windows 11. For each response length and noise level, the protocol was executed 10,000 times to collect data. Random noise in the responses was simulated using random sampling and a normal distribution to introduce variability into each response. Key performance metrics--such as collision rate, key recovery latency, key recovery throughput, and failure rate--were recorded. These metrics were evaluated across various noise levels and different values of the parameter \(P\) to assess the protocol's resilience and efficiency under various conditions. Furthermore, increasing the length of \(P\) leads to improved performance, particularly in handling higher levels of noise. As the response length is extended, the protocol becomes more resilient to noise-induced errors and maintains successful key recovery at increasingly higher noise levels. This suggests that longer response lengths enhance the protocol's overall performance and reliability, enabling effective operation, even in noisy environments. Figure 4 compares the theoretical model depicted in Equation (1) with the empirical data collected from our experiments. This comparison assesses the alignment between the theoretical predictions and the observed performance under different noise levels and response lengths. The experimental data closely align with the model's predictions, which shows a significant correlation between the two. This alignment can be attributed to the use of a random number generator for simulating noise injection within the protocol. However, it is important to note that actual noise conditions might exhibit variations from the model due to the complex nature of physical phenomena and experimental environments. The results demonstrate that longer responses exhibit greater resilience to higher noise levels because there is less likelihood of finding exact same responses, which reduces collision rates. The close match between the theoretical and experimental  
Figure 3: Reduction in error rates following enhancement across various response lengths. This preliminary enhancement step significantly lowers error rates, particularly in instances with initially high error counts, thereby streamlining the key recovery process. Without this crucial enhancement, cases with large error quantities might be deemed infeasible for key recovery due to the excessive computational effort required to sift through numerous possible key combinations. The red line represents \(y=x\). Dots on the line indicate no difference in error rate before and after the enhancement, while dots below the red line represent a lower error rate after the enhancement. results validates the effectiveness and accuracy of our model in predicting the protocol's performance. Furthermore, this graph provides valuable insights for configuring the system based on specific use cases and environmental conditions. By analyzing the relationship between noise levels and collision rates, we can determine the optimal response length to balance performance and resource constraints. Figure 5 depicts the key recovery throughput measured in keys-per-second across different noise levels and response lengths (\(P\)). As anticipated, the bar graph reveals a clear relationship between the noise level and the effectiveness of key recovery for varying response lengths. As the noise level increases, the shorter response lengths show decreased capability in recovering keys, resulting in reduced efficiency. This observation aligns with expectations since shorter response lengths are more susceptible to the adverse effects of noise interference and higher error rates. However, it is noteworthy that, even with higher noise levels, longer response lengths can still remain effective for key recovery until the threshold reaches slightly above 40 percent noise.