# Secure Cryptographic Key Encapsulation and Recovery Scheme in Noisy Network Conditions
## 6 Experimental Results
This behavior is due to the minimal or zero collisions found in longer responses. Equation (1) explains how longer responses can tolerate higher noise levels without collisions. Consequently, key recovery can be performed more efficiently, increasing throughput for longer responses. At 50 percent noise, the response becomes almost random and indistinguishable from each other. Below 40 percent, the probability of collisions remains very low because longer responses are still distinguishable. These findings show the importance of response length selection when considering noise levels in the system. Shorter response lengths may be suitable in low-noise environments (where key recovery throughput remains efficient). On the other hand, longer response lengths are more advantageous in scenarios where noise levels are expected to be high, since they provide a greater degree of resilience and enable the successful recovery of keys despite the presence of significant noise interference. Figure 6 demonstrates the efficiency of the key recovery protocol in managing error correction under varying levels of injected noise. The vertical lines in the figure represent the levels of noise introduced into the system, illustrating the protocol's tolerance to high  
Figure 4: Comparative analysis of collision rates: model predictions vs. experimental results across different noise levels. The plot demonstrates the relationship between collision rates and varying noise levels where the black lines represent the theoretical model and the colored lines depict the experimental data for different values of parameter \(P\). percentages of noise. The curve plotted shows that the protocol rapidly corrects up to slightly more than 20 erratic bits, maintaining a latency of less than 2 to 3 s. However, when the noise level approaches slightly below 40%, the number of errors begins to exceed 20, which delays the key recovery process. This result is attributed to the searching mechanism discussed in Algorithm 2 which identifies the precise locations of errors. By streamlining the search process for key recovery, the system effectively bypasses the computationally intensive approach of \"brute force\" searching, which results in fast and accurate error correction even in the presence of high noise levels. Figure 5: Key recovery throughput. This bar graph highlights the rate at which keys are successfully recovered per second thus illustrating the impact of different response lengths and noise levels on recovery efficiency. Figure 6: Key recovery latency versus error count in noisy cryptographic environments. This plot demonstrates the protocol’s capacity to quickly correct a substantial quantity of errors found in the ephemeral key. It shows the efficiency of key recovery processes. The vertical bars represent the noise injection rate, illustrating how varying error rates impact the recovery latency. The red line represents the latency and the dots are the data points. Figure 7 illustrates the effect of noise injection on the failure rate in correctly identifying matches. Specifically, it highlights the frequency at which the system fails to pinpoint the matching position across all three lists (Onematch, Collisions, and Nomatch). Such failures result in unsuccessful key recovery attempts since the potential key combinations do not align with the correct key due to these errors. However, note that the plot shows the resilience of longer response lengths to errors, indicating their ability to maintain lower failure rates despite increasing noise levels.