# Secure Cryptographic Key Encapsulation and Recovery Scheme in Noisy Network Conditions
## 7 Discussion  
The analysis of the protocol shows its robustness and efficiency in key recovery, even in substantial noise interference, which is a common challenge in cryptographic systems operating within networks affected by poor coverage or jamming. Our results in collision rate and throughput illustrate how response lengths can be tailored to the demands of the application.  
The strength of our protocol lies in its error detection mechanism, which compares responses within a predefined search window. With longer responses, this approach significantly reduces collisions while providing valuable positional information about any mismatches. This, in turn, accelerates key recovery by eliminating the need for brute-force searching, requiring only a few bit-flipping corrections to reconstruct the original key.  
In terms of memory usage, at higher noise levels, longer responses consume less memory than shorter responses during the key recovery process. This is because longer responses result in fewer collisions, reducing the space required for searching the matching key. In contrast, shorter responses have a higher collision rate, necessitating more bit-flipping operations to identify the correct key, which in turn increases both memory consumption and processing time.  
With no noise, the scenario changes significantly. For shorter response lengths (below 64 bits), occasional collisions still occur due to the higher probability of generating identical responses. In this range, both time complexity and space complexity decrease as response length increases, since longer responses reduce collision rates and minimize the need for additional computations. However, beyond a certain response length, the complexity begins to increase. This is because, with longer responses, no errors are encountered, and the primary factor influencing computational cost becomes the length of the response itself. As a result, once collisions stop appearing in our key recovery protocol, both time and space complexity follow a linear growth of \(O(P)\).  
One limitation of our approach is that the error correction mechanism is specifically designed for CRP-based key encapsulation protocols. As a result, while our method effectively recovers cryptographic keys encapsulated using our scheme, it does not detect errors in conventionally transmitted data over standard communication channels. This specificity highlights the need for further evaluation in diverse real-world scenarios.  
While our simulated implementation has produced promising results, real-world deployment is essential for a more accurate assessment of performance. The findings presented in this paper offer valuable insights into expected outcomes and potential limitations in practical settings. However, deviations from our results are anticipated, particularly due to the unpredictable nature of noise in certain environments. In such cases, the protocol may not maintain performance at noise levels up to 40 percent as demonstrated here. This limitation, however, can be mitigated by increasing response lengths or adjusting other critical parameters that may prove influential during real-world implementation.