# Secure Cryptographic Key Encapsulation and Recovery Scheme in Noisy Network Conditions
## 6 Experimental Results
#### Comparison with Other Works  
As illustrated in Figure 8, our methodology, R-KEM, demonstrates a significant enhancement in performance compared to the RBC protocol, as described in the works of [22; 24]. Similar to our approach, RBC is a CRP-based error detection and correction scheme implemented on the server side. However, while RBC relies on exhaustive search methods for key recovery, RBC_4 and RBC_8 incorporate a fragmentation approach that divides the key into n fragments, adds padding, and then proceeds with key recovery. As n increases, key recovery becomes faster; for instance, RBC_8 is relatively fast due to higher fragmentation. Nevertheless, increasing n further can compromise security, as attackers can more easily gain information about the key when the fragmented portions are smaller, making it easier to find a match. In contrast, the R-KEM protocol's advanced error correction capability is attributed to its innovative erratic position detection technique, which identifies the correct key faster without the need for fragmentation, even with a high number of errors. While RBC may be suited for servers with abundant computational resources, our approach is tailored to endpoint devices, which may be limited in computational power. This capability to effectively correct errors in noisy environments using average computing resources, without sacrificing security, distinctively positions our protocol as advantageous over conventional methods. Figure 7: The impact of noise levels on match detection failure. This plot illustrates how high noise levels contribute to the increased likelihood of failing to identify a matching position within ‘Collisions’ or ‘NoMatch’ lists (which leads to unsuccessful key recovery attempts). Notably, extending the response length tends to reduce these failure rates, thus enhancing the reliability of match detection (even in the presence of noise). Table 1 compares the search spaces needed for key recovery in RBC and R-KEM. The RBC search space is calculated using the binomial coefficient formula, which illustrates the combinatorial nature of RBC's error correction process for a space of 256 potential error positions. This search space represents the total number of unique pairs of error positions that RBC can process when correcting several errors. On the other hand, the R-KEM search space is derived from the formula based on the product of lengths of sublists (Equation (2)). This method reveals a consistently sized search space despite an increase in the number of errors that can be corrected. In the context of this comparison, each collision is considered equivalent to a single error, with the understanding that each collision involves the need to examine at least two positions. Therefore, when the table indicates that R-KEM is correcting for 15 errors, it is implied that a minimum of 30 positions require examination. The search space presented in the table reflects the minimum possible combinations, under the assumption that each collision involves only two positions to be checked. This highlights the efficiency of R-KEM in environments prone to high noise levels, where error susceptibility is greater. Such a robust error correction capability demonstrates R-KEM's potential for significantly improving reliability in adverse conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**RBC \# of Errors**} & **R-KEM \# of** & \multirow{2}{*}{**RBC Search Space**} & **R-KEM Search** \\  & **Collisions** & & **Space** \\ \hline
1 & 8 & 256 & 256 \\
2 & 15 & 32,640 & 32,768 \\
3 & 21 & 2,097,152 & 2,097,152 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of error correction capabilities and search space sizes for RBC and R-KEM protocols derived from theoretical formulas. Figure 8: Comparative analysis of latency in error correction: RBC protocol versus R-KEM protocol on a logarithmic scale. Note: in the R-KEM protocol, the number of errors represents the number of collisions (with each collision requiring correction of at least 2 positions).