## 6 Conclusions  
This research presents an approach to the parallel generation of rainbow tables using the Message Passing Interface standard. The proposed approach is based on a modified master-slave model, where each process independently generates starting points, and the master process resolves chain conflicts. Our implementation achieves significant im \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Aspect** & **Our Work (This Paper)** & **[PERSON] et al. [37]** & **[PERSON] [10]** & **[PERSON] et al. [38]** \\ \hline \multirow{3}{*}{Problem Addressed} & \multirow{3}{*}{\begin{tabular}{c} High inter-process communication \\ \end{tabular} } & Long time required to generate rainbow tables and search them & Long time required to generate rainbow tables & Inefficiency in the precomputation phase of rainbow tables related with chain discarding \\ \hline \multirow{3}{*}{Parallelization Model} & \begin{tabular}{c} Modified master-slave \\ (start points generated \\ independently) \\ \end{tabular} & Not mentioned & \begin{tabular}{c} Classic master-slave \\ (master assigns tasks to \\ slaves) \\ \end{tabular} & Not mentioned \\ \hline \begin{tabular}{c} Number of Computing \\ Nodes/CPU Cores \\ Used \\ \end{tabular} & 15 nodes & 32 CPU cores & 201 nodes (1 master, 200 slaves) & 5 nodes on a personal computer \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} Performance \\ Improvement \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} Near-linear speedup \\ (efficiency: 95-99\%) \\ \end{tabular} } & Significant reduction in execution time (from 6 years to around 6 days) & Significant reduction in execution time (from 7.14 days to 46.45 min) & 2.56 times faster \\ \hline \multirow{3}{*}{Execution Time} & \multirow{3}{*}{41.73 min} & \multirow{3}{*}{\(\sim\)6 days} & \multirow{3}{*}{\(\sim\)46.45 min} & \multirow{3}{*}{Not mentioned} \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of comparative analysis. provements in performance and efficiency. The reduction in inter-process communication compared to traditional approaches enhances scalability and execution speed, as demonstrated through experimental evaluations. The experimental evaluation is composed of three experiments. In the first experiment, we evaluated the parallel performance for four cryptographic hash functions (SHA-256, SHA-512, MD5 and NTLMv2), achieving near-linear speedup and maintaining efficiency between 95% and 99% across different numbers of computing nodes. This demonstrates the scalability and robustness of the implementation, even for computationally demanding functions like SHA-512. The second experiment highlighted the scalability of the implementation by varying the number of processed chains from 100 to 100,000. The results revealed that the execution time increases with larger workloads, with SHA-512 exhibiting the highest computational cost due to its complexity. In the third experiment, we analyzed the influence of chain length on execution time. The findings showed that longer chains significantly increased execution times, with SHA-512 once again showing the steepest growth, while MD5 and NTLMv2 had relatively lower computational overhead. In addition, the study acknowledges certain limitations, including the absence of a chain regeneration mechanism and constraints imposed by the available computing infrastructure. It is important to note that our implementation could be extended to longer and more complex passwords by adjusting the reduction function and search space size. Obviously, this would require additional computational resources due to the exponential increase of the search space. Overall, the proposed approach contributes a practical and efficient solution to the computational demands of rainbow table generation, advancing the field of cryptanalysis and password recovery.