Classification of Cipher Text by Clustering of S-Topological Rough Group

Rough set theory provides valuable tools for handling and analyzing ciphertext, making it a prominent asset in cryptographic applications. Its ability to manage uncertainty and reduce complexity can enhance various aspects of ciphertext management, from pattern recognition, classification to cryptanalysis and security checks. By imposing the principles of rough sets, cryptographic systems can become more robust, efficient, and secure. The fundamental nature of the symmetric group within the context of rough topological groups makes it a powerful tool in both theoretical and applied mathematics. Some cryptographic protocols and coding theories depend on the properties of topological rough symmetric groups for security and error detection or correction. This paper aims to generalize topological rough group structures and investigate their properties. Additionally, an algorithm is established to classify the symmetric group
$S_{n}$
, and experimental result is provided to explore the effectiveness of the algorithm. It provides practical tools for analyzing imprecise or incomplete data, benefiting fields such as medical diagnostics, economic forecasting, and geographical information systems.