Matrix-based cryptography: The characteristic product

For many years, the need to store information and data has been a fundamental challenge for human society, driving the development of various systems to meet this requirement. In this study, we focus on the encryption and decryption of soft sets, aligning with their specific representations. To achieve this, we employ the Rijndael algorithm and extend it by introducing encryption and decryption algorithms that utilize the characteristic multiplication of soft matrices. The proposed methods were tested on several examples, and the experimental results confirm that the plaintexts are securely encrypted and accurately recovered without any loss of information. These results demonstrate the effectiveness and reliability of the proposed approach. Moreover, the proposed approach highlights the flexibility of soft matrices in handling sensitive and uncertain data, thereby providing a mathematically robust foundation for cryptographic applications.