Cryptography using Automata Theory

Encryption and decryption are the two most crucial components of cryptography. Data protection is the main objective of both systems. We utilised encryption to transform plain text into ciphertext. Decryption, which works the other way around from encryption, is the process of converting encrypted text back into plain text. By using a finite state machine and the LU decomposition method, the created encryption solution ensures data secrecy for safe communication. In our suggested approach, we additionally employ lower and upper triangular matrices, which are obtained by decomposing a square matrix. During encryption, the key will be a lower triangular matrix modulated by a prime number, and during decryption, an upper triangular matrix modulated by a prime number. The tactic is beneficial. This tactic is helpful in sectors such as finance and military services where confidential material must be delivered