# Enhancing Visual Data Security: A Novel FSM-Based Image Encryption and Decryption Methodology
Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 01008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON]  
2 Department of Artificial Intelligence Technologies, Faculty of Information Technologies, L.N. Gumilyov Eurasian National University, Astana 010008, Kazakhstan; [EMAIL_ADDRESS] (A.K.) [PERSON] protective measure for data, whether stored within a computer system or transmitted across the Internet. The crux of any encryption lies in the encryption key, which is classified into public and private keys [4]. Both keys are integral to the processes of encryption and decryption, with public keys accessible to all, while private keys necessitate strict confidentiality. The strength of encryption is directly proportional to the key size [5], rendering the decryption of data progressively more formidable with larger key sizes. The decryption process involves the conversion of encrypted text into a readable and comprehensible form by employing the requisite codes or keys manually. The absence of the secret key poses a formidable challenge to decoding data, ultimately yielding the original text post-decryption. In the domain of cryptography, automata theory finds varied applications. Deterministic finite automaton (DFA) [6], a branch of the Theory of Computation grounded in Automata, generates a unique encoded string for every given string character input. The terms \"deterministic\" and \"uniqueness of computation\" are synonymous in this context. Non-deterministic finite automata, on the other hand, permit zero, one, or multiple transitions from one state to another for a comparable input symbol. If S represents a non-empty collection of k, j, l states, the outcome is an element of S for deterministic automata and a subset of S for non-deterministic automata. Consequently, a finite state machine (FSM) functions as an algorithm characterized by a fixed count of states and transitions. This methodology is presently extensively employed in cryptography for data encoding, ensuring the preservation of data privacy. In cryptography, there are three main groups of methods. These methods represent different approaches to cryptography, utilizing various principles and techniques for securing information and communication. The Vernam Cipher focuses on perfect secrecy through one-time pad usage [7], finite automaton public key cryptosystems involve computational models for key generation [8], and cellular automata may find applications [9] in certain cryptographic processes. The Vernam Cipher, also known as the one-time pad, is a symmetric key algorithm where the key is as long as the message and is completely random. The key is used only once, making it theoretically unbreakable if used correctly. It operates by combining each character of the plaintext with a corresponding character in the key using modular addition.