S-Boxes Generation Using Chaotic Maps without Fixed Points

As society increasingly depends on digital technology, the need to protect (encrypt) multimedia transmissions has grown substantially. Cryptography, which involves encoding information through secret codes or transformations, has evolved from early mechanical methods to advanced mathematical techniques. In this study, we analyze the properties of several families of linear discrete mappings and investigate their potential applications in encryption schemes, particularly for substitution box (S-box) generation. These mappings exhibit chaotic behavior over certain intervals, making them suitable for cryptographic applications. Based on the results of the Strict Avalanche Criteria (SAC) and the Bit Independence Criterion (BIC) tests, the cryptographic performance of the generated S-boxes appears promising.