Abstract
Modern block ciphers deal with the development of security mechanisms to meet the security needs in several fields of application. The substitution box, which is an important constituent in block ciphers, necessarily has sufficient cryptographic robustness to counter different attacks. The basic problem with S-box design is that there is no evident pattern in its cryptographic properties. This study introduces a new mathematical algorithm for developing S-box based on the modular group coset graphs and a newly invented mathematical notion "matrix transformer". The proficiency of the proposed S-box is assessed through modern performance evaluation tools, and it has been observed that the constructed S-box has almost optimal features, indicating the effectiveness of the invented technique.