A novel approach for designing secure substitution boxes based on Catalan number and elliptic curve

While using the internet, sending confidential emails, or dealing with financial information that affects many aspects of our everyday life, security is one of the most important considerations. We can prevent illegal access to our data with the aid of security. Cryptography is one of the methods used for encryption and decryption in this context to safeguard data. The S-box is the most important and the sole nonlinear component of any cryptographic algorithm that adds uncertainty to the data. Based on the combination of the Catalan number and the elliptic curve, the proposed method constitutes a unique algorithm. The strength of S-boxes is then assessed using nonlinearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities. Performance studies show that the proposed S-boxes have exceptional functionality and can give cryptosystems a significant amount of nonlinearity. Furthermore, the comparison shows that the newly proposed S-boxes offer enhanced security features in contrast to other S-boxes that are already in use literature.