Modern cryptographic systems use substitution boxes (S-boxes) throughout the encryption process to enhance the security of the plaintext. The integrity of the communication process is ensured by these S-boxes, which are vital in converting the ciphertext back into the original plaintext during the decryption phase. The cryptographic strength of a certain S-box has a substantial impact on the overall security of a given cipher. As a result, many researchers have used innovative construction techniques to create robust S-boxes. The method used in this paper is a novel combination of a specific map on the direct product of cyclic groups of order and an inversion map of a Galois field with order 256. This strategy aims to produce dynamic S-boxes. The proposed method can produce a large number of strong S-boxes by making little changes to the map’s parameters. Four S-boxes were created and their performance was analyzed using industry standards such as bijectivity, the strict avalanche criterion (SAC), nonlinearity (NL), the bit independence criterion (BIC), linear probability (LAP), and differential probability (DAP). The performance of the recommended S-boxes was compared to that of state-of-the-art S-boxes to show their efficacy. The proposed S-box also exhibits considerable potential as a candidate for modern cryptosystems aiming at securing multimedia information, as shown by a suggested method for protecting the privacy of digital images using it. The effectiveness of the encryption method was then assessed using several tests including contrast, correlation, homogeneity, entropy, energy, Number of Pixel change rate (NPCR), and Unified Average changing intensity (UACI). We observed the efficacy of the suggested method for image encryption by comparing our results with different methods.