Image encryption methods offer a significant means of safeguarding data during the secure transmission of information over public networks. Traditional ciphers often prove to be insufficient for large volumes of interconnected data, such as image data. Various image ciphers have been developed utilizing algebraic structures to address this issue. Most of these image ciphers involve substitution operations on algebraic structures. The study introduces a novel method that enhances the robustness and complexity of the image cipher by employing two finite local rings (Quasi-Galois rings and the ring \(\:{\mathbb{Z}}_{{2}^{16}}\) ) and a DNA sequence. We used Quasi-Galois rings to construct the S-boxes, which are used for substitution and permutation purposes. These S-boxes are generated by splitting the subgroup of the units of the ring into two subsets. One subset is constructed for the S-box used for substitution, while the other subset is mapped to a Galois field to construct an S-box used for the permutation process. The ring \(\:{\mathbb{Z}}_{{2}^{16}}\) is utilized by applying three linear transformations from the ring to permute the pixels, making the algorithm resistant to various attacks. Finally, DNA sequences are randomly applied to enhance the scheme’s robustness. The findings of the experiments show that the proposed cipher can swiftly generate images that resemble randomness and can withstand a variety of demanding security tests, such as differential attacks, NIST tests, and statistical measurements.
