Constructing S-boxes with strong cryptographic properties is critical to the security and effectiveness of modern cryptographic systems. We develop an 8×8 S-box by compounding the two-dimensional Hénon map with a one-step Baker map. We iterate the Hénon map 256 times, normalize \((x,y)\) to \([0,1]^2\) , apply one Baker step to intensify mixing, sort to obtain a permutation, and refine it via a lightweight hill-climbing swap strategy. As applications, we assess robustness using standard criteria—nonlinearity (NL), strict avalanche criterion (SAC), bit independence criterion (BIC), linear probability (LP), and differential probability (DP), and validate the S-box within an image encryption scheme on standard grayscale images (Lena, Baboon, Cameraman). Comparative analysis against S-boxes shows that the proposed S-box is cryptographically robust and suitable for integration into contemporary systems. Our best results are as follows: ciphertext entropy 7.9969–7.9972; adjacent-pixel correlations \(-0.00575\) to 0.00108; contrast 10.4519–10.5350; energy 0.01564–0.01565; homogeneity 0.3891–0.3895; and SAC = 0.4968; BIC-NL = 103.7; BIC-SAC = 0.5007; LP = 0.14062; DP = 0.0469 with Boolean-function nonlinearity 108–110.
