An improved Bülban map and its application in multiple image encryption

Abstract

This article proposes a hybrid satellite image encryption algorithm integrating a modified 1D Bülban chaotic map, a Chinese Go-inspired permutation, and Deoxyribonucleic Acid-based encoding. The Bülban variant adds a sinusoidal perturbation to widen chaotic regions and heighten plaintext and key sensitivity for lightweight, high-entropy key-streams suited to on-board constraints, the Chinese Go permutation utilizes movement and capture logs to remap pixel coordinates in a manner dependent on both the key and plaintext. This effectively breaks the long-range spatial structures typical of satellite imagery, and Deoxyribonucleic Acid encoding supplies per-byte rule variability to strengthen diffusion with low computational cost. Security analysis demonstrates exceptional performance: near-ideal entropy (


$$\approx 7.99$$


≈
7.99




), near-zero pixel correlation, and strong differential resistance with number of pixel change rate and unified average changing intensity values of


$$99.5927\%$$


99.5927
%




and


$$29.27038\%$$


29.27038
%




, respectively. The algorithm also achieves a massive key space of


$$2^{478}$$


2
478




, exhibits robustness to occlusion and noise attacks, and allows for lossless decryption (Structural Similarity Index Measure = 1). With an encryption time of 1.469 seconds for each of the images in a


$$256\times 256 \times 256$$


256
×
256
×
256




pixels image cube, the proposed algorithm balances high security with practical efficiency for satellite imaging pipelines.