Multi-image encryption algorithm based on three-dimensional simplified quadratic sine map and global index swizzle

Abstract Aiming at the problems of low scrambling dimension, complex diffusion mechanism and weak anti-exploit competency in multi-image encryption, this paper proposes a multi-image enctyption algorithm based on three-dimensional simplified quadratic sine map (3D-SQSM) and three-dimensional coordinate matrix. First, a new 3D-SQSM chaotic system is designed, and its strong chaotic characteristics and high stochasticity in a wide parameter interval are verified by bifurcation diagram, Lyapunov exponent, 0–1 test and NIST stochastic test. Second, a global scrambling mechanism based on three-dimensional coordinate matrix is proposed: stack multiple images into a three-dimensional matrix, take advantage of the chaotic sequence generated by 3D-SQSM to construct a three-dimensional coordinate point set, and generate a three-dimensional index matrix through global dictionary order sequencing, so as to realize the cross-image and cross-dimensional global reflow of picture element positioning. Subsequently, in the diffusion stage, multi-channel XOR Actions based on chaotic sequences are adopted, combined with the SHA-256 hash function to generate a secret key strongly related to the plaintext, ensuring that the algorithm has strong resistance to chosen-plaintext exploit. Simulation studies and security analysis demonstrate that the proposed method possesses a sufficiently large key space, exhibits high sensitivity to minor key variations, achieves uniform distribution in the histogram of encrypted images, reduces the correlation between neighboring pixels to near zero, attains entropy values approaching the theoretical maximum of 8, and yields NPCR and UACI values close to their ideal benchmarks. Furthermore, it demonstrates strong resilience against cropping and noise attacks. These experimental findings confirm the algorithm’s superior performance in terms of cryptographic security, key sensitivity, and attack resistance, offering an effective and dependable approach for secure multi-image transmission.