Fractal–Chaos-Based Controllable Compressive Sensing and Adaptive Matching Embedding for Multi-Image Encryption and Concealment

In this paper, a multi-image encryption and hiding scheme based on controllable compressive sensing and adaptive matching embedding is proposed. The highlights of this scheme include the use of adaptive data segmentation, controllable integer compressive sensing, and adaptive matching embedding. Firstly, a 512-bit master key, together with an HMAC-SHA512-based session key derivation mechanism incorporating plaintext hashes and random noise, is used to initialize the proposed Fractal–Chaos Hybrid Map—a novel chaotic system combining the Lorenz system with Mandelbrot fractal perturbations. This produces high-quality random sequences with superior randomness and a large key space. Secondly, the scheme applies DCT and adaptive data segmentation to process the plain images. The sparse data obtained from segmentation is compressed using a sensing matrix generated from random sequences, and then encoded and encrypted via random flipping. Finally, the adaptive matching embedding technique is used to embed the encrypted data into the carrier image. The proposed scheme performs excellently in both the compression encryption of plain images and the embedding of encrypted data into the carrier image. It supports the encryption and hiding of up to six plain images with an acceptable trade-off between embedding capacity and carrier image quality. A comprehensive security analysis, including statistical and differential attack evaluations, confirms the scheme’s strong resistance to various cryptographic threats while maintaining high efficiency.