Reversible data hiding in encrypted images using chaos theory and Chinese Remainder Theorem

Reversible data hiding in encrypted images (RDHEI) has recently garnered attention for embedding secret data within anonymized images, overcoming the spatial-correlation dependency of traditional RDH methods. In particular, this paper introduces a new RDHEI scheme based on chaos theory and Chinese Remainder Theorem (CRT). Initially, the host image is encrypted using a chaos-based symmetric cipher that adheres to strong cryptographic principles and demonstrates robust security features. Next, bits from the secret image are XORed with a random bit sequence generated by a chaotic function, initiated by a data-hiding key. Subsequently, a new data embedding method, based on pixel fusion and the CRT, is introduced. This data-hiding and encoding process, which incorporates two encrypted image bytes and one secret image bit, maintains a consistent embedding capacity of 0.5 bits per pixel (BPP), independent of the host image's complexity, while ensuring reversibility. At the receiving end, both the original host image and the embedded secret data can be flawlessly recovered. Furthermore, the proposed scheme enables extraction of the secret image based solely on the data-hiding key, without necessitating the decryption key, thereby achieving the method's semi-separability property. Experimental results indicate that the proposed scheme, which offers a fixed embedding capacity and induces only a minimal increase in the watermarked-to-original image size ratio (WOSR), upholds essential theoretical values necessary for encryption and withstands common cryptographic attacks. Moreover, as a fully reversible and semi-separable technique, the proposed scheme demonstrates both feasibility and efficiency in data hiding, surpassing several state-of-the-art methods in certain performance metrics.