Generating visually coherent encrypted images with reversible data hiding in wavelet domain by fusing chaos and pairing function

For secure transmission of digital images, existing cryptographic algorithms transform coherent visual information into a noise-like appearance prompting an adversary of the presence of a possible cipher. This paper proposes an algorithm that produces a visually coherent and meaningful cipher image. The proposed algorithm consists of a permutation-substitution subroutine to obtain a partial cipher. The Arnold-3D map does the permutation, and a delayed logistic map performs the substitution in this subroutine. The hiding of this partial cipher is done in the reference image using an integer wavelet transform. The pixels of the partial cipher are embedded in the four sub-bands of the decomposed reference image as 4 to 1-pixel encoding using Cantor-like pairing function. In addition to the lossless encryption scheme, the integer nature of all the sub-bands in the wavelet decomposition and the invertible pairing function facilitates the perfect reconstruction of the reference image. One of the significant novelty of this work lies in the subtle use of simple pairing functions, which prohibits the unnecessary increase in the size of the cipher, thereby reducing the storage and transmission costs.