Dual-domain image encryption scheme based on fractional wavelet transform and hyperchaotic system

Abstract This paper presents a novel dual-domain encryption scheme that integrates hyperchaotic system with the fractional wavelet transform (FRWT). To enhance the security of the algorithm, a new two-dimensional cosine-coupled Logistic-Cubic mapping (2D-CLCM) is developed, which exhibits hyperchaotic characteristics across an extensive parameter range. By utilizing keys generated from plaintext-related SHA algorithm, the 2D-CLCM produces highly sensitive chaotic sequences for the encryption process. Improved scrambling and diffusion methods based on the FRWT are also proposed. Initially, a folded coding process is designed in the spatial domain, which decomposes the plaintext image into two smaller complex-valued images through pixel resampling and diagonal phase encoding. This process scrambles the image while reducing the computational load for subsequent stages. Next, the random phase mask is applied to perform FRWT decomposition on the complex-valued images. This step converts the images into the fractional wavelet domain, which helps in sparsifying and obscuring their pixel values. Finally, the proposed distribution-based diffusion method employs a uniform random matrix to conceal the distribution characteristics of the images' fractional wavelet coefficients, ultimately reconstructing the images into an encrypted form. Security analysis results demonstrate that the ciphertext images effectively resist various attacks. Compared to other methods in the experiment, the proposed algorithm excels in both security and efficiency.