Optical cryptosystem for reversible text-in-image hiding using weighted fractional Fourier transform, 4D Chen hyperchaos and DWT-SVD steganography

A reversible text-in-image cryptosystem is proposed by using the synergistic integration of optical encryption and robust digital steganography. The plaintext is converted into a cipher-image via the proposed L-Arnold scrambling, Weighted Fractional Fourier Transform (WFrFT)-enhanced double random phase encoding driven by a 4D Chen hyperchaotic system, and subsequently embedded into a cover image through semi-blind Singular Value Decomposition (SVD) in the Discrete Wavelet Transform (DWT) domain. The scrambled text matrix is encoded in both spatial and frequency domains, where the double random phase modulation is performed twice to enhance the security and unpredictability. Compared with conventional Fractional Fourier Transform (FrFT), the WFrFT introduces additional fractional orders, thereby significantly expanding the key space, while the semi-blind SVD approach reduces the side information required for extraction. The parameters in the L-Arnold transformation, the fractional orders in the WFrFT, and the initial values of the 4D Chen chaotic system are regarded as the keys in the proposed scheme. Extensive numerical simulations are made to test the validity and robustness of the proposed cryptosystem. Experimental results demonstrate that the system achieves 100% lossless text recovery with stego-image PSNR exceeding 42 dB, exhibits exceptional key sensitivity (decryption failure occurs with deviations of 10⁻⁶ in chaotic values or 10⁻⁵ in fractional orders), and maintains satisfactory resistance against JPEG compression (quality factor ≥ 70) and Gaussian noise attacks (variance ≤ 0.01).