An image compression encryption based on the semi-tensor product and the DFT measurement matrix

Abstract

As the volume of image data increases, optical image encryption algorithms often require more time and space to operate. To solve the problem, compression is generally used, and compressed sensing algorithms are among the most frequently used compression algorithms recently. However, most existing compressed sensing algorithms suffer from low reconstruction quality and large measurement matrix size. To address this issue, we proposed a novel compression encryption scheme using the semi-tensor product, DFT (discrete Fourier transform) measurement matrix, and cascaded diffraction system. When the amount of image data grows, the key space grows according to the factorial growth rate without an upper limit, making brute-force attacks virtually impossible. Compared with algorithms without using a semi-tensor product, the storage space shrinks to one-fourth of its original size. Experiment results proved better reconstruction quality compared with existing compressed sensing algorithms. Furthermore, our approach is robust against various attacks, which is validated through rigorous testing.