Security-enhanced multiple-image encryption based on quick response codes and modified double random phase encoding in the fractional Fourier transform domain

A security-enhanced multiple-image encryption method is proposed based on quick response (QR) codes and modified double random phase encoding (DRPE) in the fractional Fourier transform (FrFT) domain in this paper, where each plaintext is first converted into QR code, and then each QR code is employed to generate the corresponding binary key for decryption with the help of random binary plaintext (RBP). Subsequently, the used RBP is encrypted into noise-like ciphertext by using the modified DRPE in the FrFT domain. In the modified DRPE method, the first random phase mask is activated by the initial FrFT with chaotic phase, and the wavelength of light and the fractional orders as well as the focal lengths of lenses are all used as digital keys to expand the key space. Moreover, the sensitivities of these digital keys are extremely high because the digital keys are closely mapped with the initial values of the chaotic system in the encryption process, which contributes to an extremely high security of the multiple-image encryption method. Furthermore, the high feasibility and strong robustness of the proposed security-enhanced multiple-image encryption method are also demonstrated by using computational simulations.