Security enhancement of image encryption method based on Fresnel diffraction with chaotic phase

In the traditional image encryption methods based on Fresnel diffraction (FRT), the Fresnel diffraction distance and the wavelength of light are considered as two essential secret keys, named distance key and wavelength key, respectively. However, these two keys are both vulnerable to be attacked due to their low sensitivities, resulting in an inadequate intensity of secret key for several high-security applications. This is a common and serious problem in image encryption methods based on FRT. In this paper, a security-enhanced image encryption method based on Fresnel diffraction with chaotic phase (CPFRT) is proposed and verified, where CPFRT is an alternative algorithm of diffraction calculation that combines ordinary FRT with special phase generated by chaotic system. In such a way, the sensitivities of distance key and wavelength key could be substantially improved thanks to the nonlinear, pseudo-random, high sensitivity of initial value of chaotic phase, which effectively solves the previous common problem, contributing to an extremely high security of image encryption method meanwhile the number of secret keys is not increased. Moreover, computational simulations are performed to demonstrate the validity of the proposed security-enhanced image encryption method, and the results confirm that the proposed method has a substantially enhanced security in distance key and wavelength key, and the high quality of correct decrypted image could be successfully maintained. Furthermore, the proposed method based on CPFRT can also be applied to double-phase image encryption by replacing FRT with CPFRT. Analogously, the sensitivities of distance key and wavelength key in double-phase image encryption are also greatly improved, which leads to an outstanding anti-attack capability. In addition, the effectiveness of the proposed double-phase image encryption method based on CPFRT is also verified by rigorous computational simulation, and the proposed method based on CPFRT shows a promising potential for other image encryption methods in order to substantially enhance their securities.