Double Image Encryption System Using a Nonlinear Joint Transform Correlator in the Fourier Domain

In this work, we present a new nonlinear joint transform correlator (JTC) architecture in the Fourier domain (FD) for the encryption and decryption of two simultaneous images. The main features of the proposed system are its increased level of security, the obtention of a single real-valued encrypted signal that contains the ciphered information of the two primary images and, additionally, a high image quality for the two final decrypted signals. The two images to be encrypted can be either related to each other, or independent signals. The encryption system is based on the double random phase encoding (DRPE), which is implemented by using a nonlinear JTC in the FD. The input plane of the JTC has four non-overlapping data distributions placed side-by-side with no blank spaces between them. The four data distributions are phase-only functions defined by the two images to encrypt and four random phase masks (RPMs). The joint power spectrum (JPS) is produced by the intensity of the Fourier transform (FT) of the input plane of the JTC. One of the main novelties of the proposal consists of the determination of the appropriate two nonlinear operations that modify the JPS distribution with a twofold purpose: to obtain a single real-valued encrypted image with a high level of security and to improve the quality of the decrypted images. The security keys of the encryption system are represented by the four RPMs, which are all necessary for a satisfactory decryption. The decryption system is implemented using a 4f-processor where the encrypted image and the security keys given by the four RPMs are introduced in the proper plane of the processor. The double image encryption system based on a nonlinear JTC in the FD increases the security of the system because there is a larger key space, and we can simultaneously validate two independent information signals (original images to encrypt) in comparison to previous similar proposals. The feasibility and performance of the proposed double image encryption and decryption system based on a nonlinear JTC are validated through computational simulations. Finally, we additionally comment on the proposed security system resistance against different attacks based on brute force, plaintext and deep learning.