Nonlinear Joint Transform Correlator-Based Encryption System in the Fourier Domain for Simultaneous Authentication of Three Images

With the aim of simultaneously authenticating three images, an encryption–decryption system based on a nonlinear Joint Transform Correlator (JTC) in the Fourier domain is proposed. At first, the images to authenticate may be either related to or independent of one another. The input plane of the encryption system is fully phase encoded and includes one primary image to encrypt, four random phase masks (RPMs), and three phase-only distributions containing the information of the three images to be thereafter authenticated. These latter seven phase-only distributions serve as the security keys of the proposed encryption system. The encrypted output is a real-valued distribution derived from two new nonlinear modifications of the joint power spectrum (JPS), which improves resistance to direct inversion and plaintext-based inference. In the decryption system, authentication and image recovery are jointly performed: when all seven security keys are correct, the decrypted image preserves the information that enables the successful simultaneous authentication of the three images due to the two new nonlinear modifications of the JPS; otherwise, the retrieved distribution becomes noise-like. Unlike the nonlinear JTC previously reported for two-image authentication, adding a third authentication distribution generates additional JPS terms that prevent correct recovery of the primary image during decryption, even when all keys match, ultimately precluding simultaneous authentication of the three images. The two new nonlinear JPS modifications overcome this limitation for correct-key decryption. A key-space analysis confirms strong resistance to brute-force attacks, and robustness tests under additive noise, multiplicative noise, and partial occlusion for the encrypted signal are incorporated to assess practical performance. Numerical results indicate that the proposed architecture preserves reliable authentication under moderate degradation of the encrypted distribution. These results support the use of nonlinear JTC architectures as a practical framework for optical multi-image authentication and secure image encryption.