Asymmetric optical cryptosystem with secret-key sharing based on coherent superposition and normalized decomposition

In this paper, we present an asymmetric optical cryptosystem that performs multiple image encryption (MIE) featured with a secret image sharing (SIS) attribute, which holds significant potential for various security applications. The system is based on a novel normalized decomposition algorithm that breaks down the spectrum of each plain image into a set of M phase-only masks (POMs). Among these masks, one is unified and shared across all images, serving as the cipher image, while \((M-1)\) masks are unique to each image and act as the corresponding secret key for that image. This approach enables the sharing of the \((M-1)\) secret phase-only keys among authorized users, thereby enhancing the access security. To realize the MIE-SIS cryptosystem, a compact optical system is presented that employs Mach-Zehnder interferometer and spatial light modulators (SLMs) charged by POMs. The silhouette problem is completely resolved by applying a chaotic random amplitude mask (CRAM) to the image spectrum prior to the decomposition process. Numerical experiments verify the effective integrity of the MIE-SIS cryptosystem. Even a small deviation of 0.02 rad in any of the decomposed POMs results in a correlation coefficient value of less than 0.015, indicating high sensitivity to the phase keys. The results prove the unlimited encryption capacity of the MIE-SIS cryptosystem and demonstrate its robustness against Gaussian noise and statistical attacks.