Optical image encryption based on 3D double-phase encoding algorithm in the gyrator transform domain

In this paper, we propose an optical image encryption scheme based on modified 3D double-phase encoding algorithm (3D-DPEA) in the gyrator transform (GT) domain, in which a plaintext is encrypted into two sparse volumetric ciphertexts under the constraints of chaos-generated binary amplitude masks (BAMs). Then, the two volumetric ciphertexts are multiplexed into the corresponding 2D ciphertexts for convenient storage and transmission. First, due to the synergistic adjustment of the two sparse volumetric ciphertexts during the iterative process, the 3D-DPEA would achieve higher recovery quality of the decrypted image with fewer iterations. In addition, because the BAMs are generated by the logistic-tent (LT) chaotic map which is closely related to the rotation angles of GT, and the LT chaotic map has several advantages such as nonlinear, pseudorandom behavior, and high sensitivity of initial conditions, the sensitivity of the secret key could be significantly improved by several orders of magnitude, reaching up to 10⁻¹⁴. As a result, the 3D-DPEA scheme not only eliminates the explicit/linear relationship between the plaintext and the ciphertext but also substantially enhances security. For decryption, the corresponding decrypted image can be achieved by recording an intensity pattern when a coherent beam crosses two sparse volumetric ciphertexts sequentially. Furthermore, BAMs wouldn’t impose an additional burden on the storage and transmission of secret keys. A series of numerical simulations are performed to verify the effectiveness and security of the proposed encryption scheme.