Nonlinear optical multi-image encryption scheme with two-dimensional linear canonical transform

•A nonlinear optical multi-image encryption scheme based on chaotic system and two-dimensional linear canonical transform is proposed.•The keys used in the chaotic systems are calculated from the pixels of the original images.•Multiple images are combined into one image in the presented scheme, and the values and the positions of pixels in the image are both changed. A nonlinear optical multi-image encryption scheme based on chaotic system and two-dimensional linear canonical transform (2D LCT) is designed. Firstly, the low-frequency sub-bands of the four grayscale images are extracted with the contourlet transform (CT), respectively. Then the four sub-bands are synthesized into a one-dimensional (1D) sequence, which is scrambled with a chaotic sequence produced by the two-dimensional (2D) logistic map. Subsequently, the image converted from the resulting 1D sequence is re-encrypted into a white noise-like image by phase truncation and phase reservation in the 2D LCT domain. Finally, the XOR operation based on the 2D logistic map is performed on the white noise-like image to yield the final ciphertext image. The parameters of the 2D LCT and the logistic map as the main keys enlarge the key space of the proposed multi-image encryption scheme. In addition, the keys regarded as the initial values of the chaotic systems are related to the original images. The phase truncation and the bitwise XOR operation, as nonlinear processes, improve the robustness of the presented multi-image encryption scheme against chosen-plaintext attack. Numerical simulation results demonstrate the validity and the reliability of the proposed optical multi-image encryption scheme with good performance.