Mixed Multi-Chaos Quantum Image Encryption Scheme Based on Quantum Cellular Automata (QCA)

Abstract

The advent of quantum computers could enable the resolution of complex computational problems that conventional cryptographic protocols find challenging. As a result, the formidable computing capabilities of quantum computers may render all present-day cryptographic schemes that rely on computational complexity ineffectual. Inspired by these possibilities, the primary purpose of this paper is to suggest a quantum image encryption scheme based on quantum cellular automata with mixed multi-chaos hybrid maps and a hyperchaotic system with quantum operations. To achieve desirable encryption outcomes, we designed an encryption scheme involving two main operations: (1) pixel-level diffusion and (2) pixel-level permutation. Initially, the secret keys generated using the hyperchaotic system were closely tied to the original image. During the first phase, the establishment of correlations among the image pixels, in addition to the three chaotic sequences obtained from the hyperchaotic system, was achieved with the application of a quantum-state superposition and measurement principle, wherein the color information of a pixel is described using a single qubit. Therefore, the three channels of the plain image were subjected to quantum operations, which involve Hadamard transformation and the quantum-controlled NOT gate, before the diffusion of each color channel with the hyperchaotic system. Subsequently, a quantum ternary Toffoli gate was used to perform the diffusion operation. Next, the appropriate measurement was performed on the three diffused channels. To attain the confusion phase, a blend of mixed multi-chaos hybrid maps and a two-dimensional quantum cellular automaton was used to produce random and chaotic sequence keys. Subsequently, the circular shift was utilized to additionally shuffle the rows and columns of the three diffused components, in order to alter the positions of their pixel values, which significantly contributes to the permutation process. Lastly, the three encoding channels, R, G, and B, were merged to acquire the encrypted image. The experimental findings and security analyses established that the designed quantum image encryption scheme possesses excellent encryption efficiency, a high degree of security, and the ability to effectively withstand a diverse variety of statistical attacks.

Color image encryption algorithm based on quantum random walk and multiple reset scrambling*

“…In 2022, Zhao et al proposed a color image encryption scheme based on Rubik's Cube control and quantum random walk [18]. To sum up, current research in the field of image encryption mainly focuses on evaluation indicators such as the security of the optimization algorithm, computational complexity, and clarity of decrypted images [19][20][21].…”

Performance of Cipher Image Transmission in Free Space Optics Under Foggy Weather

“…Test result shows when the encrypted image is added salt and pepper noise as displayed in Fig.20, as well as occlusion attack shown in Fig.21, we can still decrypt the encrypted image. PSNR can be measured as the following formula[50]:𝑃𝑃𝐴𝐴𝑁𝑁𝐴𝐴 = 10 log � 𝑀𝑀 × 𝑁𝑁 × 255 2 ∑ ∑ [𝑃𝑃(𝑖𝑖, 𝑗𝑗) − 𝐷𝐷(𝑖𝑖, 𝑗𝑗)]where M and N represent the length and width of the image, respectively. 𝑃𝑃(𝑖𝑖, 𝑗𝑗) represents the pixel value of an original image, and 𝐷𝐷(𝑖𝑖, 𝑗𝑗) represents the pixel value of the decrypted image.…”