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Journal of Electronic Imaging

Quantum representation model of color digital images based on encryption

Chia-Ho Lin, Chin‐Chi Cheng, Chih‐Wei Tang

Published May 5, 2025• 0 citations
Publisher

Abstract

Quantum processors enable real-time image processing and provide no-cloning theorem-based security for quantum image encryption. Most classical image encryption methods cannot be directly applied to quantum images due to the implementation complexity of using the quantum circuit, and most existing secure quantum image encryption methods are designed for grayscale images. Thus, we propose a quantum color image encryption method. The proposed method is designed for the existing efficient-storage quantum representation model of color digital image (QRCI) representation. The proposed QRCI-based encryption method benefits from a small number of qubits in total (i.e., 2n+7 qubits), where the QRCI representation uses 2n+6 qubits and two pseudorandom number sequences use only 1 qubit. The improved chaos-based pseudorandom number generator strikes a balance between reduced computation and security level. The two-round exclusive-OR-based diffusion method for quantum encryption significantly improves key sensitivity. Low gate costs are required. Experimental results show that the proposed method outperforms state-of-the-art quantum color image encryption methods in terms of security measures. In addition, the number of qubits of the proposed quantum image encryption method is small (2n+7 qubits).

DOI
10.1117/1.jei.34.3.033004

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Quantum processors enable real-time image processing and provide no-cloning theorem-based security for quantum image encryption. Most classical image encryption methods cannot be directly applied to quantum images due to the implementation complexity of using the quantum circuit, and most existing secure quantum image encryption methods are designed for grayscale images. Thus, we propose a quantum color image encryption method. The proposed method is designed for the existing efficient-storage quantum representation model of color digital image (QRCI) representation. The proposed QRCI-based encryption method benefits from a small number of qubits in total (i.e., 2n+7 qubits), where the QRCI representation uses 2n+6 qubits and two pseudorandom number sequences use only 1 qubit. The improved chaos-based pseudorandom number generator strikes a balance between reduced computation and security level. The two-round exclusive-OR-based diffusion method for quantum encryption significantly improves key sensitivity. Low gate costs are required. Experimental results show that the proposed method outperforms state-of-the-art quantum color image encryption methods in terms of security measures. In addition, the number of qubits of the proposed quantum image encryption method is small (2n+7 qubits).
Security of quantum image encryption is ensured by the no-cloning theorem. Most existing high-secure quantum image encryption methods are designed for grayscale images. Thus, this paper proposes a quantum color image encryption method. It combines efficient-storage QRCI (Quantum Representation model of Color digital Images) representation and high-security quantum image encryption. The first-round encryption combines scrambling and diffusion while the second-round encryption adopts diffusion only. Tests results show that the proposed scheme achieves high NPCR and UACI. The encrypted image has much uniform color distribution than the original image.
In the wake of the information security era, ensuring the privacy, accuracy, and reliability of images has become imperative. In this paper, a quantum image encryption method combining quantum Arnold transform and a hyper 5D chaotic system is devised. Furthermore, first, a nonlinear color quantization model (NCQI) is used to convert digital images in standard RGB format into quantum color images. Then, based on the size of the converted quantum color image, the corresponding encryption key is generated using the hyper 5D chaotic system. In the encryption stage, we use the key to encrypt the converted quantum color image. This process entails two principal steps: First, we use quantum Arnold transform to scramble the pixel positions in the image and, subsequently, diffuse the pixel values through a carefully designed cyclic shift strategy to achieve the preliminary encryption of the image. To further strengthen the encryption security, we use a quantum rotation gate to perform quantum rotation transformation on the color channel of each pixel point in the encrypted image separately. These well-designed encryption processes, in succession, significantly enhance the security of the image. This paper provides the corresponding quantum circuit design and validates both the efficacy and security of the quantum image encryption scheme through simulation experimental results.
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.
In order to improve the security of quantum color images, this study proposes a novel algorithm for quantum color image encryption based on three-dimensional chaotic systems. The encrypted quantum color image is represented by the novel quantum image representation for color digital image model. The original image is first perturbed by the Arnold transform and then the RGB channel is perturbed separately from the chaotic sequence generated by the new three-dimensional chaotic system by the xor operation. Evaluation metrics such as histogram, information entropy, and correlation of neighboring pixels of the image are analyzed using MATLAB. The simulation results show that the pixel values of the encrypted image are uniformly distributed and the algorithm enhances the security of quantum color images. The specific quantum circuit diagram of the encryption algorithm is given in the paper. The superposition and entanglement properties of quantum physics greatly improve the efficiency of complex image processing algorithms, and the overall complexity of the circuit is O(n), which is efficient and implementable.
In order to further improve the security and efficiency of quantum image encryption, a three-layer encryption scheme for quantum color images based on 6D hyperchaos is proposed for the improved quantum representation model. The sequences generated by the 6D hyperchaotic system are applied to each layer of image encryption as keys. First, the quantum Fibonacci matrix is used to scramble the pixel value positions of the image to achieve the spatial scrambling of the quantum image; then, the position exchange of red, green, and blue channels and the bit-level cycle shift of pixel value are carried out alternately to realize the bit-level scrambling of quantum images; Finally, the XOR operation is performed on the quantum image whose position has been scrambled to realize the bit-level diffusion of the quantum image and obtain the final encrypted image. Simulation results show that the encryption algorithm is highly sensitive to the initial key, and the pixel values of the encrypted image are evenly distributed. In addition, quantum circuits are designed to implement the image encryption steps of each layer.
Quantum image encryption (QIE) loads a digital image into qubits and ciphers it with unitary circuits, usually keyed by chaotic maps, quantum walks or quantum random numbers. This review follows the field from an early geometric-transformation scheme (2013) to designs executed on 127-qubit IBM processors (2025). We organise the literature by image representation (FRQI, NEQR, amplitude encoding), confusion and diffusion mechanism, key source and validation level, and we compare recent schemes on entropy, NPCR, UACI, correlation and key space. Reported statistics sit close to their ideals almost everywhere; recent quantum-walk and chaos-based designs report NPCR of 99.6 to 99.97% and UACI of 33.5 to 33.9%, so these metrics no longer separate strong schemes from weak ones. Three gaps stand out. Most evidence comes from classical simulation. The secret usually sits in a classical key generator rather than in the quantum circuit. And loading an image into qubits, then reading it back, remains the main hardware bottleneck. Hybrid designs that distribute keys with BB84 and cipher the image classically offer the most deployable route today. We close with a research agenda: attack-based benchmarks, error-aware hardware validation, cheaper state preparation and explicit security definitions.