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arXiv:2506.23039

A novel approach to multi-image quantum encryption/decryption using qudits

Claire Levaillant

Published Jun 28, 2025• 0 citations
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Abstract

We introduce groundbreaking techniques in image encryption, assuming the existence of quantum computing ressources functioning with qudits, where d is a power of 2. Our quantum representation of color multi-image is based on space-filling curves and allows to reduce the storage space. We generalize the quantum baker map, so that it may scramble two n-qudits. By doing so, we enlarge its parameter space exponentially, leading to a better security. We define two new concepts of mixed scrambling and mixed diffusion, and present a variety of schemes, depending on the needs of the users.

DOI
10.48550/arxiv.2506.23039

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We introduce groundbreaking techniques in image encryption, assuming the existence of quantum computing ressources functioning with qudits, where d is a power of 2. Our quantum representation of color multi-image is based on space-filling curves and allows to reduce the storage space. We generalize the quantum baker map, so that it may scramble two n-qudits. By doing so, we enlarge its parameter space exponentially, leading to a better security. We define two new concepts of mixed scrambling and mixed diffusion, and present a variety of schemes, depending on the needs of the users.
After introducing a bit-plane quantum representation for a multi-image, we present a novel way to encrypt/decrypt multiple images using a quantum computer. Our encryption scheme is based on a two-stage scrambling of the images and of the bit planes on one hand and of the pixel positions on the other hand, each time using quantum baker maps. The resulting quantum multi-image is then diffused with controlled CNOT gates using a sine chaotification of a two-dimensional Hénon map as well as Chebyshev polynomials. The decryption is processed by operating all the inverse quantum gates in the reverse order.
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.
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).
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.
Quantum image processing has become a significant aspect within the field of quantum information processing because the image is an essential carrier of information, and quantum computation has powerful image processing ability. Image scrambling algorithms are often required as initial image operations in quantum image processing applications such as quantum image encryption and watermarking. However, the efficiency of existing quantum image scrambling algorithms needs to be improved urgently, especially in terms of periodicity. Therefore, a novel quantum image scrambling algorithm based on discrete Baker map is proposed in this paper, which can be implemented by swapping qubits with low circuit complexity. The quantum version of discrete Baker map is deduced and the corresponding quantum circuit is designed. The simulation results show that the scrambling algorithm has the characteristic of long period, which can further enhance the security of quantum image encryption algorithms. Besides, for generalized discrete Baker maps, the conditions that they can be implemented by swapping qubits are given. Moreover, the number of discrete Baker maps satisfying the conditions is also calculated.