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Nonlinear and Quantum Methods for Image Processing and Cryptography

Zhishun Xian

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

In this study, a powerful representation of Quantum Images (PRQI) is proposed to represent images in quantum computers. The color information can be stored in either phase or amplitude, which is powerful for Quantum Image Compression (QIC) and Quantum Image Encryption (QIE). The construction process begins with a pure state on which several operations are applied to generate the expected quantum state. This advantage makes the method more flexible compared with other methods. To evaluate the lossless compression performance, the quantum compression ratio is employed as a standard. Furthermore, to explore the potential of the new method, a novel quantum image encryption method based on quantum chaotic Baker map and random phase mask is discussed. Supported by detailed numeric simulations and analysis, the new method provides a more efficient and secure way to transmit quantum information. In conclusion, PRQI opens a door not only to express quantum images but also to explore practical aspects of quantum image processing.

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In this study, a powerful representation of Quantum Images (PRQI) is proposed to represent images in quantum computers. The color information can be stored in either phase or amplitude, which is powerful for Quantum Image Compression (QIC) and Quantum Image Encryption (QIE). The construction process begins with a pure state on which several operations are applied to generate the expected quantum state. This advantage makes the method more flexible compared with other methods. To evaluate the lossless compression performance, the quantum compression ratio is employed as a standard. Furthermore, to explore the potential of the new method, a novel quantum image encryption method based on quantum chaotic Baker map and random phase mask is discussed. Supported by detailed numeric simulations and analysis, the new method provides a more efficient and secure way to transmit quantum information. In conclusion, PRQI opens a door not only to express quantum images but also to explore practical aspects of quantum image processing.
Flexible Representation of Quantum Images (FRQI) is proposed to provide a representation of images that enables efficient preparation and image processing operators on quantum computers. FRQI captures colors and their corresponding positions in an image into a quantum state. The preparation with polynomial simple operations for FRQI turning a quantum computer from the initialized state to the FRQI state is done by using Hadamard and controlled rotation gates. The Quantum Image Compression (QIC) algorithm reduces simple operations used in the preparation process based on the minimization of Boolean equations are from same color groups of positions. Quantum image processing operators on FRQI based unitary transforms dealing with only colors, colors at some positions and the combination by the quantum Fourier transform of both colors and positions are addressed. The experiments for the storage and retrieval of images using FRQI are implemented in Matlab. The compression ratio of QIC among same color groups ranges from 6.67% to 31.62% on the Lena image.
Background: Quantum image processing is rapidly developing in the field of quantum computing, and it can be successfully implemented on the Noisy Intermediate-Scale Quantum (NISQ) device. Quantum image encryption holds a pivotal position in this domain. However, the encryption process often encounters security vulnerabilities and entails complex computational complexities, thereby consuming substantial quantum resources. To address this, the present study proposes a quantum image encryption algorithm based on four-dimensional chaos. Methods: The classical image is first encoded into quantum information using the Generalized Quantum Image Representation (GQIR) method. Subsequently, the trajectory of the four-dimensional chaotic system is randomized, and multi-dimensional chaotic keys are generated to initially encrypt the pixel values of the image. Then, the Arnold transformation is applied to randomly encrypt the pixel positions, resulting in the encrypted image. During the decryption process, the inverse process of encryption is employed to restore the original image. Results: We simulated this process in the Python environment, and the information entropy analysis experiment showed that the information entropy of the three encrypted images reached above 7.999, so the system has good encryption. At the same time, the correlation of the pixel distribution after the encryption algorithm is weak, which proves that the control parameters of the chaotic system can effectively reduce the correlation between pixels in the image. In the final key space analysis, the key space issued by our encryption can reach $10 140 \gg 2 128 $. Conclusion: Our method is resistant to destructive attacks and can produce scrambled images with higher encryption and usability. This algorithm solves the problems of general encryption algorithms such as periodicity, small key space, and vulnerability to statistical analysis, and proposes a reliable and effective encryption scheme. By making full use of the characteristics of Arnold transformation permutation, ergodicity and the randomness of the four-dimensional chaotic system, the encryption algorithm uses the larger key space provided by the four-dimensional Lorenz system.
Quantum image representation is an essential component of quantum image processing and plays a critical role in quantum information processing. Flexible Representation of Quantum Images (FRQI) presents pixel colors and associated locations as a state to represent images on quantum computers. A fundamental part of the quantum image processing system is quantum image compression (QIC), which is utilized to maintain and retrieve binary images. This compression allows us to minimize the number of controlled rotation gates in the quantum circuits. This paper designed optimized quantum circuits and simulated them using Qiskit on a real quantum computer based on minimum boolean expressions to retrieve the 8×4 binary single-digit images. To demonstrate the feasibility and efficacy of quantum image representation, quantum circuits for images were developed using FRQI, and quantum image representation experiments were done on IBM Quantum Experience (IBMQ). We were able to visualize quantum information by doing the quantum measurement on the image information that we had prepared. Without utilizing this method, the number of controlled rotation gates is equal to the number of pixels in the image; however, we showed that by using the QIC algorithm, we could decrease the number of gates significantly. On these images, the maximum and minimum compression ratios of QIC are 90.63% and 68.75%, respectively.
This paper presents a new quantum image encryption (QIE) algorithm that integrates a newly developed 4D Quantum Logistic-Jerk Hyperchaotic System (4D-QLJHS) with a quantum image representation (QIR) model, enabling secure and efficient image transmission.By reducing qubit usage and circuit depth, the proposed QIE framework significantly improves quantum resource efficiency.Additionally, incorporating the enhanced 4D-LJHS map strengthened security and resistance against both quantum and classical attacks, surpassing the robustness and scalability of current quantum image encryption techniques.The new 4D-QLJHS is created by combining a logistic map and a jerk system, and then converted to a quantum hyperchaotic system using a Hamiltonianbased method.These systems help create a Quantum Pseudo-Random Number Generator (QPRNG) that generates random bit sequences used to alter and rearrange data at the quantum bit-plane level during the encryption process.The quantum encryption method uses the Quantum Image Representation based on Bit Planes (QIRBP) model, which enables modifying individual pixels and color channels via CNOT and SWAP gates.We evaluate various statistical tests to confirm the security and efficiency of our system.The experiments demonstrate that the system is highly secure, featuring adequate randomness, robust protection against specific attacks, and uniform distribution in the encrypted image data.Experimental simulations of some images indicate that the system provides a satisfactory level of security for image encryption, given the computational costs.This makes it suitable for real-time image communication where security is a priority.
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.
Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing.