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.
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.
Abstract Quantum computation can improve the efficiency of image processing by utilizing parallelism and superposition characteristics. In this paper, a quantum cryptosystem based on Baker map and deoxyribonucleic acid (DNA) circular shift operation is designed. Firstly, the digital image to be encrypted is firstly represented with a novel enhanced quantum representation model. Then quantum Baker map is used to permutate the position information of the prepared quantum image. Next, the designed DNA circular shift operation is performed to preliminarily change the color information of the scrambled image. Finally, the ciphertext image is obtained by implementing the exclusive OR (XOR) operation between the pseudo-random sequence generated by a four-dimensional (4D) hyper-chaotic system and the DNA shift operated image. Numerical experimental results and security analysis verify that the proposed scheme has good performance at securing information storage and transmission as the histograms of ciphertexts are uniform, the correlation coefficient values of three directions are very close to 0, the average information entropy is 7.9972, the key space is more than 10 15×4 to resist brute-force attack. Furthermore, it has lower computational complexity compared with classical algorithms.
Abstract The parallel computing power of quantum computing and the special properties of qubits provide an effective solution for image processing tasks. This paper presents a quantum image encryption algorithm based on Fisher-Yates algorithm and Logistic mapping. Firstly, the Fisher-Yates algorithm is used to generate three key sequences, one of which is used to encode the coordinate qubits of the image. Using the other two keys and the preset rules, the quantum coordinate scrambling operation is designed based on the encoded coordinate qubit, which effectively scrambles the spatial information of the plaintext image. Next, another set of key sequences is generated, one of which is used to encode the color qubits of the image. Using two other key sequences and different rules, a qubit plane scrambling operation based on coded color qubits is designed, and the color information of image is scrambled successfully. Finally, the quantum key image is generated based on Logistic mapping, and the key image is scrambled based on Fisher-Yates algorithm to improve the key complexity. The final ciphertext image is obtained by performing XOR operation between the original image and the scrambled key image. The complete quantum circuit diagram of the scheme is given in this paper. The experimental results and security analysis prove the effectiveness of the scheme, which provides a large key space and the computational complexity is only O(n).
Given the limitations of current classic image encryption algorithms and the unconditional security characteristics of quantum key distribution protocols, the author proposes an image encryption method based on quantum key distribution and pixel scrambling. The author first analyzed the security issues of quantum image encryption algorithms based on image scrambling methods, namely that image scrambling methods have periodicity, which can ensure that the image can be restored after scrambling. If an image cannot be guaranteed to return to its original state after performing scrambling operations, legitimate users cannot obtain the secret information in the original image, and image scrambling loses its original meaning; However, the periodicity of image scrambling methods not only ensures that legitimate users can decrypt images, but also provides convenience for attackers to steal original image information. Secondly, it is pointed out that when evaluating and analyzing quantum image encryption algorithms, the evaluation indicators should include two parts: One is performance analysis, which is the analysis of the network complexity of quantum circuits. In quantum computing, the network complexity of quantum circuits is usually represented by the number of quantum basic logic gates. The second is security analysis, which mainly includes key analysis (including key space size and key sensitivity analysis), statistical analysis (including pixel correlation, histogram analysis, information fusion, and scatter plot distribution density analysis). Finally, experimental simulations have shown that the NPCR values of the plaintext and ciphertext images of the three images tend to 100%. The encrypted image histogram is evenly distributed, with very weak pixel correlation and high pixel change rate and information entropy.
Image scrambling on classical computers has been widely studied, however, the corresponding quantum algorithms are rare. This paper proposes a block-based image scrambling scheme for the generalized model of novel enhanced quantum representation (GNEQR). It is not only suit for grayscale images and color images, but also can be used in 2n× 2mimages (i.e., rectangular images). To realize the image scrambling method, we use geometric transformations and an operation of bitplane scrambling to perform position and pixel scrambling, respectively. Furthermore, the complexity of the implementation circuit of the proposed image scrambling is only O(n2) for a 2n× 2nimage. Therefore, it shows our proposed quantum image scrambling is efficient. Then, the result analysis of simulation experiments demonstrates that our proposed image scrambling is effective. In addition, security analysis shows that the proposed scrambling algorithm is secure.
In encryption technology, image scrambling is a common processing operation. This paper proposes a quantum version of the 3D Mobius scrambling transform based on the QRCI model, which changes not only the position of pixels but also the gray values. The corresponding quantum circuits are devised. Furthermore, an encryption scheme combining the quantum 3D Mobius transform with the 3D hyper-chaotic Henon map is suggested to protect the security of image information. To facilitate subsequent processing, the RGB color image is first represented with QRCI. Then, to achieve the pixel-level permutation effect, the quantum 3D Mobius transform is applied to scramble bit-planes and pixel positions. Ultimately, to increase the diffusion effect, the scrambled image is XORed with a key image created by the 3D hyper-chaotic Henon map to produce the encrypted image. Numerical simulations and result analyses indicate that our designed encryption scheme is secure and reliable. It offers better performance in the aspect of key space, histogram variance, and correlation coefficient than some of the latest algorithms.
In order to boost the security and confidentiality of information in quantum images, on the foundation of the NEQR model, a novel quantum watermarking scheme combining quantum Hilbert scrambling with steganography based on the Moiré fringe is designed in this paper. First of all, for carrier image, and watermark image, the color information and position information are denoted, respectively, by the NEQR model. Next, the watermark image is converted to a disordered image by quantum Hilbert scrambling, and the message of the original watermark image cannot be gained from the disordered image. At last, the watermark image after scrambling is embedded into the carrier image through the steganography of the Moiré fringe, obtaining the watermarked image. Due to the unitary image of the quantum gate, quantum Hilbert inverse scrambling is the opposite process of quantum Hilbert scrambling. In addition, the watermark image can be completely extracted from the watermarked image. What’s more, the experimental simulation and performance analysis of the scheme are done. The experimental simulation proves the feasibility of this algorithm. Visually, there is no difference between the carrier image and the watermarked image. The PSNR between the watermarked image and the carrier image is measured, which quantitatively shows the high similarity. In addition, the time complexity of the quantum circuit is lower than some other quantum image watermarking schemes, which proves the simplicity of this scheme.