The Caputo fractional order Lotka-Volterra system is time-consuming in practical applications, since its starting point is fixed. To tackle this problem, a short memory fractional order Lotka-Volterra system (SMFrLVS) is proposed, where the chaotic attractor of the short memory fractional order Lotka-Volterra system is achieved by the predictor-corrector method. Then, a multilayer fractional order Lotka-Volterra system with short memory (MSMFrLVS) is introduced, whose chaotic behaviors are explored via Poincare sections and frequency power spectra. A quantum image encryption algorithm is proposed by combining MSMFrLVS with quantum dual-scale triangular map. A quantum circuit of the dual-scale triangular map is designed with ADDER-MOD 2n . At the permutation stage, the plaintext image is transformed into quantum form with the generalized quantum image representation model. The resulting quantum image is divided into sub-blocks and scrambled by the quantum dual-scale triangular map. Subsequently, the intra and the inter permutation operations on bit-planes are realized by sorting pseudo-random sequence and by quantum Gray code, respectively. At the diffusion stage, the initial values of the MSMFrLVS are generated with a plaintext correlation mechanism. The ciphertext image can be acquired by carrying out three-level diffusion operations. It is demonstrated that the proposed quantum image encryption algorithm performs better than some typical image encryption algorithm in terms of security, robustness, computational complexity and encryption speed.
The Caputo fractional order Lotka-Volterra system is time-consuming in practical applications, since its starting point is fixed. To tackle this problem, a short memory fractional order Lotka-Volterra system (SMFrLVS) is proposed, where the chaotic attractor of the short memory fractional order Lotka-Volterra system is achieved by the predictor-corrector method. Then, a multilayer fractional order Lotka-Volterra system with short memory (MSMFrLVS) is introduced, whose chaotic behaviors are explored via Poincare sections and frequency power spectra. A quantum image encryption algorithm is proposed by combining MSMFrLVS with quantum dual-scale triangular map. A quantum circuit of the dual-scale triangular map is designed with ADDER-MOD 2n . At the permutation stage, the plaintext image is transformed into quantum form with the generalized quantum image representation model. The resulting quantum image is divided into sub-blocks and scrambled by the quantum dual-scale triangular map. Subsequently, the intra and the inter permutation operations on bit-planes are realized by sorting pseudo-random sequence and by quantum Gray code, respectively. At the diffusion stage, the initial values of the MSMFrLVS are generated with a plaintext correlation mechanism. The ciphertext image can be acquired by carrying out three-level diffusion operations. It is demonstrated that the proposed quantum image encryption algorithm performs better than some typical image encryption algorithm in terms of security, robustness, computational complexity and encryption speed.
In recent years, the transmission security of image information has become an important research direction in the internet field. In this work, we propose a quantum image chaos encryption scheme based on quantum long-short term memory (QLSTM) network. We find that because the QLSTM network has a complex structure and more parameters, when the QLSTM network is used to improve the Lorenz chaotic sequence, its largest Lyapunov exponent is 2.5465% higher than that of the original sequence and 0.2844% higher than that the sequence improved by the classical long-short term memory (LSTM) network, while its result is closer to 1 and more stable in the 0–1 test. The improved sequence of QLSTM network has better chaotic performance and is predicted more difficultly, which improves the security of single chaotic system encryption. The original image is stored in the form of quantum states by using the NCQI quantum image representation model, and the improved sequence of QLSTM network is used to control the three-level radial diffusion, quantum generalized Arnold transform and quantum W-transform respectively, so that the gray value and pixel position of the quantum image are changed and the final encrypted image is obtained. The encryption scheme proposed in this work obtains the average information entropy of all three channels of RGB of greater than 7.999, the average value of pixel number change rate of 99.6047%, the average value of uniform average change intensity of 33.4613%, the average correlation of 0.0038, etc. In the test of statistical properties, the encryption scheme has higher security than some other traditional methods and can resist the common attacks.
This paper explores a double quantum images representation (DNEQR) model that allows for simultaneous storage of two digital images in a quantum superposition state. Additionally, a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated, offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps. Based on the DNEQR model and the hyperchaotic system, a double quantum images encryption algorithm is proposed. Firstly, two classical plaintext images are transformed into quantum states using the DNEQR model. Then, the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences. These chaotic sequences are utilized to perform pixel value and position operations on the quantum image, resulting in changes to both pixel values and positions. Finally, the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences. The corresponding quantum circuits are also given. Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission, improves the encryption efficiency, and enhances anti-interference and anti-attack capabilities.
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.
A quantum color image encryption algorithm based on geometric transformation and intensity channel diffusion was designed. Firstly, a plaintext image was transformed into a quantum state form using the quantum image representation based on HSI color space (QIRHSI) representation as a carrier. Next, a pseudo-random sequence was generated using the generalized logistic map, and the pixel positions permuted multiple two-point swap operations. Immediately afterward, the intensity values were changed by an intensity bit-plane cross-swap and XOR, XNOR operations. Finally, the intensity channel of the above image was diffused in combination with the pseudo-confusion sequence as produced by the quantum logistic map to perform a diffusion operation on the intensity bit-plane to obtain the ciphertext image. Numerical simulations and analyses show that the designed algorithm is implementable and robust, especially in terms of outstanding performance and less computational complexity than classical algorithms in terms of security perspective.
In this paper, a quantum image encryption scheme is proposed by using the inter–intra bit-level permutation strategy. The image to be encrypted is first represented by a novel enhanced quantum representation model, and then, the intra and inter permutation operations are successively performed on bit planes. The intra bit permutation is achieved by sorting chaotic sequence, and the inter bit permutation is accomplished with qubit XOR operations between the two selected bit planes. The ciphertext image is finally obtained through a chaotic diffusion procedure implemented with a quantum image XOR operation. The XOR operation is realized by controlled- NOT gates, which is controlled by a chaotic sequence generated with a logistic map. The parameters of the logistic map are sensitive, which makes the key space large enough to resist brute-force attack. The proposed scheme not only modifies the pixel positions and gray values but also makes the bit distribution more uniform. The quantum circuits for the proposed encryption algorithm are devised. The simulation results and theoretical analysis show that the proposed method is more efficient than its classical counterpart, and its security is verified by the statistical analysis, keys sensitivity, and key space analysis.
The paper proposes a lossless quantum image encryption scheme based on substitution tables (S-box) scrambling, mutation operation and general Arnold transform with keys. First, the key generator builds upon the foundation of SHA-256 hash with plain-image and a random sequence. Its output value is used to yield initial conditions and parameters of the proposed image encryption scheme. Second, the permutation and gray-level encryption architecture is built by discrete Arnold map and quantum chaotic map. Before the permutation of Arnold transform, the pixel value is modified by quantum chaos sequence. In order to get high scrambling and randomness, S-box and mutation operation are exploited in gray-level encryption stage. The combination of linear transformation and nonlinear transformation ensures the complexity of the proposed scheme and avoids harmful periodicity. The simulation shows the cipher-image has a fairly uniform histogram, low correlation coefficients closed to 0, high information entropy closed to 8. The proposed cryptosystem provides 2256 key space and performs fast computational efficiency (speed = 11.920875 Mbit/s). Theoretical analyses and experimental results prove that the proposed scheme has strong resistance to various existing attacks and high level of security.