Bit-level Permutation Research Articles

Three-level quantum image encryption based on Arnold transform and logistic map

Quantum computation improves the efficiency and security of cryptography by utilizing characteristics of quantum mechanics. In this paper, a novel three-level quantum image encryption algorithm based on Arnold transform and logistic map is proposed. To obtain satisfactory encryption results, three-level encryption procedures including block-level permutation, bit-level permutation and pixel-level diffusion are performed on the original image. First, the classical plaintext image is transformed into quantum form with novel enhanced quantum representation model. Then, quantum Arnold transform (QArT) is used to scramble the image sub-blocks by processing the qubits that denote position information. By iterating block-level permutation procedure with different block-size and different parameter of QArT, the period defect of QArT can be made up to some extent. Next the bit-level permutation is performed by scrambling the bit-plane order according to a sequence generated with logistic map. Finally, the ciphertext image can be obtained by performing bit-level diffusion through XOR operation between bit-level permutated image and a pseudo-random sequence acquired from logistic map. The corresponding quantum circuits realization are given, and simulations results show that the proposed three-level quantum image encryption scheme has high level of security and outperforms its classical counterpart in terms of efficiency.

A New Hyperchaotic Image Encryption Algorithm Based on Stochastic Signals

Image encryption is often used to protect private images during transmission on a public channel. A high dimensional chaotic map has a greater secret key space, better ergodicity and dynamic property than a low-dimensional chaotic system. A seven-dimensional (7D) hyperchaotic map is used to produce chaotic sequences. Given secret keys and SHA-512 function are employed to generate initial values for iteration. Many stochastic signals are injected into one of the variables during iteration to transfer trajectory and increase dynamic behavior of a chaotic system. Three matrices are constructed with generated chaotic sequences. Permutation is performed on the basis of a control matrix. It keeps the pixel far from its neighboring pixels. Cycle shift is executed during bit-level permutation. Characteristic values of scrambling image are calculated and temporary values are achieved successfully. Two dynamic values are also applied during the diffusion process. Experimental results display the effects of the proposed algorithm. Security analysis reveals that the proposed method has some special advantages.

New Encryption Algorithm Using Bit-Level Permutation and Non-Invertible Chaotic Map

Recently, a little research into image encryption has been used on chaotic economic maps. The current paper suggests a bit-level permutation and a non-invertible chaotic economic map to encrypt an image. Firstly, the secret key generation is linked to the plain image. So, the suggested algorithm may resist both known-plaintext and chosen-plaintext attacks. Then a bit-level permutation is performed for all the binary bits of the plain image's pixels, using the logistic map (permutation stage). It is used to improve the algorithm's security. Then pixel diffusion is applied using the 2D non-invertible chaotic economic map and bit-wise XOR operations. It is used to change the pixels' values and make them highly random. The results of the experiments and the security analyses show that the given image encryption algorithm is efficient with higher security. Some comparisons showed that the proposed algorithm outperformed many recent algorithms. Finally, the proposed algorithm may be able to withstand a variety of attacks.

A Novel Chaos-Based Color Image Encryption Scheme Using Bit-Level Permutation

To ensure the security of digital images during transmission and storage, an efficient and secure chaos-based color image encryption scheme using bit-level permutation is proposed. Our proposed image encryption algorithm belongs to symmetric cryptography. Here, we process three color components simultaneously instead of individually, and consider the correlation between them. We propose a novel bit-level permutation algorithm that contains three parts: a plain-image related rows and columns substitution, a pixel-level roll shift part, and a bit-level cyclic shift part. In the plain-related rows and columns substitution part, we involve the plain-image information to generate a control sequence by using a skew tent system. This process ensures that the correlation between three color components can be totally broken, and our cryptosystem has enough plain-image sensitivity to resist the differential attack. In the pixel-level roll shift part and bit-level cyclic shift part, we have a fully bit-level permutation controlled by two sequences using a Rucklidge system. The simulation and some common security analyses are given. Test results show that our proposed scheme has good security performance and a speed advantage compared to other works.

On the Cryptanalysis of a Bit-Level Image Chaotic Encryption Algorithm

In this paper, the security analysis of a bit-level image chaotic encryption algorithm based on the 1D chaotic map is proposed. The original image chaotic encryption algorithm includes bit-level permutation encryption, diffusion encryption, and linear transform. Deciphering of it can be divided into two stages. First, bit-level permutation encryption, diffusion encryption, and linear transform can be simplified into bit-level equivalent permutation encryption and equivalent diffusion encryption, which is a key breakthrough point of cryptanalysis. Second, the chaotic sequence generated by this algorithm is independent of the plaintext image. Therefore, the equivalent diffusion key and the equivalent permutation key can be obtained by chosen-plaintext attack, respectively. Theoretical analysis and numerical simulation experiment results verify the effectiveness of the analytical method. Finally, some suggestions are proposed to promote the security of the original image chaotic encryption algorithm.

Hyperchaotic image encryption algorithm based on bit-level permutation and DNA encoding

Many chaos-based image encryption algorithms using low-dimensional chaotic mapping and permutation diffusion structures have been proposed recently. However, low-dimensional chaotic maps are less secure than high-dimensional chaotic systems. Furthermore, the permutation process is independent of the plaintext and diffusion process. As a result, they are not very resistant to chosen plaintext attacks and chosen ciphertext attacks. In this paper, we propose a hyper-chaos-based image encryption algorithm that uses a 6-dimensional hyperchaotic system; the key stream generated by hyperchaotic system is related to the plaintext image. Then, bit-level permutation is employed to strengthen the security of the cryptosystem. Finally, DNA coding and operations are employed to change pixels. Theoretical analysis and numerical simulations demonstrate that the proposed algorithm is safe and reliable for image encryption.

Study on an efficient hyper-chaos-based image encryption scheme using global bit permutation.

BACKGROUND: The chaotic system with low dimensions has a low security compared to the high-dimensional chaotic system. Furthermore, major pixel-level permutations merely transform the pixel position and cannot change the intensity distribution of the original image. Bit-level permutation could change the intensity distribution, as it devotes more time to conduct bit-level computation.OBJECTIVE: In this study, we present a more efficient image encryption approach based on hyper-chaos and a global bit cycle shift (HC-GBCS).METHODS: According to the input image we adopted the SHA-256 secure hash algorithm to obtain the initial key, which served as the premier parameter of the chaotic system. Then we employed a 4D hyper-chaotic system for generating the chaotic series, on which we utilized global bit permutation to enhance the security of the encryption system. Finally, the diffusion process was conducted by using the generated chaotic series extended with a logistic map.RESULTS: Experimental results and analysis reveal that the presented approach encrypts plain images effectively and achieves high security and stability.CONCLUSION: The proposed method can deal with the problems inherently existing in encryption methods utilizing low-dimensional chaotic map. Furthermore, global bit permutation can transform the pixel distribution of plain images and enhance the cryptosystem security.

Cryptanalysis of a chaotic image cipher based on plaintext-related permutation and lookup table

In 2017, an efficient chaotic image cipher with dynamic lookup table driven by bit-level permutation strategy (ICDLT) was proposed (Hu et al. Nonlinear Dyn 87:1359–1375). The chaotic cipher adopts a plaintext-related image encryption mechanism as an efficient measure against chosen-plaintext/ciphertext attack. ICDLT is composed of four basic parts: inter-pixel permutation, sequential addition, intra-pixel permutation and diffusion processes, where two kinds of permutation are both related to the plaintext. Although ICDLT is built on complex nonlinear dynamics, we found that it is still vulnerable against chosen-plaintext attack and its individual sub-keys can be recovered using a divide-and-conquer strategy. Benefiting from the essential structure of ICDLT and the intrinsic properties of Latin square, the proposed attack requires only $$ (8 \cdot N^2 +256 + n_c \cdot (2 \cdot N -1))$$ plain images, where $$N^2$$ is the size of the image and $$n_c$$ is the number of cipher images that need to be cracked. Furthermore, we summarize a more general framework which is beneficial for cryptanalyzing a class of plaintext-related image ciphers. Finally, we propose an improved scheme based on the designed plaintext-related XOR encryption (PR-XOR) module to enhance the security of ICDLT. Theoretical analysis and experiments prove that the improved scheme not only maintains the excellent statistical performances of the original one, but also can resist various attacks.

Fast and Efficient Image Encryption Algorithm Based on Modular Addition and SPD.

Bit-level and pixel-level methods are two classifications for image encryption, which describe the smallest processing elements manipulated in diffusion and permutation respectively. Most pixel-level permutation methods merely alter the positions of pixels, resulting in similar histograms for the original and permuted images. Bit-level permutation methods, however, have the ability to change the histogram of the image, but are usually not preferred due to their time-consuming nature, which is owed to bit-level computation, unlike that of other permutation techniques. In this paper, we introduce a new image encryption algorithm which uses binary bit-plane scrambling and an SPD diffusion technique for the bit-planes of a plain image, based on a card game trick. Integer values of the hexadecimal key SHA-512 are also used, along with the adaptive block-based modular addition of pixels to encrypt the images. To prove the first-rate encryption performance of our proposed algorithm, security analyses are provided in this paper. Simulations and other results confirmed the robustness of the proposed image encryption algorithm against many well-known attacks; in particular, brute-force attacks, known/chosen plain text attacks, occlusion attacks, differential attacks, and gray value difference attacks, among others.

Image Encryption Algorithm Based on Bit-Level Permutation and Dynamic Overlap Diffusion

In order to guarantee the security of digital images, image encryption is a good tool. This article puts forward a novel image encryption/decryption algorithm based on bit-level permutation and dynamic overlap diffusion. Firstly, location information set by users is used to scramble the plain image in the bit-level, changing the pixel position of the image while changing the pixel value. Then, using the plaintext related method to control the iteration parameters of Arnold transform. These two parts together form the permutation process of the algorithm. Thirdly, the overlap steps are set according to the encryption security requirements, and dynamic overlap diffusion is performed on the permutation image. At the same time, the plaintext information entropy and variance are used to update the diffusion key in the five-dimensional hyperchaotic system to achieve the plaintext correlation of the encryption key. Arnold transform and dynamic overlap diffusion can ensure that different key streams are generated when encrypting different images. Finally, experimental analysis and numerical simulation show that our algorithm has high efficiency, high security, high sensitivity, and can effectively resist various attacks.

Cryptanalyzing an Image Cryptosystem Based on Circular Inter-Intra Pixels Bit-Level Permutation

Recently, a new image encryption algorithm based on chaos has been proposed [Circular inter-intra pixels bit-level permutation and chaos-based image encryption, Information Sciences, 355-356: 314-327, 2016]. In this paper, this image encryption algorithm was crypt-analyzed in detail. Some defects of it, such as its row-based scrambling being invalid for the special images and the lacking of diffusion operations in its processes, were pointed out. Meanwhile, two crack methods were presented in this paper. They are using only a pair of chosen plain-cipher images or a pair of known plain-cipher images to crack the image encryption algorithm. That is enough to demonstrate the image cryptosystem using this image encryption algorithm is insecure.

Cryptanalysis of an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps

Recently, an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps (IEC-BPMC) was proposed, which includes two main parts: bit-level permutation for high 4-bit planes and bit-wise XOR diffusion. Some security analyses and experimental simulations were presented to support it to resist various attacks. However, it is found that the diffusion and permutation parts can be cracked separately by the divide-and-conquer strategy due to its inherent pitfalls. Then the equivalent diffusion key and the equivalent permutation key can be recovered by the chosen-plaintext attack method. Both theoretical analysis and experimental results demonstrate that IEC-BPMC is insecure against chosen-plaintext attack with low data complexity and computational complexity. Moreover, some other security defects of IEC-BPMC are revealed. Finally, some suggestions for improvement are given to enhance the security.

A Symmetric Image Encryption Algorithm Based on a Coupled Logistic-Bernoulli Map and Cellular Automata Diffusion Strategy.

In this paper, the properties of the classical confusion–substitution structure and some recently proposed pseudorandom number generators using one-dimensional chaotic maps are investigated. To solve the low security problem of the original structure, a new bit-level cellular automata strategy is used to improve the sensitivity to the cryptosystem. We find that the new evolution effects among different generations of cells in cellular automata can significantly improve the diffusion effect. After this, a new one-dimensional chaotic map is proposed, which is constructed by coupling the logistic map and the Bernoulli map (LBM). The new map exhibits a much better random behavior and is more efficient than comparable ones. Due to the favorable properties of the new map and cellular automata algorithm, we propose a new image-encryption algorithm in which three-dimensional bit-level permutation with LBM is employed in the confusion phase. Simulations are carried out, and the results demonstrate the superior security and high efficiency of the proposed scheme.

Stability of stochastic impulsive reaction–diffusion neural networks with S-type distributed delays and its application to image encryption

In this paper, we study stochastic impulsive reaction–diffusion neural networks with S-type distributed delays, aiming to obtain the sufficient conditions for global exponential stability. First, an impulsive inequality involving infinite delay is introduced and the asymptotic behaviour of its solution is investigated by the truncation method. Then, global exponential stability in the mean-square sense of the stochastic impulsive reaction–diffusion system is studied by constructing a simple Lyapunov–Krasovskii functional where the S-type distributed delay is handled by the impulsive inequality. Numerical examples are also given to verify the effectiveness of the proposed results. Finally, the obtained theoretical results are successfully applied to an image encryption scheme based on bit-level permutation and the stochastic neural networks.

A Color Image Encryption Technique Based on Bit-Level Permutation and Alternate Logistic Maps

Abstract The paper presents an approach to encrypt the color images using bit-level permutation and alternate logistic map. The proposed method initially segregates the color image into red, green, and blue channels, transposes the segregated channels from the pixel-plane to bit-plane, and scrambles the bit-plane matrix using Arnold cat map (ACM). Finally, the red, blue, and green channels of the scrambled image are confused and diffused by applying alternate logistic map that uses a four-dimensional Lorenz system to generate a pseudorandom number sequence for the three channels. The parameters of ACM are generated with the help of Logistic-Sine map and Logistic-Tent map. The intensity values of scrambled pixels are altered by Tent-Sine map. One-dimensional and two-dimensional logistic maps are used for alternate logistic map implementation. The performance and security parameters histogram, correlation distribution, correlation coefficient, entropy, number of pixel change rate, and unified averaged changed intensity are computed to show the potential of the proposed encryption technique.

Cracking and Improvement of an Image Encryption Algorithm Based on Bit-Level Permutation and Chaotic System

In recent years, with the rapid development of the network communication, information security issues have become increasingly prominent. As an important carrier of information, image plays an important role in the transmission process. Therefore, lots of image encryption algorithms have been proposed. However, these algorithms are not designed in accordance with the unified security standards and requirements, so there may be a lot of security risks, and what is the worst thing is that some encryption algorithms may be cracked in an acceptable time complexity by some cryptographic analysis. This paper focuses on one of the most influential algorithm proposed by Zhang, which improved Zhu’s algorithm. The non-fixed parameter and diffusion-permutation strategy are adopted by Zhang, but there are still problems that cannot resist chosen-plaintext attack and the key space is not enough to resist brute-force attack. We use chosen-plaintext attack to crack Zhang algorithm, and then propose a further improved scheme.

Quantum Image Encryption Using Intra and Inter Bit Permutation Based on Logistic Map

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.

Cryptanalysis and Enhancement of an Image Encryption Scheme Based on Bit-Plane Extraction and Multiple Chaotic Maps

Recently, an image encryption scheme combining bit-plane extraction with multiple chaotic maps (IESBC) was proposed. The scheme extracts binary bit planes from the plain-image and performs bit-level permutation and confusion, which are controlled by a pseudo-random sequence and a random image generated by the Logistic map, respectively. As the rows and columns of the four MSBPs are permuted with the same pseudo-random sequence and the encryption process does not involve the statistical characteristics of the plain-image, the equivalent secret key of IESBC can be disclosed in the scenario of known/chosen-plaintext attacks. This paper analyzes the weak points of IESBC and proposes a known-plaintext attack and a chosen-plaintext attack on it. Furthermore, we proposed an enhanced scheme to fix the shortcomings and resist the proposed plaintext attacks. The experimental simulation results demonstrated that the enhanced scheme is excellent in terms of various cryptographic metrics.

Image encryption using sequence generated by cyclic group

Image encryption using permutation is gaining its popularity over general encryption schemes like AES, DES, RSA etc., due to its high security, less time complexity using reasonable computational overheads. Mainly chaotic functions are employed in permutation based techniques to define a sequence, based on which the pixels or bits of an image are permuted. In parallel, researches are also carried out to define permutation using non chaotic techniques. In this paper, a novel non-chaotic image encryption technique is proposed. The properties of cyclic group are used as the backbone of the proposed method and using these properties some sequences/permutations are defined. These permutations are used for row/column level permutation of pixels and bit-level permutation. Iterative pixel addition operation with bit shifting using a ‘Transform array’ transforms the pixel value of the bit permuted image. Experimental results show that the proposed scheme is secure against statistical and differential attacks and provide a secure and efficient way for digital image encryption.

A new image encryption algorithm based on two-dimensional spatiotemporal chaotic system

In this paper, a new image encryption algorithm based on the two-dimensional spatiotemporal chaotic system is proposed.This system mixes linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and it has more cryptographic features in dynamics than the system of coupled map lattices does. The two-dimensional coupled map lattices (2DCML) system is only a special case in this chaotic system. In addition, bit-level permutation is employed to strengthen security of the cryptosystem. Simulations have been carried out, and the results demonstrate that the proposed algorithm has properties of large key space, high sensitivity to key, strong resisting attack. So, it is more secure and effective algorithm for encryption of digital images.