Permutation Diffusion Research Articles

A novel one-dimensional Cosine within Sine chaotic map and novel permutation–diffusion based medical image encryption

A novel one-dimensional Cosine within Sine chaotic map and novel permutation–diffusion based medical image encryption

Enhanced image encryption with compression using improved coupled map lattices and Fisher–Yates permutation–diffusion

Enhanced image encryption with compression using improved coupled map lattices and Fisher–Yates permutation–diffusion

Cryptanalysis of an image encryption scheme based on two-point diffusion strategy and Henon map

In recent year, an image encryption scheme was proposed based on Henon map and two-point diffusion strategy. Two-point diffusion method improved the conventional permutation–diffusion architecture by allowing two cryptographic primitives, i.e. permutation and diffusion intermingling with each other in every single round. In this paper, we show the dynamical degradation of digital Henon map using state-mapping network. By comparing to the exhaustive key search, applying algebraic cryptanalysis and chosen plaintext attack require lower time complexity of computation. The recovery of equivalent keys also reduces the possible numbers of secret keys. The keystream recovery process has been verified using simulations. We also show that the two-point diffusion strategy does not improve the efficiency of the image encryption scheme and some improvement suggestions using parallel computing are given. As a nutshell, extra care needs to be taken when selecting chaotic map and assessing the security of future proposals based on the two-point diffusion strategy schemes.

A one-time-pad-like chaotic image encryption scheme using data steganography

One-time-pad-like image ciphers using chaos and hash functions have achieved outstanding performance in terms of security strength and efficiency, but they fail to consider the problem of hash value distribution, limiting their practical application significantly. Moreover, most existing algorithms are designed based on independent permutation and sequential diffusion operations, which may lead them to end up being broken by chosen-plaintext attacks. In this paper, we propose a one-time-pad-like chaotic image cipher using data steganography. The whole scheme consists of an encryption process for the plain-image and an embedding process for the encrypted image. Different from the permutation–diffusion type image ciphers, we remove the permutation stage and use only a plaintext-dependent non-sequential diffusion operation. The encryption algorithm exploits the security potential of the encryption order and can achieve a satisfactory level of security with only once scanning of the entire image. During the embedding process, a reversible data-hiding technique is adopted to embed the hash value of the plain-image into the cipher-image so that it can be transmitted together to the receiver, overcoming the practical limitation encountered by the existing one-time-pad-like ciphers. Experimental results indicate that the proposed algorithm is secure against all common attacks and outperforms state-of-the-art approaches in terms of both security and efficiency.

Multiple-Image Encryption Scheme Based on an N-Dimensional Chaotic Modular Model and Overlapping Block Permutation–Diffusion Using Newly Defined Operation

Some existing chaotic maps have the drawbacks of a narrow range of chaotic parameters and discontinuities, which may be inherited by new chaotic systems generated from them as seed maps. We propose a chaotic model that can generate N-dimensional chaotic systems to overcome the problem. By fixing the original parameters of the seed map in the chaotic range, we then introduce new parameters and use modular operations to widen the range of the parameters and increase the complexity. Simulation results show that the generated chaotic system has good chaotic dynamics. Based on this chaotic model, we propose a multiple-image encryption algorithm that is not limited by image type, number, and size. The resistance to plaintext attacks is enhanced by a permutation–diffusion algorithm based on overlapping blocks. We design a newly defined lookup table operation based on Latin squares with enhanced nonlinearity and randomness. By adjusting the overlapping block parameters and the number of Latin squares, users can design different encryption levels to balance encryption efficiency and encryption effectiveness. The experimental results show that the proposed image encryption algorithm can effectively encrypt multiple images, and all the evaluation indexes reach the expected value.

A novel simultaneous permutation–diffusion image encryption scheme based on a discrete space map

The constant increase of devices connected to the internet and the development and spread of technologies such as 5G leads to substantial growth in data-sharing over non-secure channels in real-time applications, augmenting the need for fast cryptography algorithms. Algorithms such as the Advanced Encryption Standard (AES) are not optimized for image encryption, and hence, as an alternative, chaotic encryption strategies have been explored by researchers. However, due to the use of floating-point arithmetic and inefficient memory access, the performance of these chaotic ciphers is insufficient for the encryption of high-resolution images. Thus, this work proposes generating the chaotic sequences based on fixed-point arithmetic to increase computational efficiency, and using a simultaneous permutation–diffusion operation and block encryption to deal with the inefficient memory access. The proposed scheme leads to a throughput 353 times higher than the AES, 75 times higher than the previously higher value in the literature and 11 times higher than the Ascon algorithm. The cipher security evaluation is performed based on statistical attacks, with metrics such as Pearson, histogram variance, Shannon’s entropy, correlation coefficients, and NIST tests; differential attacks, with the NPCR, UACI, and MSE metrics; chosen plain-text, with the SSIM metric; brute-force, with the key-space; noise and occlusion attacks, with the PSNR metric.

A Novel Image Encryption Algorithm Based on 2D Self-Coupling Sine Map

Since the current general image encryption algorithms based on chaotic systems and classical permutation diffusion structures typically suffer from stochastic degradation, simple algorithm structures, and reduced execution efficiency when dealing with images with large data, this paper proposes a new multiprocess image encryption algorithm based on a new hyperchaotic coupled sine map. To begin with, by performing dynamic analyses of the map, including equilibrium points, bifurcation diagrams, Lyapunov exponent diagrams, and phase diagrams, associated performance analyses show high spectral entropy (SE) values and permutation entropy (PE) values. Meanwhile, sequences generated by the proposed map are able to pass the NIST randomness test, which shows its suitability for the design of encryption algorithms. Then, a chaos-based image encryption algorithm is proposed in this paper: In the preprocessing stage, the images are sparsely sampled using a compressed-sensing method; in the permutation stage, the image is decomposed into eight bit-plane images containing only 0s and 1s and a clockwise cyclic shift operation based on a chaotic sequence is applied in each bit-plane image to achieve a bit-level permutation effect; in the diffusion stage, the block DNA random computing is applied to the permuted image to modify the pixel values and the final cipher image is obtained. In addition, the initial value of the map is determined by the preset initial value, user-defined strings, and the Hash value of the plain image, where the Hash value of the plain image is calculated by the SHA-256 algorithm. Finally, the analysis of the algorithm demonstrates that the algorithm exhibits extremely strong plaintext correlation externally and excellent encryption performance in terms of attack resistance and execution efficiency.

Cryptanalysis of an Image Encryption Algorithm Based on a 2D Hyperchaotic Map.

Recently, an image encryption scheme based on a 2D hyperchaotic map is proposed. It adopts the permutation-diffusion architecture and consists of three steps, which are permutation, forward diffusion, and backward diffusion. In this paper, we break this cipher with both the chosen-plaintext attack (CPA) and the chosen-ciphertext attack (CCA). According to our analysis, we found the two complex diffusion processes could be simplified into two simple diffusions and a modular addition operation. Based on this, the equivalent key can be obtained with CPA and CCA. Detailed theoretical derivations and the results of experiments confirmed the feasibility of our attack methods. When the image size was 256×256, the running time of the attacks was less than 2 hours on a laptop with a 2.59 GHz Intel Core i7 and 16 GB DDR3 memory. Other sizes of images were also tested, and some rules were found. In addition, the probability of other attacks has also been discussed, and some suggestions for improvements are given. The source codes are publicly available and can be found online.

Security Analysis of the Image Encryption Algorithm Based on a Two-Dimensional Infinite Collapse Map.

This paper analyzes the security of the image encryption algorithm based on a two-dimensional (2D) infinite collapse map. The encryption algorithm adopts a permutation–diffusion structure and can perform two or more rounds to achieve a higher level of security. By cryptanalysis, it is found that the original diffusion process can be split into a permutation–diffusion structure, which comes after the original permutation, so these two permutations can be merged into one. Then, some theorems about round-down operation are summarized, and the encryption and decryption equations in the diffusion process are deduced and simplified accordingly. Since the chaotic sequences used in encryption algorithm are independent of the plaintext and ciphertext, there are equivalent keys. The original encryption algorithm with single-round, two-round, and multi-round of permutation–diffusion processes is cracked, and the data complexity of the cryptanalysis attacks is analyzed. Numerical simulation is carried out by MATLAB, and the experimental results and theoretical analysis show the effectiveness of the cryptanalysis attacks. Finally, some suggestions for improvement are given to overcome the shortcomings of the original encryption algorithm.

Cryptographic system based on double parameters fractal sorting vector and new spatiotemporal chaotic system

Information security and image encryption have rapidly developed in recent years. This study presents an iterative method for vectors with fractal characteristics. Based on the idea of combining fractal and algebraic theories, the double parameters fractal sorting vector (DPFSV) was originally proposed, which incorporates features such as complexity, self-similarity, and iteration. Based on the practical application requirements, the DPFSV has a good regulatory vector length and increases the diversity of information location change laws. Hence, this study uses the DPFSV to control iterative node relationships in spatiotemporal chaotic systems. The new spatiotemporal chaotic system proposed based on DPFSV exhibits better dynamics than that of the coupled map lattice (CML) system, verified by comparing their Kolmogorov–Sinai entropy, bifurcation diagram, information entropy, and mutual information. Therefore, DPFSV–CML is more suitable in cryptography than CML. Combining the DPFSV and spatiotemporal chaotic system, this study constructs a new cryptographic system to implement permutation–diffusion synchronous encryption. This new encryption method has a good encryption effect and is resistant to various attacks. The security of this proposed cryptographic system is verified through various security analyses and simulated attack validations.

A plain-text independent color image encryption system with multi-thread permutation and multi-channel diffusion

In this paper, we present a novel multi-threaded parallel permutation and channel-combined diffusion for image encryption which is independent of plain text. In our proposed method, the coupled map lattice is used to generate the key sequences for multi-thread permutation and diffusion. Then intra- and inter-thread permutations are achieved using multi-threading in combination with the tent mapping. For the subsequent diffusion, this paper introduces a method based on channel-combined diffusing which simultaneously diffuses three channels. Experimental results indicate a high encryption performance with the capability of effectively resisting the known plain text and differential attacks. Our proposed method also has a lower computational complexity which enables its applicability in practical scenarios.

Cryptanalysis of a New Chaotic Image Encryption Technique Based on Multiple Discrete Dynamical Maps.

Recently, a new chaotic image encryption technique was proposed based on multiple discrete dynamic maps. The authors claim that the scheme can provide excellent privacy for traditional digital images. However, in order to minimize the computational cost, the encryption scheme adopts one-round encryption and a traditional permutation–diffusion structure. Through cryptanalysis, there is no strong correlation between the key and the plain image, which leads to the collapse of cryptosystem. Based on this, two methods of chosen-plaintext attacks are proposed in this paper. The two methods require 3 pairs and 258 pairs of plain and cipher images, respectively, to break the original encryption system. The simulation results show the effectiveness of the two schemes.

Color image encryption based on joint permutation and diffusion

Image encryption plays an essential role in the community of image security. Most existing image encryption approaches adopt a permutation–diffusion scheme to permute pixel positions and change pixel values separately. One limitation of this scheme is that it has a high risk of being cracked. To solve this problem, we propose an approach that jointly permutates and diffuses (JPD) the pixels in a color image for encryption. First, a 4D hyperchaotic system with two positive Lyapunov exponents is used to generate a sequence for almost all encryption procedures. To enhance security, the plain image’s information is introduced to the hyperchaotic system’s initial parameters. Then, the hyperchaotic sequence is used to permute and diffuse the pixels in images jointly. More specifically, two index matrices that determine which pixels will be permuted and diffused and one mask matrix that determines how the pixels will be diffused are generated by the hyperchaotic sequence. We test the proposed JPD with several popular images. Experimental results and security analysis demonstrate that the JPD is capable of resisting various types of attacks. Moreover, the JPD can accelerate the encryption process. All these indicate that the JPD is effective and efficient for color image encryption.

An image encryption scheme based on double chaotic cyclic shift and Josephus problem

In recent years, image encryption has become a very popular and effective method to protect digital images. Among many image encryption methods, the image encryption algorithm based on chaotic map has extensive application and profound theoretical basis. In this paper, a novel image encryption algorithm is proposed by combining chaotic map with Josephus problem. The whole encryption process adopts the classical permutation–diffusion structure. In the permutation process, the double chaotic cycle shift algorithm has been proposed by improving the chaotic shift transform method. In the diffusion stage, we extend the definition of Josephus problem by using chaotic map to preserve the Josephus sequence diversity. We then divide the image into sub-blocks and pick one randomly according to Josephus sequence. Furthermore, we change the pixel values of the image through performing modular addition and XOR operations on the pixels between blocks. Through the above process, we get the image encryption algorithm based on double chaotic cycle shift and Josephus problem (JP-DCCS). In the simulation experiment and security analysis, we compare JP-DCCS with the other advanced image encryption algorithms. The results show that JP-DCCS has better performance and higher security.

A Dynamic DNA Color Image Encryption Method Based on SHA-512.

This paper presents a dynamic deoxyribonucleic acid (DNA) image encryption based on Secure Hash Algorithm-512 (SHA-512), having the structure of two rounds of permutation–diffusion, by employing two chaotic systems, dynamic DNA coding, DNA sequencing operations, and conditional shifting. We employed the SHA-512 algorithm to generate a 512-bit hash value and later utilized this value with the natural DNA sequence to calculate the initial values for the chaotic systems and the eight intermittent parameters. We implemented a two-dimensional rectangular transform (2D-RT) on the permutation. We used four-wing chaotic systems and Lorentz systems to generate chaotic sequences and recombined three channel matrices and chaotic matrices with intermittent parameters. We calculated hamming distances of DNA matrices, updated the initial values of two chaotic systems, and generated the corresponding chaotic matrices to complete the diffusion operation. After diffusion, we decoded and decomposed the DNA matrices, and then scrambled and merged these matrices into an encrypted image. According to experiments, the encryption method in this paper not only was able to withstand statistical attacks, plaintext attacks, brute-force attacks, and a host of other attacks, but also could reduce the complexity of the algorithm because it adopted DNA sequencing operations that were different from traditional DNA sequencing operations.

Multiobjective evolutionary optimization techniques based hyperchaotic map and their applications in image encryption

Chaotic-based image encryption approaches have attracted great attention in the field of information security. The properties of chaotic maps such as randomness and sensitivity have given new ways to develop efficient encryption approaches. But chaotic maps require initial parameters to develop random sequences. The selection of these parameters is a tedious task. To obtain the optimal initial parameters, evolutionary optimization approaches have been utilized in image encryption. Therefore, in this paper, a hyper-chaotic map is optimized using a multiobjective evolutionary optimization approach. A dual local search based multiobjective optimization (DLS-MO) is used to obtain the optimal parameters of a hyper-chaotic map and encryption factors. Then, using optimal parameters, a hyper-chaotic map develops the secret keys. These secret keys are then used to perform permutation and diffusion on a plain image to develop the encrypted image. To perform encryption, permutation–permutation–diffusion–diffusion architecture is adopted for better confusion and diffusion. Experimental results show that the proposed approach provides better performance in comparison to existing competitive approaches.

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.

Colour image encryption scheme based on enhanced quadratic chaotic map

In this study, an enhanced quadratic map (EQM) is proposed and has been applied in a new colour image encryption scheme. The performance evaluations show that the EQM has excellent performances such as better Lyapunov exponent and larger chaotic ranges when compared with the classical quadratic map. The sequences generated from this EQM are successfully used in a new proposed colour image encryption scheme with excellent confusion and diffusion properties. The encryption structure is based on the permutation–diffusion process, and then adopted on the classical permutation, it is characterised by a high speed of diffusion, which enables the encryption of the three components of the plaintext image at the same time, and these encrypted components are simultaneously related to each other. The proposed scheme is tested on the USC-SIPI image dataset and on the real-life image dataset; its effectiveness is also compared with five latterly proposed image encryption schemes. The simulation results indicate that the proposed scheme has the properties of large key space, a weaker correlation between neighbouring pixels, higher sensitivity towards key, greater randomness of pixels and the capacity to withstand statistical analysis, plaintext/chosen-plaintext attacks, and differential attacks, thus that it has higher security and can be appropriate for image encryption.

Improved Security in Multimedia Video Surveillance Using 2D Discrete Wavelet Transforms and Encryption Framework

As the rate of the video is increasing on the internet, the security of video data is considered as a critical issue. In case of video surveillance application, the multimedia video streams require the video to be transmitted in a more secure way to its corresponding monitoring site. The multimedia video security is improved in this paper using a compression based encryption module. 2D Discrete Wavelet Transforms method is used for the compression process. The wavelet transform eliminates the low visual information, and it is scrambled and rotated for the encryption process. The encryption is handled using a series of the permutation–diffusion framework that helps in encrypting each video frame for possible secured transmission. The diffusion is carried out using Logistic chaotic maps, and the permutated blocks are encrypted with block-wise encryption. The experimental results show that the proposed video security framework achieves an improved performance against the existing method in terms of PSNR, SSIM, key size, and compression ratio, error rate.

A Simple Chaotic Map-Based Image Encryption System Using Both Plaintext Related Permutation and Diffusion.

Recently, to conquer most non-plain related chaos-based image cryptosystems’ security flaws that cannot resist the powerful chosen/knownn plain-text attacks or differential attacks efficiently for less plaintext sensitivity, many plain related chaos-based image cryptosystems have been developed. Most cryptosystems that have adopted the traditional permutation–diffusion structure still have some drawbacks and security flaws: (1) most plaintext related image encryption schemes using only plaintext related confusion operation or only plaintext related diffusion operation relate to plaintext inadequately that cannot achieve high plaintext sensitivity; (2) in some algorithms, the generation of security key that needs to be sent to the receiver is determined by the original image, so these algorithms may not applicable to real-time image encryption; (3) most plaintext related image encryption schemes have less efficiency because more than one round permutation–diffusion operation is required to achieve high security. To obtain high security and efficiency, a simple chaotic based color image encryption system by using both plaintext related permutation and diffusion is presented in this paper. In our cryptosystem, the values of the parameters of cat map used in permutation stage are related to plain image and the parameters of cat map are also influenced by the diffusion operation. Thus, both the permutation stage and diffusion stage are related to plain images, which can obtain high key sensitivity and plaintext sensitivity to resist chosen/known plaintext attacks or differential attacks efficiently. Furthermore, only one round of plaintext related permutation and diffusion operation is performed to process the original image to obtain cipher image. Thus, the proposed scheme has high efficiency. Complete simulations are given and the simulation results prove the excellent security and efficiency of the proposed scheme.