Compound Chaos Research Articles

Dynamic DNA coding multi-image encryption based on compound chaos

We present a dynamic DNA coding multi-image encryption algorithm based on integer lifting wavelet transform and compound chaos. In the encryption process, the low-frequency sub-bands of four plaintexts are extracted to get a combined image containing the multiple plaintext image information. With the help of a chaotic system, the pixel positions and pixel values of the combined image are modified by the permutation and the diffusion operations. Then we divide the image into equal-sized blocks, and the dynamic DNA coding method is used to complete the final encryption. To enhance security, we employ the RSA algorithm to protect the keys used in our encryption algorithm. Simulation results and security analysis demonstrate the robustness and the security.

A bit plane image encryption algorithm based on compound chaos

A bit plane image encryption algorithm based on compound chaos

Cryptanalysis of a Bilateral-Diffusion image encryption algorithm based on dynamical compound chaos

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General image encryption algorithm based on deep learning compressed sensing and compound chaotic system

Many image compression and encryption algorithms based on traditional compressed sensing and chaotic systems are time-consuming, have low reconstruction quality, and are suitable only for grayscale images. In this paper, we propose a general image compression encryption algorithm based on a deep learning compressed sensing and compound chaotic system, which is suitable for grayscale images and RGB format color images. Color images can be directly compressed and encrypted, but grayscale images need copying from 1 channel to 3 channels. First, the original image is divided into multiple 3 × 33 × 33 non-overlapping image blocks and the bilinear interpolation Bilinear and convolutional neural network are used to compress the image, so that the compression network has no restriction on the sampling rate and can obtain high-quality compression of image. Then a composite chaotic system composed of a two-dimensional cloud model and Logistic is used to encrypt and decrypt the compressed image (sliding scrambling and vector decomposition), and finally the decrypted image is reconstructed. In the reconstruction network, the convolutional neural network and bilinear interpolation Bilinear are mainly responsible for reconstructing the contour structure information, and the fully connected layer is mainly responsible for reconstructing and combining the color information to reconstruct a high-quality image. For grayscale images, we also need to calculate the average value of the corresponding positions of the 3 channels of the reconstructed image, and change the 3 channels into 1 channel. The experimental results show that the general image encryption algorithm based on deep learning compressed sensing and compound chaos system has great advantages in data processing quality and computational complexity. Although in the network the color images are used for training, the quality of grayscale image reconstruction is still better than that of other algorithms. The image encryption algorithm has a large enough key space and associates the plaintext hash value with the key, which realizes the encryption effect of one image corresponding to one key, thus being able to effectively resist brute force attacks and selective plaintext attacks. Compared with it in the comparison literature, the correlation coefficient is close to an ideal value, and the information entropy and the clear text sensitivity index are also within a critical range, which enhances the confidentiality of the image.

Image Hiding Technology Based on Low Dimensional Compound Chaos Algorithm

Image Hiding Technology Based on Low Dimensional Compound Chaos Algorithm

Image encryption scheme based on a novel fractional order compound chaotic attractor

Many image encryption algorithms have too small key space to prevent exhaust attacks. Based on a novel compound chaotic system, an algorithm with expanded key space is proposed to aim at the problem. Firstly, an adaptive method is provided to design switching controllers during creating a novel compound chaos. Secondly, general Arnold transform is used to realise pixel scrambling technology. Finally, the novel fractional compound chaos is applied in pixel diffusion to improve security of the image encryption algorithm. In numerical simulation, classical colour image, gray image, binary image and non-square image are encrypted sufficiently to identify the encryption algorithm. Both theoretical analysis and experimental results show that the algorithm has larger key space and is suitable for different types of digital images, and encryption image can resist some kinds of external attacks.

Blended Chaos Control of Permanent Magnet Linear Synchronous Motor

Aiming at the chaos problem of permanent magnet linear synchronous motor in direct-drive wave power generation system, based on the ideal chaotic model with increased rotor edge effect, the permanent magnet linear synchronous motor system chaotic system was analyzed and a new sliding mode compound chaos control strategy was proposed. This strategy compensates for the shortcomings of the sliding mode control lag and chattering by using the complementary advantages of compound control, and can correct system parameters in real time. By using Lyapunov stability criterion, it was proved that the global convergence of the system is consistent. The simulation results show that the composite chaos control strategy can rapidly disengage the chaotic state of the motor system, suppress system chattering, weaken the control overshoot phenomenon, and has strong robustness and high control precision.

On the bifurcation of Marotto’s map and its application in image encryption

The aim of this paper is to address the codimension-one bifurcation of Marotto’s map and its utility in image encryption. First of all, local stability analysis and local bifurcation analysis of fixed points of the considered map are investigated in details. According to the classical bifurcation theory and the center manifold theorem, the map exhibits various bifurcation types such as transcritical, flip and Neimark–Sacker bifurcations. Second of all, the map is proven to be chaotic in the sense of Marotto. Since image encryption based on chaotic maps is very promising for cryptography, Marotto’s map, compound chaos, and spatiotemporal chaos are combined to encrypt and decrypt images. Numerical simulations agree with the analytical framework for the complex dynamics of the map. Furthermore, different test images are used to demonstrate the effectiveness of the method implemented for encryption.

Security evaluation of bilateral-diffusion based image encryption algorithm

Recently, a novel bilateral-diffusion image encryption algorithm based on dynamical compound chaos function and LFSR was proposed. The core idea of the algorithm is to introduce the bilateral-diffusion approach. The present paper focuses mainly on security evaluation of this approach. As it is well known, the security of a cryptosystem must depend only on the secrecy of the key rather than the secrecy of the algorithm according to Kerckoff’s principle. The security of the original algorithm is determined by two initial keys. Since the keys are fixed, the chaotic keystream keeps unchanged for different images. Thus, our purpose is to reveal the keystream. The cryptanalytic results show that the whole keystream can be broken by using two images including a chosen image and a known image, with a combination of chosen-plaintext attack and known-plaintext attack.

An Image Encryption Algorithm Based on Scrambling and Chaos

With the rapid development of multimedia technology, secure algorithm of image communication becomes more and more important. Based on scrambling transformation and compound chaos, an encryption algorithm in spatial domain is proposed. Firstly, it scrambles pixel positions and confuses pixel values according to corresponding coordination under the control of chaos. Secondly, it takes nonlinear substitution and difiusion for all lines in the image. It iterates the upper two steps for at least 3 times to get the cipher-text. In the process of scrambling and substitution, pixel values are introduced to perturb compound chaos for adaptive encryption, and the scrambling function is compatible with images at any ratio of length to width without any preprocessing. Theoretical analysis shows that the algorithm has huge key space, and the mapping relation between the plaintext and the cipher-text is complex to e‐ciently defend attacks. Experiments show that the algorithm achieves strong sensitivity, conforms to confusion and difiusion principles in cryptography, and gets high security.

New color image encryption algorithm based on compound chaos mapping and hyperchaotic cellular neural network

We propose an image encryption/decryption algorithm based on chaotic control parameter and hyperchaotic system with the composite permutation-diffusion structure. Compound chaos mapping is used to generate control parameters in the permutation stage. The high correlation between pixels is shuffled. In the diffusion stage, compound chaos mapping of different initial condition and control parameter generates the diffusion parameters, which are applied to hyperchaotic cellular neural networks. The diffusion key stream is obtained by this process and implements the pixels’ diffusion. Compared with the existing methods, both simulation and statistical analysis of our proposed algorithm show that the algorithm has a good performance against attacks and meets the corresponding security level.

An Improved Reversible Watermarking Algorithm in Wavelet Domain for Two-Dimensional CAD Engineering Graphics

With the development of digital design and processing and the explosive growth of the demand for two-dimensional CAD engineering graphics, more attention has been paid on the security and the copyright issues of engineering graphics. In this paper, an improved reversible watermarking algorithm in wavelet domain for two-dimensional CAD engineering graphics is proposed. Firstly, the watermark information is preprocessed by compound chaos sequence. And then, block the graphic and extract all vertexes in each blocks of the 2D CAD engineering graphics, Log-polar Mapping (LPM) and wavelet transform are done to them respectively to achieve the invariance of affine transform. Finally, the encrypted watermark is embedded into detailed coefficients by using improved quantization index modulation (IQIM) scheme. Compared with the original previous algorithm, theoretical analysis and experimental results show that the proposed algorithm has not only good visibility and good reversibility, but also stronger robust against the attacks such as transformation, rotation, equal scaling and entity deleting, tampering or adding etc.

Novel bilateral-diffusion image encryption algorithm with compound chaos and LFSR

In order to solve the problem of short cycle and low precision of one-dimensional (1D) chaotic function, the new compound two-dimensional chaotic function is presented by exploiting two 1D chaotic functions which are switched randomly. A new chaotic sequence generator is designed by the compound chaos and linear feedback shift register (LFSR). The random properties of compound chaotic functions and LFSR are also proved rigorously. The novel bilateral-diffusion image encryption algorithm and permutation algorithm are proposed based on the compound chaotic function and LFSR, which can produce more avalanche effect and larger key space. The entropy analysis, differential analysis, statistical analysis, cipher random analysis and cipher sensitivity analysis are introduced to test the security of new scheme. The results show that the novel image encryption method passes SP 800-22 standard tests and solves the problem of short cycle and low precision of 1D chaotic function.

Research on compound chaos image encryption method with clock- varying

In this paper, we suggest one compound chaos image encryption method with time- varying multilevel initial parameters. This algorithm combines Subsection-linearity mapping, Chebyshev mapping with Logistic mapping in order to disturbing values of each image point and the array of original images based on chaotic second-scrambling way. The chaotic system uses time-varying system clock to change the first chaotic mapping initial parameter, and takes those chaotic sequences which generated by the first chaotic mapping as the initial parameters for the second chaotic mapping, then generate two-dimensional image pixel position scrambling matrix, and uses the same system clock to lock Chebyshev mapping initial parameter, then generate two-dimensional image pixel value transforming matrix. By this way for using the time-varying system clock, The encryption system can randomly changes many initial parameters of chaotic image encryption system to enhance image transmission security, has the capability of “one time one secret”. The simulation results show that this algorithm is simple, safe, easy to achieve with software and has huge secret key space.

The novel bilateral – Diffusion image encryption algorithm with dynamical compound chaos

Chaos may be degenerated because of the finite precision effect, hence the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which are switched randomly. A new chaotic sequence generator is designed by the compound chaos which is proved by Devaney's definition of chaos. The properties of dynamical compound chaotic functions and LFSR are also proved rigorously. A novel bilateral-diffusion image encryption algorithm is proposed based on dynamical compound chaotic function and LFSR, which can produce more avalanche effect and more large key space. The entropy analysis, differential analysis, statistical analysis, cipher random analysis, and cipher sensitivity analysis are introduced to test the security of new scheme. Many experiment results show that the novel image encryption method passes SP 800-22 and DIEHARD standard tests and solves the problem of short cycle and low precision of one-dimensional chaotic function.

A Novel Encryption Scheme for Digital Images Based on Compound Chaos Algorithm

A compound Chaos encryption algorithm for digital images is designed in this paper. Lorenz Chaotic system and Logistics map are linked in cascade to generate Chaos sequences. Then the permutation matrix is constructed to encrypt the digital image. The new algorithm can expand the key space and improve anti-aggressive ability. Matlab7.0 is used for simulation testing of the image encryption. Experimental results show that the algorithm is feasible and it can satisfy the security requirement for image transmission and storage. The compound Chaos algorithm can be also used for color digital image encryption.

Feedback image encryption algorithm with compound chaotic stream cipher based on perturbation

In this paper, two new one-dimensional chaotic functions are designed using Devaney chaotic definition. And a dynamically shifting compound chaotic function is constructed based on the two new one-dimensional chaotic functions. The properties of compound chaotic functions are also proved. A new feedback image encryption algorithm is designed using the new compound chaos and an image pixel permutation, 3D baker scheme is described in detail. In the scheme, a new dynamic block dividing the 3D baker is put forward using the compound chaotic map, and the key space expands. In order to produce avalanche effect and sensitivity of cipher to plaintext, the round times are designed to control the cycle. The entropy analysis, difference analysis, weak-key analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new scheme of image encryption. The tests show that the image encryption method passes the random tests of NIST FIPS 140-2(2001) and SP 800-22 standards. This paper also solves the problem of short periods and low precision of one-dimensional chaotic function by perturbation.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney’s definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved. A new image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and an image pixel permutation, 3D baker scheme is described in detail. In the scheme a new dynamic block dividing of the 3D baker scheme is put forward using the compound chaotic map. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to compound chaos with 2D baker and DES encryption methods, we come to the conclusion that the new image encryption method with speed and high security solves the problem unable to resist chosen plaintext attack and low precision of one-dimensional chaotic function by perturbation.

COMPOUND CHAOS

Compounding is a statistical notion. Essentially, it comprises of regarding the parameters in a particular statistical distribution as random variables with a prescribed distribution. The compound distribution then acquires the parameters of the compounding distribution as its own. As deterministic chaos, in spite of being deterministic, appears like a statistical phenomenon, the notion of compounding can be extended to chaotic systems. It is shown with illustrations that a chaotic system can be compounded by another chaotic system, giving rise to compound chaos which is, in general, “chaoticer”. The concept can also be used to make a periodic system chaotic, thus opening possibilities of “chaoticization”. Examples of compound chaos and chaoticization are given using Lorenz and Rössler systems, including their attractors and limit cycles as “compoundee” and/or “compounder” systems. The conclusions are based on quantitative studies of Lyapunov exponents and correlation dimensions.