Chaotic system constructed by product trigonometric function and polynomial and applied to color image encryption

2021 ◽  
Author(s):  
Wanbo Yu ◽  
Siyu Gong
Keyword(s):  
Dynamical System ◽  
Color Image ◽  
Polynomial System ◽  
Linear Part ◽  
Fractal Dimensions ◽  
Trigonometric Function ◽  
Domain Space ◽  
Key Space ◽  
Pixel Correlation ◽  
Encrypted Images

In the applied research of nonlinear system, the low degree of chaos in the dynamical system leads to the limitation of using the chaos method to solve some practical problems. In this paper, we use the product trigonometric function and ternary polynomial to build a dynamical system, which has strong chaotic characteristics. The dynamical system is constructed by two product trigonometric functions and a ternary linear equation, and its chaotic properties are verified by bifurcation diagrams, Lyapunov exponents, fractal dimensions, etc. The system has many parameters and large parameter intervals and is not prone to cycles. The conditions for the non-divergence of this system are given by mathematical derivation, and it is found that the linear part of the system can be replaced by an arbitrary ternary polynomial system and still not diverge, and the bifurcation diagram is drawn to verify it. Finally, the chaotic sequence is distributed more uniformly in the value domain space by adding the modulo operation. Then, the bit matrix of multiple images is directly permuted by the above system, and the experiment confirms that the histogram, information entropy, and pixel correlation of its encrypted images are satisfactory, as well as a very large key space.

A Novel Color Image Encryption Algorithm Based on Hyperchaotic System and Permutation-Diffusion Architecture

2019 ◽  
Vol 29 (09) ◽  
pp. 1950115 ◽  
Author(s):  
Guangfeng Cheng ◽  
Chunhua Wang ◽  
Hua Chen
Keyword(s):  
Image Encryption ◽  
Color Image ◽  
Encryption Algorithm ◽  
Hyperchaotic System ◽  
Color Image Encryption ◽  
Key Space ◽  
Encryption Algorithms ◽  
Block Permutation ◽  
Encrypted Images ◽  
Differential Attacks

In recent years, scholars studied and proposed some secure color image encryption algorithms. However, the majority of the published algorithms encrypted red, green and blue (called [Formula: see text], [Formula: see text], [Formula: see text] for short) components independently. In the paper, we propose a color image encryption scheme based on hyperchaotic system and permutation-diffusion architecture. The encryption algorithm utilizes a block permutation which is realized by mixing [Formula: see text], [Formula: see text], [Formula: see text] components to strengthen the dependence of each component. Besides, it can reduce time consumption. Then, the key streams generated by the hyperchaotic system are exploited to diffuse the pixels, the three components affect each other again. And in the diffusion process, we can get two totally different encrypted images even though we change the last pixel because the [Formula: see text] component is diffused in reverse order. The experimental results reveal that our algorithm possesses better abilities of resisting statistical attacks and differential attacks, larger key space, closer information entropy to 8, and faster encryption speed compared with other chaos-based color image encryption algorithms.

scholarly journals A Symmetric Key Multiple Color Image Cipher Based on Cellular Automata, Chaos Theory and Image Mixing

2021 ◽  
Vol 50 (1) ◽  
pp. 55-75
Author(s):  
K SundaraKrishnan ◽  
RAJA SP ◽  
JAISON B
Keyword(s):  
Cellular Automata ◽  
Performance Metrics ◽  
Color Image ◽  
Signal To Noise Ratio ◽  
Logistic Map ◽  
Public Network ◽  
Key Space ◽  
Image Cipher ◽  
Zigzag Pattern ◽  
Encrypted Images

The transmission of significant masses of sensitive and secret images over a public network is inevitable, and demands effective tools and technology to safeguard and conceal the data. In this paper, a symmetric multiple color image encryption technique is proposed by adopting a dual permutation and dual substitution framework. Firstly, the input images are combined into a large image and then segmented into many small and equal-sized pure-image elements. Secondly, using the elementary cellular automata Rule-30, these pure-image elements are permuted to obtain mixed-image elements. Thirdly, second-level permutation is undertaken on the mixed-image elements by applying zigzag pattern scanning. Fourthly, pixel values are substituted by employing the circular shift method; subsequently, second-level pixel substitution is realized through using chaotic random sequences from a 2D logistic map. Finally, the big encrypted image is segmented into smaller encrypted images. Additionally, the keys are calculated from the input images to attain input sensitivity. The efficiency of this method is quantified, based on the unified average changing intensity (UACI), information entropy, number of pixels change rate (NPCR), key sensitivity, key space, histogram, peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) performance metrics. The outcome of the experiments and a comparative analysis with two similar methods indicate that the proposed method produced high security results.

Image encryption based on Fractional wavelet transform, Arnold transform with the double random phases in HSV color domain

2020 ◽  
Vol 13 ◽  
Author(s):  
Aarushi Shrivastava ◽  
Janki Ballabh Sharma ◽  
Sunil Dutt Purohit
Keyword(s):  
Wavelet Transform ◽  
Image Encryption ◽  
Fractional Fourier Transform ◽  
Color Image ◽  
Random Phase ◽  
Arnold Transform ◽  
Time Frequency ◽  
Key Space ◽  
Secret Keys ◽  
Fractional Wavelet Transform

Objective: In the recent multimedia technology images play an integral role in communication. Here in this paper, we propose a new color image encryption method using FWT (Fractional Wavelet transform), double random phases and Arnold transform in HSV color domain. Methods: Firstly the image is changed into the HSV domain and the encoding is done using the FWT which is the combination of the fractional Fourier transform with wavelet transform and the two random phase masks are used in the double random phase encoding. In this one inverse DWT is taken at the end in order to obtain the encrypted image. To scramble the matrices the Arnold transform is used with different iterative values. The fractional order of FRFT, the wavelet family and the iterative numbers of Arnold transform are used as various secret keys in order to enhance the level of security of the proposed method. Results: The performance of the scheme is analyzed through its PSNR and SSIM values, key space, entropy, statistical analysis which demonstrates its effectiveness and feasibility of the proposed technique. Stimulation result verifies its robustness in comparison to nearby schemes. Conclusion: This method develops the better security, enlarged and sensitive key space with improved PSNR and SSIM. FWT reflecting time frequency information adds on to its flexibility with additional variables and making it more suitable for secure transmission.

On the Analysis of Time-Periodic Nonlinear Hamiltonian Dynamical Systems

1995 ◽  
Author(s):  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Normal Form ◽  
Linear Part ◽  
Normal Form Theory ◽  
Mathieu’S Equation ◽  
Form Theory ◽  
Hamiltonian Dynamical Systems ◽  
Time Invariant ◽  
Time Periodic

Abstract In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. Unlike the traditional perturbation or averaging methods, these techniques are applicable to systems whose Hamiltonians contain ‘strong’ parametric excitation terms. First, the well-known Liapunov-Floquet (L-F) transformation is utilized to convert the time-periodic dynamical system to a form in which the linear pan is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. It is demonstrated that this approach is simple and straightforward as opposed to the traditional methods where a complicated set of algebraic manipulations are required. Since these operations yield Hamiltonians whose quadratic parts are integrable and time-invariant, further analysis can be carried out by the application of action-angle coordinate transformation and Hamiltonian perturbation theory. In the second approach, the resulting quasilinear time-periodic system (with a time-invariant linear part) is directly analyzed via time-dependent normal form theory. In many instances, the system can be analyzed via time-independent normal form theory or by the method of averaging. Examples of a nonlinear Mathieu’s equation and coupled nonlinear Mathieu’s equations are included and some preliminary results are presented.

A Color Image Encryption Algorithm Based on Improved DES

2015 ◽  
Vol 743 ◽  
pp. 379-384 ◽  
Author(s):  
Zhang Li Lan ◽  
Lin Zhu ◽  
Yi Cai Li ◽  
Jun Liu
Keyword(s):  
Random Function ◽  
Color Image ◽  
Logistic Function ◽  
Color Images ◽  
Encryption Algorithm ◽  
Key Generation ◽  
Color Image Encryption ◽  
Generation Algorithm ◽  
Key Space ◽  
Image Encryption Algorithm

Key space will be reduced after using the traditional DES algorithm to directly encrypt color images. Through combining the chaotic capability of the logistic function and by means of a specific algorithm, the fake chaotic son key’s space which is produced by the logistic chaotic pseudo-random function could be acquired. Then use the key generation algorithm to replace the traditional DES key generation algorithm. Experiment illustrates that the proposed algorithm has stronger robustness and anti-jamming capability to noise, and larger key’s space, sensitive initial keys, and better encryption effect, meanwhile it is better immune to multiple attacks.

Low-Order Modeling of Nonlinear High-Frequency Transversal Thermoacoustic Oscillations in Gas Turbine Combustors

2016 ◽  
Author(s):  
Tobias Hummel ◽  
Klaus Hammer ◽  
Pedro Romero ◽  
Bruno Schuermans ◽  
Thomas Sattelmayer
Keyword(s):  
Dynamical System ◽  
Gas Turbine ◽  
High Frequency ◽  
Linear Part ◽  
Combustion Noise ◽  
Dynamical System Theory ◽  
Flame Dynamics ◽  
The Impact ◽  
Thermoacoustic Oscillations ◽  
Low Order

This paper analyzes transversal thermoacoustic oscillations in an experimental gas turbine combustor utilizing dynamical system theory. Limit cycle acoustic motions related to the first linearly unstable transversal mode of a given 3D combustor configuration are modeled, and reconstructed by means of a low order dynamical system simulation. The source of nonlinearity is solely allocated to flame dynamics, saturating the growth of acoustic amplitudes, while the oscillation amplitudes are assumed to always remain within the linearity limit. First, a Reduced Order Model (ROM), which reproduces the combustor’s modal distribution and damping of acoustic oscillations is derived. The ROM is a low-order state-space system, which results from a projection of the Linearized Euler Equations (LEE) into their truncated eigenspace. Second, flame dynamics are modeled as a function of acoustic perturbations by means of a nonlinear transfer function. This function has a linear and a nonlinear contribution. The linear part is modeled analytically from first principles, while the nonlinear part is mathematically cast into a cubic saturation functional form. Additionally, the impact of stochastic forcing due to broadband combustion noise is included by additive white noise sources. Then, the acoustic and the flame system is interconnected, where thermoacoustic non-compactness due to the transversal modes’ high frequency is accounted for by a distributed source term framework. The resulting nonlinear thermoacoustic system is solved in frequency and time domain. Linear growth rates predict linear stability, while envelope plots and probability density diagrams of the resulting pressure traces characterize the thermoacoustic performance of the combustor from a dynamical systems theory perspective. Comparisons against experimental data are conducted, which allow the rating of the flame modes in terms of their capability to reproduce the observed combustor dynamics. Ultimately, insight into the physics of high-frequency, transversal thermoacoustic systems is created.

scholarly journals A Nature Inspired Color Image Encryption Technique to Protect the Satellite Images

2019 ◽  
Vol 9 (03) ◽  
Author(s):  
Bhagyashri I. Pandurangi R ◽  
Meenakshi R. Patil
Keyword(s):  
Image Encryption ◽  
Color Image ◽  
Random Sequence ◽  
Correlation Coefficients ◽  
Secret Key ◽  
Color Image Encryption ◽  
Encrypted Images ◽  
Differential Attacks ◽  
Crossover And Mutation ◽  
Image Encryption Algorithm

A color image encryption algorithm based on chaotic maps is proposed in this paper. The algorithm is based on two bio-operations: crossover and mutation. To enhance the robustness against differential attacks, the mutated image is subjected to scrambling process operated on the pixel values of the image using a random sequence. Experimental results show that the proposed algorithm is capable of generating encrypted images with uniform distribution of the pixel values and very low correlation coefficients of adjacent pixels. It is very sensitive to any change in the secret key values. The results show that the algorithm is robust to statistical and differential attacks.

scholarly journals A digital image encryption algorithm based on chaotic mapping

2019 ◽  
Vol 13 ◽  
pp. 174830261985347 ◽  
Author(s):  
Zhijuan Deng ◽  
Shaojun Zhong
Keyword(s):  
Image Encryption ◽  
Digital Image ◽  
Encryption Algorithm ◽  
Experimental Simulation ◽  
Secret Key ◽  
Chaotic Mapping ◽  
Key Space ◽  
Encrypted Images ◽  
Digital Image Encryption ◽  
Image Encryption Algorithm

In this article, we introduced a digital image encryption algorithm based on the chaotic mapping designed by Xiong et al. In their paper, the authors theoretically analyzed the algorithm and pointed out that the algorithm did not need to have the prior knowledge of the orbital distribution and one can select any chaotic model. In this way, the algorithm greatly expanded the cryptographic space and greatly reduced the number of iterations of the mapping. Since the algorithm has many characteristics, for instance, it is sensitive to the secret key, its key space is big, the pixel is well distributed after being encrypted, etc., the security of the encrypted images can be assured effectively. However, since the algorithm applied the image scrambling for encryption, and did not take the chosen-plaintext attacks into consideration, the algorithm is relatively weak in resisting the chosen-plaintext attacks. Therefore, we put forward a kind of image replacement method based on chaos, which can resist the chosen-plaintext attacks. And the experimental simulation proves that this algorithm not only has many characteristics, for instance, it is sensitive to the secret key, its key space is big, the pixel is well distributed after being encrypted, etc., but also can resist the chosen-plaintext attacks effectively. In the meanwhile, the algorithm is very sensitive to the small changes of the plaintexts, and its encrypted images will completely lose the features of the original ones.

A Color Image Watermarking Scheme Based on Chaotic Maps

2014 ◽  
Vol 543-547 ◽  
pp. 2304-2307
Author(s):  
Rui Song Ye ◽  
Hui Qing Huang ◽  
Rui Feng Chen
Keyword(s):  
Chaotic Maps ◽  
Color Image ◽  
Image Watermarking ◽  
Chaotic Sequence ◽  
Color Image Watermarking ◽  
Tent Map ◽  
Chebyshev Map ◽  
Key Space ◽  
Blue Channel ◽  
Watermarking Scheme

A color image watermarking scheme using the chaotic properties of 2D tent map and Chebyshev map is proposed. Given control parameters and initial values, one can iterate the 2D tent map to get one chaotic sequence and obtain one permutation by sorting the chaotic sequence in ascending order. The permutation is then utilized to shuffle the blue channel components of color image as a preprocessing stage to enhance the security, imperceptibility and robustness of watermarking. Meanwhile, one can iterate the Chebyshev map to generate another chaotic sequence to determine the embedding bit positions and strengthen the security as well. Experiment results show that the watermarking scheme is secure with large key space, imperceptible and robust against cropping, noise attacks.

scholarly journals Secure Image Encryption Based on an Ideal New Nonlinear Discrete Dynamical System

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
R. M. Lin ◽  
T. Y. Ng
Keyword(s):  
Dynamical System ◽  
Image Encryption ◽  
Discrete Dynamical System ◽  
Chaotic Sequence ◽  
Encryption Algorithm ◽  
Plain Text ◽  
System Parameters ◽  
Key Space ◽  
Highly Nonlinear ◽  
Image Encryption Algorithm

It is well known that encryption algorithms developed based on Logistic map suffer from limited key space due to the narrow regions of system parameters which can be used, potential risk of security in the presence of numerous periodic windows within the key space, and weakness in known-plain-text attack due to the inherent correlation among the chaotic sequence used for encryption. To overcome these existing problems, this paper presents a secure image encryption algorithm based on a new highly nonlinear discrete dynamical system with ideal chaotic characteristics. Transcendental functions are introduced together with modulo operations which physically represent discontinuous time-varying nonlinearities, leading to extremely complex chaotic behavior that is highly sensitive to system parameters and initial conditions, both of which are considered as the key for the cryptosystem. Extensive numerical experiment results have revealed that the proposed image encryption algorithm offers advantages of unlimited key space and high-level security, since those problematic periodic windows are no longer present within the key space, and it is extremely robust against known-plain-text attack, since the chaotic sequence generated bears no correlation whatsoever due to the folding effect of modulo operation. The algorithm makes truly efficient yet highly secure image encryption based on chaotic systems a reality.

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