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ADOPTION OF FRACTIONAL DIFFERENTIAL EQUATIONS UNDER IMPROVED VARIATIONAL ITERATIVE algorithm COMBINED WITH DNA CODING algorithm IN image encryption

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FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2022年第2期30卷 2240062-2240062页

作者： Li, Xu Kateb, Faris Wu, Shaofei Hubei Univ Econ Law & Business Coll Wuhan 430205 Peoples R China Wuhan Inst Technol Hubei Prov Key Lab Intelligent Robots Wuhan Peoples R China Wuhan Inst Technol Sch Comp Sci & Engn Wuhan Peoples R China King Abdulaziz Univ Fac Comp & Informat Technol Dept Informat Technol Jeddah Saudi Arabia

To explore the application of improved variational iterative method in solving fractional differential equations and the effect of DNA coding algorithm based on logistic chaos mapping in image encryption, combining Chebyshev polynomial with variational iterative method, a new algorithm for solving fractional differential equations is proposed. In order to solve the initial value problem, the simulation software is used to compare the approximate solution after the change of values of a and k in the solution process to investigate the influence of different parameters on the accuracy of fractional order system. Subsequently, the logistic chaos sequence is used to generate discrete binary sequences, and an image encryption algorithm based on DNA coding is proposed. In order to verify the encryption performance of the proposed algorithm, Matlab simulation software is used to simulate and verify the image encryption processing. The results show that when a approaches 1, the solution is closer to the exact solution than that when a approaches 0.5, 0.7, and 0.9;compared with 1, 3, 5, and 7, the constructed algorithm has the highest accuracy when k value is 9. The simulation results of the fuzzy partial fractional order system show that the chaotic sequence is sensitive to the initial value, and the logistic mapping sequence is suitable for the information encryption of the secure communication system. The simulation results of the image encryption algorithm based on DNA coding show that the algorithm can effectively encrypt the image, and the image histogram after encryption is approximately a horizontal line;slight changes in the initial value will affect the decryption effect of the image;the correlation analysis results show that there is no correlation between adjacent pixels in the image after encryption, which indicates that combining Chebyshev polynomials with variational iteration method can reduce the computational burden and improve the computational accuracy, a

关键词： Chebyshev Polynomial Variational Iterative Method Logistic Chaos Mapping DNA Coding image encryption algorithm

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Breaking a novel image encryption scheme based on an improper fractional order chaotic system

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MULTIMEDIA TOOLS AND APPLICATIONS 2017年第2期76卷 1817-1826页

作者： Norouzi, Benyamin Mirzakuchaki, Sattar Iran Univ Sci & Technol Elect Res Ctr Sch Elect Engn POB 16846-13114 Tehran Iran

In this paper, we analyze the security of a recent image encryption algorithm based on an improper fractional-order chaotic system suggested by Zhao et al. The fatal flaw in the cryptosystem is that the keystream generated depends on neither the plain-image nor the cipher-image. Another main issue with this algorithm is using the same key (the last key in the keystream) in all encryption equations. Based on these points, it is easy to recover the plain-image and the keystream by applying chosen plaintext attack in only one plain-image. Both mathematical analysis and experimental results confirm the feasibility of this attack. As a result, the cryptosystem under study is not suitable for cryptography.

关键词： image encryption algorithm Cryptanalysis Keystream Chosen plaintext attack

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2D arcsine and sine combined logistic map for image encryption

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VISUAL COMPUTER 2023年第4期39卷 1517-1532页

作者： Ding, Yi Duan, Zhikui Li, Shiren Hunan Univ Arts & Sci Changde Peoples R China Foshan Univ Foshan Peoples R China Sun Yat Sen Univ Guangzhou Peoples R China

Chaotic system is widely applied in field of information security because of its excellent properties of unpredictability, no periodicity, pseudo-randomness, and high sensitivity to initial parameters. In this paper, we propose a new chaotic map, named 2D arcsine and sine combined logistic map (2D-ASLM), which is a combination of arcsine, Sine, and Logistic maps. Compared with the existing chaotic maps, the proposed one has the better pseudo-randomness and ergodicity from the viewpoint of chaotic performance. Besides, it also has a more unpredictable chaotic rang as well as a relatively low implementation cost. A chaotic tree transform (CTT) is introduced to effectively disrupt the image pixel positions. Then, the image can be encrypted by combining 2D-ASLM and CTT. Extensive results on encryption simulation and security analysis have shown the effectiveness of the proposed algorithm from different aspects.

关键词： 2D arcsine and sine combined logistic mapping A chaotic tree transform image encryption algorithm Chaotic mapping

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image encryption based on Fisher-Yates shuffling and three dimensional chaotic economic map

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IET image PROCESSING 2019年第12期13卷 2086-2097页

作者： Karawia, Abdelrahman Qassim Univ Comp Sci Unit Deanship Educ Serv Buraydah 51452 Saudi Arabia Mansoura Univ Dept Math Fac Sci Mansoura 35516 Egypt

Recently, few researchers investigated algorithms of image encryption using different chaotic economic maps (CEMs). However, the authors investigated the effect of these maps on the encryption of the plain image. In the current study, an image encryption algorithm via Fisher-Yates shuffling (FYS) combined with a three-dimensional (3D) CEM is given. FYS is used to generate the random permutation of a finite sequence. First, it is used to shuffle the rows and the columns of the plain image. Second, the 3DCEM is used in the substitution stage to confuse the pixels of the shuffling image. The proposed algorithm is applied to several types of images. Many measurements are performed to check the security and performance of the proposed algorithm. In addition, numerical simulations and experimental results have been implemented to verify that the proposed algorithm can resist different attack types.

关键词： chaos cryptography image processing plain image image encryption algorithm FYS three-dimensional CEM 3DCEM shuffling image Fisher-Yates shuffling chaotic economic maps substitution stage

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Dynamic analysis of an improper fractional-order laser chaotic system and its image encryption application

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OPTICS AND LASERS IN ENGINEERING 2020年 129卷 106031-106031页

作者： Yang, Feifei Mou, Jun Ma, Chenguang Cao, Yinghong Dalian Polytech Univ Sch Informat Sci & Engn Dalian 116034 Liaoning Peoples R China

The fractional-order chaotic systems have characteristics of the all chaotic systems, however, the improper fractional-order chaotic systems have more complexity random sequences, which more suitable for chaotic cryptosystems. To investigate the application of improper fraction order chaotic system in chaotic cryptography, in this paper, an improper fractional-order laser chaotic system is constructed and applied in image encryption algorithm. The dynamic performances of the system are studied through phase diagrams, Lyapunov exponents spectrum, bifurcation diagrams and C-0 complexity. Meanwhile, the improper fractional-order laser chaotic system is realized based on DSP platform. In addition, the performances of the designed encryption scheme are analyzed by key space, correlation coefficients, information entropy, histogram, differential attacks and robustness analysis. The experimental simulation results indicate that the improper fractional-order laser chaotic system not only has the abundant dynamic characteristics, but also has better security when it is used to image encryption algorithm. Therefore, this research would provide theoretical basis for the improper fractional-order laser chaotic system in security communications application.

关键词： Improper fractional-order laser chaotic system DSP Implementation image encryption algorithm

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image encryption Application of Chaotic Sequences Incorporating Quantum Keys

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International Journal of Automation and computing 2020年第1期17卷 123-138页

作者： Bin Ge Hai-Bo Luo School of Computer Science and Engineering Anhui University of Science and Technology

This paper proposes an image encryption algorithm LQBPNN（logistic quantum and back propagation neural network）based on chaotic sequences incorporating quantum keys. Firstly, the improved one-dimensional logistic chaotic sequence is used as the basic key sequence. After the quantum key is introduced, the quantum key is incorporated into the chaotic sequence by nonlinear operation. Then the pixel confused process is completed by the neural network. Finally, two sets of different mixed secret key sequences are used to perform two rounds of diffusion encryption on the confusing image. The experimental results show that the randomness and uniformity of the key sequence are effectively enhanced. The algorithm has a secret key space greater than 2182. The adjacent pixel correlation of the encrypted image is close to 0, and the information entropy is close to 8. The ciphertext image can resist several common attacks such as typical attacks, statistical analysis attacks and differential attacks.

关键词： Logistic chaotic system quantum key nonlinear operation sequence performance image encryption algorithm

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image encryption combining discrete fractional angular transform with Arnold transform in image bit planes

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OPTICA APPLICATA 2018年第2期48卷 225-236页

作者： Zhou, Zhihong Yu, Jing Liao, Qinghong Gong, Lihua Shanghai Jiao Tong Univ Sch Cyber Secur Shanghai Key Lab Integrate Adm Technol Informat S Shanghai 200240 Peoples R China Nanchang Univ Sch Informat Engn Nanchang 330031 Jiangxi Peoples R China Univ Pittsburgh Dept Elect & Comp Engn Pittsburgh PA 15261 USA

A new image encryption algorithm by using a discrete fractional angular transform and Arnold transform in image bit planes is investigated. In the image encryption algorithm, the original image is encrypted by the Arnold transform in image bit planes firstly, and then the resulting image is encrypted by the discrete fractional angular transform further. The key of the image encryption algorithm includes the parameters of the Arnold transform and the order of the discrete fractional angular transform. It is shown that the proposed image encryption algorithm is of high security and strong enough to counteract some conventional image attack manners.

关键词： Arnold transform bit plane discrete fractional angular transform image encryption algorithm

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DNA image encryption Scheme Based on a Chaotic LSTM Pseudo-Random Number Generator

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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 2023年第6期33卷 2350067-2350067页

作者： Koubaa, Karama Derbel, Nabil Univ Sfax Natl Engn Sch Sfax Control & Energy Management Lab CEMLab BP 1173 Sfax 3038 Tunisia

Deoxyribonucleic Acid (DNA) coding technology is a new research field developed by the combination of computer science and molecular biology, that has been gradually applied in the field of image encryption in recent years. Furthermore, sensitivity to initial conditions, pseudo-random properties, and state ergodicity of coupled chaotic maps can help produce good pseudo-random number generators and meet the requirements of an image encryption system well. In this paper, an image encryption algorithm based on high-dimensional coupled chaotic maps and DNA coding is proposed. A pseudo-random sequence is generated by a long short-term memory (LSTM) architecture using the proposed maps and evaluated through a set of statistical tests to show the high performance of the proposed generator. All intensity values of an input image are converted to a binary sequence, which is scrambled globally by the high-dimensional coupled chaotic maps. The DNA operations are performed on the scrambled binary sequences instead of binary operations to increase the algorithm efficiency. Simulation results and performance analyses demonstrate that the proposed encryption scheme is extremely sensitive to small changes in secret keys, provides high security and can resist differential attack.

关键词： DNA coding high-dimensional coupled chaotic maps image encryption algorithm long short-term memory pseudo-random sequence

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Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application

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SIGNAL PROCESSING 2020年第0期169卷 107373-000页

作者： Yang, Feifei Mou, Jun Liu, Jian Ma, Chenguang Yan, Huizhen Dalian Polytech Univ Sch Informat Sci & Engn Dalian 116034 Peoples R China Univ Jinan Sch Math Sci Jinan 250022 Peoples R China

To explore characteristic of a new system with fractional order and complex variables, based on Adomian decomposition method (ADM), its nonlinear dynamical behaviors are discussed by bifurcation diagram, Lyapunov exponent spectrum, spectral entropy (SE) complexity, and DSP implementation. It is found that, for each parameter and order, there exists a large interval to make the system remain a hyper-chaotic state, which illustrates that the hyper-chaotic sequence could be more random to be applied in image encryption. Especially, a novel image encryption algorithm is proposed based on the fractional order hyper-chaotic complex system and Galois field (GF). The column cyclic shift is used to scrambling part, the GF(17) algorithm is to diffuse pixel value. The security performances of algorithm are also analyzed. Finally, experiment results indicate that the proposed algorithm not only can effectively encrypt image, but also has better security features. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Fractional-order hyperchaotic complex system image encryption algorithm DSP implementation

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A color image encryption and decryption scheme based on extended DNA coding and fractional-order 5D hyper-chaotic system

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 254卷

作者： Meng, Fan-Qi Wu, Gang Yancheng Teachers Univ Sch Math & Stat Yancheng 224002 Peoples R China

With the advancement of information technology, the security of digital images has become increasingly important. To ensure the integrity of images, this paper presents a novel color image encryption and decryption architecture. Firstly, a fractional-order five-dimensional hyper-chaotic system (F5DHS) is proposed and used to generate chaotic sequences for permutation and diffusion processes. Secondly, the extended DNA encoding scheme is employed to generate more DNA encoding rules and four DNA computation methods are used to improve the security of the encryption scheme. Thirdly, a blocked image encryption method is designed to divide the color image into sub-blocks and then determine the DNA encoding, DNA decoding and DNA arithmetic rules for each sub-block based on chaotic sequences. Finally, the results of simulation experiments and security analysis show that the color image encryption algorithm has good encryption performance, a large secret key space, and strong robustness to noise and data loss attacks, indicating that the proposed encryption algorithm can effectively protect the secure communication of digital images.

关键词： image encryption algorithm Blocked encryption method Fractional-order hyper-chaotic system Extended DNA coding technology

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