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Enhancing Post-Quantum Information Security: A Novel Two-Dimensional Chaotic System for Quantum Image Encryption
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作者 Fatima Asiri Wajdan Al Malwi 《Computer Modeling in Engineering & Sciences》 2025年第5期2053-2077,共25页
Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematica... Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematical and computer modeling of a novel two-dimensional(2D)chaotic system for secure key generation in quantum image encryption(QIE).The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence,named as Trigonometric-Rational-Saturation(TRS)map.Through rigorous mathematical analysis and computational simulations,the map is extensively evaluated for bifurcation behaviour,chaotic trajectories,and Lyapunov exponents.The security evaluation validates the map’s non-linearity,unpredictability,and sensitive dependence on initial conditions.In addition,the proposed TRS map has further been tested by integrating it in a QIE scheme.The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation(NEQR)technique,the TRS map is used for the generation of secure diffusion key,which is XOR-ed with the quantum-ready image to obtain the encrypted images.The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks.The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62%and 33.47%results for Number of Pixels Change Rate(NPCR)and Unified Average Changing Intensity(UACI).The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats,making it suitable for secure image encryption in IoT and edge-based applications. 展开更多
关键词 Information security chaotic map modeling post-quantum security quantum image encryption chaotic map image encryption
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Secure Medical Image Transmission Using Chaotic Encryption and Blockchain-Based Integrity Verification
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作者 Rim Amdouni Mahdi Madani +2 位作者 Mohamed Ali Hajjaji El Bay Bourennane Mohamed Atri 《Computers, Materials & Continua》 2025年第9期5527-5553,共27页
Ensuring the integrity and confidentiality of patient medical information is a critical priority in the healthcare sector.In the context of security,this paper proposes a novel encryption algorithm that integrates Blo... Ensuring the integrity and confidentiality of patient medical information is a critical priority in the healthcare sector.In the context of security,this paper proposes a novel encryption algorithm that integrates Blockchain technology,aiming to improve the security and privacy of transmitted data.The proposed encryption algorithm is a block-cipher image encryption scheme based on different chaotic maps:The logistic Map,the Tent Map,and the Henon Map used to generate three encryption keys.The proposed block-cipher system employs the Hilbert curve to perform permutation while a generated chaos-based S-Box is used to perform substitution.Furthermore,the integration of a Blockchain-based solution for securing data transmission and communication between nodes and authenticating the encrypted medical image’s authenticity adds a layer of security to our proposed method.Our proposed cryptosystem is divided into two principal modules presented as a pseudo-random number generator(PRNG)used for key generation and an encryption and decryption system based on the properties of confusion and diffusion.The security analysis and experimental tests for the proposed algorithm show that the average value of the information entropy of the encrypted images is 7.9993,the Number of Pixels Change Rate(NPCR)values are over 99.5%and the Unified Average Changing Intensity(UACI)values are greater than 33%.These results prove the strength of our proposed approach,demonstrating that it can significantly enhance the security of encrypted images. 展开更多
关键词 Medical image encryption chaotic maps blockchain substitution-Box security INTEGRITY
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Sine-Polynomial Chaotic Map(SPCM):A Decent Cryptographic Solution for Image Encryption in Wireless Sensor Networks
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作者 David S.Bhatti Annas W.Malik +1 位作者 Haeung Choi Ki-Il Kim 《Computers, Materials & Continua》 2025年第10期2157-2177,共21页
Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies,limiting their use for lightweight,secure image encryption in resource-constrained Wireless Sensor Networks(WSNs).We propose the SPCM,a n... Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies,limiting their use for lightweight,secure image encryption in resource-constrained Wireless Sensor Networks(WSNs).We propose the SPCM,a novel one-dimensional discontinuous chaotic system integrating polynomial and sine functions,leveraging a piecewise function to achieve a broad chaotic range()and a high Lyapunov exponent(5.04).Validated through nine benchmarks,including standard randomness tests,Diehard tests,and Shannon entropy(3.883),SPCM demonstrates superior randomness and high sensitivity to initial conditions.Applied to image encryption,SPCM achieves 0.152582 s(39%faster than some techniques)and 433.42 KB/s throughput(134%higher than some techniques),setting new benchmarks for chaotic map-based methods in WSNs.Chaos-based permutation and exclusive or(XOR)diffusion yield near-zero correlation in encrypted images,ensuring strong resistance to Statistical Attacks(SA)and accurate recovery.SPCM also exhibits a strong avalanche effect(bit difference),making it an efficient,secure solution for WSNs in domains like healthcare and smart cities. 展开更多
关键词 Chaos theory chaotic system image encryption CRYPTOGRAPHY wireless sensor networks(WSNs)
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A Novel Bit-level Image Encryption Method Based on Chaotic Map and Dynamic Grouping 被引量:2
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作者 张国基 沈彦 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第10期520-524,共5页
In this paper,a novel bit-level image encryption method based on dynamic grouping is proposed.In the proposed method,the plain-image is divided into several groups randomly,then permutation-diffusion process on bit le... In this paper,a novel bit-level image encryption method based on dynamic grouping is proposed.In the proposed method,the plain-image is divided into several groups randomly,then permutation-diffusion process on bit level is carried out.The keystream generated by logistic map is related to the plain-image,which confuses the relationship between the plain-image and the cipher-image.The computer simulation results of statistical analysis,information entropy analysis and sensitivity analysis show that the proposed encryption method is secure and reliable enough to be used for communication application. 展开更多
关键词 image encryption permutation-diffusion dynamic grouping bit-level
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High Security Nested PWLCM Chaotic Map Bit-Level Permutation Based Image Encryption 被引量:1
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作者 Qassim Nasir Hadi H. Abdlrudha 《International Journal of Communications, Network and System Sciences》 2012年第9期548-556,共9页
Chaotic systems produce pseudo-random sequences with good randomness;therefore, these systems are suitable to efficient image encryption. In this paper, a low complexity image encryption based on Nested Piece Wise Lin... Chaotic systems produce pseudo-random sequences with good randomness;therefore, these systems are suitable to efficient image encryption. In this paper, a low complexity image encryption based on Nested Piece Wise Linear Chaotic Map (NPWLCM) is proposed. Bit planes of the grey or color levels are shuffled to increase the encryption complexity. A security analysis of the proposed system is performed and presented. The proposed method combine pixel shuffling, bit shuffling, and diffusion, which is highly disorder the original image. The initial values and the chaos control parameters of NPWLCM maps are derived from external secret key. The cipher image generated by this method is the same size as the original image and is suitable for practical use in the secure transmission of confidential information over the Internet. The experimental results of the proposed method show advantages of low complexity, and high-level security. 展开更多
关键词 encryption CHAOS PIECEWISE chaotic MAPS Security
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Image encryption using high-dimension chaotic system 被引量:14
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作者 孙福艳 刘树堂 吕宗旺 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第12期3616-3623,共8页
In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a new approach for image encryption based on a hi... In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. This paper proposes a new approach for image encryption based on a high-dimensional chaotic map. The new scheme employs the Cat map to shuffle the positions, then to confuse the relationship between the cipher-image and the plain-image using the high-dimensional Lorenz chaotic map preprocessed. The results of experimental, statistical analysis and key space analysis show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission. 展开更多
关键词 Arnold cat map image encryption chaotic encryption
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New chaotical image encryption algorithm based on Fisher–Yatess scrambling and DNA coding 被引量:9
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作者 Xing-Yuan Wang Jun-Jian Zhang +1 位作者 Fu-Chen Zhang Guang-Hui Cao 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第4期121-130,共10页
Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used ... Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used as the initial value of the chaotic system. Second, the chaotic sequence and Fisher–Yatess scrambling are used to scramble the plaintext,and a sorting scrambling algorithm is used for secondary scrambling. Then, the chaotic sequence and DNA coding rules are used to change the plaintext pixel values, which makes the ciphertext more random and resistant to attacks, and thus ensures that the encrypted ciphertext is more secure. Finally, we add plaintext statistics for pixel-level diffusion to ensure plaintext sensitivity. The experimental results and security analysis show that the new algorithm has a good encryption effect and speed, and can also resist common attacks. 展开更多
关键词 Fisher–Yatess SCRAMBLING chaotic sequence DNA CODING image encryption
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Digital image encryption with chaotic map lattices 被引量:8
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作者 孙福艳 吕宗旺 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第4期132-138,共7页
This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels o... This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks, the secret key is modified after encrypting each block of sixteen pixels of the image. The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency. 展开更多
关键词 image encryption image decryption chaotic map lattice CRYPTOGRAPHY spatiotemporal chaotic system
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An improved image encryption algorithm based on chaotic maps 被引量:4
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作者 徐淑奖 王继志 杨素香 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第11期4027-4032,共6页
Recently, two chaotic image encryption schemes have been proposed, in which shuffling the positions and changing the grey values of image pixels are combined. This paper provides the chosen plaintext attack to recover... Recently, two chaotic image encryption schemes have been proposed, in which shuffling the positions and changing the grey values of image pixels are combined. This paper provides the chosen plaintext attack to recover the corresponding plaintext of a given ciphertext. Furthermore, it points out that the two schemes are not sufficiently sensitive to small changes of the plaintext. Based on the given analysis, it proposes an improved algorithm which includes two rounds of substitution and one round of permutation to strengthen the overall performance. 展开更多
关键词 CHAOS chaotic cryptosystem image encryption chosen plaintext attack
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Repeater jamming suppression method for pulse Doppler fuze based on identity recognition and chaotic encryption 被引量:9
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作者 Jian Dai Xin-hong Hao +2 位作者 Qiang Liu Xiao-peng Yan Ping Li 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2021年第3期1002-1012,共11页
Pulse Doppler(PD) fuze is widely used in current battlefield. However, with the threat of repeater jamming, especially digital radio frequency memory technology, the deficiency in the anti-repeater jamming of a tradit... Pulse Doppler(PD) fuze is widely used in current battlefield. However, with the threat of repeater jamming, especially digital radio frequency memory technology, the deficiency in the anti-repeater jamming of a traditional PD fuze increasingly emerges. Therefore, a repeater jamming suppression method for a PD fuze based on identity(ID) recognition and chaotic encryption is proposed. Every fuze has its own ID which is encrypted with different chaotic binary sequences in every pulse period of the transmitted signal. The thumbtack-shaped ambiguity function shows a good resolution and distance cutoff characteristic. The ability of anti-repeater jamming is emphatically analyzed, and the results at different signal-to-noise ratio(SNR) show a strong anti-repeater jamming ability and range resolution that the proposed method possesses. Furthermore, the anti-repeater jamming ability is influenced by processing gain, bit error rate(BER) and correlation function. The simulation result validates the theoretical analysis, it shows the proposed method can significantly improve the anti-repeater jamming ability of a PD fuze. 展开更多
关键词 Pulse Doppler fuze ID chaotic binary code encryption Repeater jamming
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Chaotic Image Encryption Algorithm by Correlating Keys with Plaintext 被引量:6
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作者 Zhu Congxu Sun Kehui 《China Communications》 SCIE CSCD 2012年第1期73-79,共7页
A novel image encryption scheme based on the modified skew tent map was proposed in this paper. In the key generating procedure, the algorithm generates a plaintext-dependent secret keys set. In the encryption process... A novel image encryption scheme based on the modified skew tent map was proposed in this paper. In the key generating procedure, the algorithm generates a plaintext-dependent secret keys set. In the encryption process, the diffusion operation with cipher output feedback is introduced. Thus, cipher-irmge is sensitive to both initial keys and plaintext through only one round diffusion operation. The key space is large. As a resuk, the algorithm can effectively resist differential attacks, statistical attacks, brute-force attacks, known plaintext and chosen plaintext attacks. Perforrmnce test and security analysis demonstrates that this algorithm is eficient and reliable, with high potential to be adopted for secure comnmnications. 展开更多
关键词 skew tent map chaotic system image encryption secure corrrrmnieation
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An image encryption algorithm based on improved baker transformation and chaotic S-box 被引量:4
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作者 Xing-Yuan Wang Huai-Huai Sun Hao Gao 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第6期216-225,共10页
The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic sys... The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic system as an encryption key. Specifically, in the image scrambling stage, the algorithm primarily uses an improved baker transform method to process the image. In the image diffusion stage, the algorithm first uses the chaotic S-box method to process the encryption key. Secondly, an exclusive OR(XOR) operation is performed on the image and the encryption key to initially diffuse the image. Finally, the image is again diffused using the method of ortho XOR. Simulation analysis shows that the algorithm can achieve good encryption effect, simple and easy implementation, and good security. In the digital image communication transmission, it has good practical value. 展开更多
关键词 image encryption improved baker transformation chaotic S-box chaotic sequence
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Image Encryption Application of Chaotic Sequences Incorporating Quantum Keys 被引量:3
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作者 Bin Ge Hai-Bo Luo 《International Journal of Automation and computing》 EI CSCD 2020年第1期123-138,共16页
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 cha... 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. 展开更多
关键词 Logistic chaotic system quantum key nonlinear operation sequence performance image encryption algorithm
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New Chaotic Image Encryption Algorithm Based on Cross-Mapping 被引量:2
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作者 TONG Xiaojun LIU Yang +1 位作者 ZHANG Miao SHI Hongyu 《Wuhan University Journal of Natural Sciences》 CAS 2012年第6期461-467,共7页
Chaotic cryptography has been applied to image encryption;however,only the traditional low-dimensional chaotic systems has been widely analyzed or deciphered,which does not show satisfied security and efficiency.To so... Chaotic cryptography has been applied to image encryption;however,only the traditional low-dimensional chaotic systems has been widely analyzed or deciphered,which does not show satisfied security and efficiency.To solve this problem,a new algorithm based on cross-chaos map has been created in this article.The image pixels are scrambled under control of high-dimensional chaotic sequence,which is generated by cross chaotic map.The image pixels are substituted by ciphertext feedback algorithm.It can relate encryption required parameters with plaintext and can make a plaintext byte affect more ciphertext bytes.Proved by theoretical analysis and experimental results,the algorithm has higher complex degree and has passed SP800-22 pseudo-random number standard tests,and it has high encryption speed,high security,etc.It can be widely applied in the field of image encryption. 展开更多
关键词 CHAOS image encryption cross chaotic map cross-scrambling SUBSTITUTE
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Cryptanalysis and improvement of a digital image encryption method with chaotic map lattices 被引量:2
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作者 王兴元 刘林涛 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第5期198-202,共5页
A digital image encryption scheme using chaotic map lattices has been proposed recently. In this paper, two fatal flaws of the cryptosystem are pointed out. According to these two drawbacks, cryptanalysts could recove... A digital image encryption scheme using chaotic map lattices has been proposed recently. In this paper, two fatal flaws of the cryptosystem are pointed out. According to these two drawbacks, cryptanalysts could recover the plaintext by applying the chosen plaintext attack. Therefore, the proposed cryptosystem is not secure enough to be used in the image transmission system. Experimental results show the feasibility of the attack. As a result, we make some improvements to the encryption scheme, which can completely resist our chosen plaintext attack. 展开更多
关键词 CRYPTANALYSIS chosen plaintext attack image encryption chaotic map lattice
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Fractal sorting vector-based least significant bit chaotic permutation for image encryption 被引量:1
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作者 Yong-Jin Xian Xing-Yuan Wang +2 位作者 Ying-Qian Zhang Xiao-Yu Wang Xiao-Hui Du 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第6期226-235,共10页
The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV... The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security. 展开更多
关键词 chaotic image encryption fractal sorting vector bit-level permutation FSV-based LSB chaotic permutation
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An image encryption scheme based on three-dimensional Brownian motion and chaotic system 被引量:6
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作者 Xiu-Li Chai Zhi-Hua Gan +2 位作者 Ke Yuan l Yang Lu Yi-Ran Chen 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第2期99-113,共15页
At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional(3D) bit matrices, and thus bits cannot move to any position, th... At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional(3D) bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion(BCB3DBM)is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system(LTS). Furthermore, block confusion based on position sequence group(BCBPSG) is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed. 展开更多
关键词 image encryption logistic-tent system(LTS) memristive chaotic system three-dimensional(3D) Brownian motion
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Image encryption based on a delayed fractional-order chaotic logistic system 被引量:1
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作者 王震 黄霞 +1 位作者 李宁 宋晓娜 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第5期107-112,共6页
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the prop... A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system.In the process of generating a key stream,the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security.Such a scheme is described in detail with security analyses including correlation analysis,information entropy analysis,run statistic analysis,mean-variance gray value analysis,and key sensitivity analysis.Experimental results show that the newly proposed image encryption scheme possesses high security. 展开更多
关键词 image encryption fractional-order chaotic logistic system DELAY
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Double Encryption Using Trigonometric Chaotic Map and XOR of an Image 被引量:2
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作者 Orawit Thinnukool Thammarat Panityakul Mahwish Bano 《Computers, Materials & Continua》 SCIE EI 2021年第12期3033-3046,共14页
In the most recent decades,a major number of image encryption plans have been proposed.The vast majority of these plans reached a highsecurity level;however,their moderate speeds because of their complicated processes... In the most recent decades,a major number of image encryption plans have been proposed.The vast majority of these plans reached a highsecurity level;however,their moderate speeds because of their complicated processes made them of no use in real-time applications.Inspired by this,we propose another efficient and rapid image encryption plan dependent on the Trigonometric chaotic guide.In contrast to the most of current plans,we utilize this basic map to create just a couple of arbitrary rows and columns.Moreover,to additionally speed up,we raise the processing unit from the pixel level to the row/column level.The security of the new plot is accomplished through a substitution permutation network,where we apply a circular shift of rows and columns to break the solid connection of neighboring pixels.At that point,we join the XOR operation with modulo function to cover the pixels values and forestall any leaking of data.High-security tests and simulation analyses are carried out to exhibit that the scheme is very secure and exceptionally quick for real-time image processing at 80 fps(frames per second). 展开更多
关键词 Double image encryption target image random image trigonometric chaotic map
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Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem 被引量:2
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作者 Zeyu Liu Tiecheng Xia Jinbo Wang 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第3期161-176,共16页
We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bif... We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. 展开更多
关键词 CHAOS fractional two-dimensional triangle function combination discrete chaotic map image encryption Menezes-Vanstone elliptic curve cryptosystem
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