With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propo...With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propose a 2D-lag complex logistic map with complex parameters(2D-LCLMCP)and corresponding encryption schemes.Firstly,we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points,Lyapunov exponent,bifurcation diagram,phase diagram,etc.Secondly,a block cipher algorithm based on the 2D-LCLMCP is proposed,the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP.Based on the generalized Feistel cipher structure,a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm.The generalized Feistel cipher structure consists of two F functions,four XOR operations,and one permutation operation per round.The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP.Finally,experimental simulation and performance analysis tests are conducted.The results show that the block cipher algorithm has low complexit,good diffusion and a large key space.When the block length is 64 bits,only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.展开更多
The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,tr...The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.展开更多
In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it su...In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.展开更多
The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three...The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three corollaries about the fixed points of logistic mappingare proposed and proved respectively. These theorem and corollaries provide a theoretical basis forchoosing parameter of chaotic sequences in chaotic secure communication and chaotic digitalwatermarking. And they are testified by simulation.展开更多
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences of the system parameter and the impulsive forces on the dynamics of the system are studied res...The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincar6 map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.展开更多
We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability...We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.展开更多
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
Secure transmission of images over a communication channel, with limited data transfer capacity, possesses compression and encryption schemes. A deep learning based hybrid image compression-encryption scheme is propos...Secure transmission of images over a communication channel, with limited data transfer capacity, possesses compression and encryption schemes. A deep learning based hybrid image compression-encryption scheme is proposed by combining stacked auto-encoder with the logistic map. The proposed structure of stacked autoencoder has seven multiple layers, and back propagation algorithm is intended to extend vector portrayal of information into lower vector space. The randomly generated key is used to set initial conditions and control parameters of logistic map. Subsequently, compressed image is encrypted by substituting and scrambling of pixel sequences using key stream sequences generated from logistic map.The proposed algorithms are experimentally tested over five standard grayscale images. Compression and encryption efficiency of proposed algorithms are evaluated and analyzed based on peak signal to noise ratio(PSNR), mean square error(MSE), structural similarity index metrics(SSIM) and statistical,differential, entropy analysis respectively. Simulation results show that proposed algorithms provide high quality reconstructed images with excellent levels of security during transmission..展开更多
Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to...Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to scrambling blocks in this paper. At first, the original image is scrambled by using logistic mapping to obtain the encrypted image, and then the encrypted image is divided into many blocks. Finally, the position of the blocked image is scrambled by using the improved Josephus ring to get the encrypted image. According to the experiments, the information entropy of the encrypted image reaches 7.99 and the adjacent correlations in three directions are within ±0.1. The experimental results show that the proposed algorithm has advantages of large key space, high key sensitivity and can effectively resist the attacks of statistical analysis and gray value analysis. It has good encryption effect on digital image encryption.展开更多
基金Project supported by the Shandong Province Natural Science Foundation(Grant Nos.ZR2023MF089,R2023QF036,and ZR2021MF073)the Industry-University-Research Collaborative Innovation Fund Project of Qilu University of Technology(Shandong Academy of Sciences)(Grant Nos.2021CXY-13 and 2021CXY-14)+2 种基金the Major Scientific and Technological Innovation Projects of Shandong Province(Grant No.2020CXGC010901)the Talent Research Project of Qilu University of Technology(Shandong Academy of Sciences)(Grant No.2023RCKY054)the Basic Research Projects of Science,Education and Industry Integration Pilot Project of Qilu University of Technology(Shandong Academy of Sciences)(Grant No.2023PX081)。
文摘With the rapid development of internet technology,security protection of information has become more and more prominent,especially information encryption.Considering the great advantages of chaotic encryption,we propose a 2D-lag complex logistic map with complex parameters(2D-LCLMCP)and corresponding encryption schemes.Firstly,we present the model of the 2D-LCLMCP and analyze its chaotic properties and system stability through fixed points,Lyapunov exponent,bifurcation diagram,phase diagram,etc.Secondly,a block cipher algorithm based on the 2D-LCLMCP is proposed,the plaintext data is preprocessed using a pseudorandom sequence generated by the 2D-LCLMCP.Based on the generalized Feistel cipher structure,a round function F is constructed using dynamic S-box and DNA encoding rules as the core of the block cipher algorithm.The generalized Feistel cipher structure consists of two F functions,four XOR operations,and one permutation operation per round.The symmetric dynamic round keys that change with the plaintext are generated by the 2D-LCLMCP.Finally,experimental simulation and performance analysis tests are conducted.The results show that the block cipher algorithm has low complexit,good diffusion and a large key space.When the block length is 64 bits,only six rounds of encryption are required to provide sufficient security and robustness against cryptographic attacks.
文摘The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.
文摘In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.
基金This work was financially supported by the National Natural Science Foundation of China(No.69772014).]
文摘The fixed points in logistic mapping digital-flow chaos strange attractor arestudied in detail. When k=n in logistic equation, there exist no more than 2n fixed points, whichare deduced and proved theoretically. Three corollaries about the fixed points of logistic mappingare proposed and proved respectively. These theorem and corollaries provide a theoretical basis forchoosing parameter of chaotic sequences in chaotic secure communication and chaotic digitalwatermarking. And they are testified by simulation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11202180,61273106,and 11171290)the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BK2010292 and BK2010293)+2 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.10KJB510026)the National Training Programs of Innovation and Entrepreneurship for Undergraduates,China(Grant No.201210324009)the Training Programs of Practice and Innovation for Jiangsu College Students,China(Grant No.2012JSSPITP2378)
文摘The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influ- ences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincar6 map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map.
基金National Natural Science Foundation of China(Grant Nos.11672257,11632008,11772306,and 11972173)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20161314)+1 种基金the 5th 333 High-level Personnel Training Project of Jiangsu Province of China(Grant No.BRA2018324)the Excellent Scientific and Technological Innovation Team of Jiangsu University.
文摘We study a novel class of two-dimensional maps with infinitely many coexisting attractors.Firstly,the mathematical model of these maps is formulated by introducing a sinusoidal function.The existence and the stability of the fixed points in the model are studied indicating that they are infinitely many and all unstable.In particular,a computer searching program is employed to explore the chaotic attractors in these maps,and a simple map is exemplified to show their complex dynamics.Interestingly,this map contains infinitely many coexisting attractors which has been rarely reported in the literature.Further studies on these coexisting attractors are carried out by investigating their time histories,phase trajectories,basins of attraction,Lyapunov exponents spectrum,and Lyapunov(Kaplan–Yorke)dimension.Bifurcation analysis reveals that the map has periodic and chaotic solutions,and more importantly,exhibits extreme multi-stability.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61072147 and 11271008)
文摘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.
文摘Secure transmission of images over a communication channel, with limited data transfer capacity, possesses compression and encryption schemes. A deep learning based hybrid image compression-encryption scheme is proposed by combining stacked auto-encoder with the logistic map. The proposed structure of stacked autoencoder has seven multiple layers, and back propagation algorithm is intended to extend vector portrayal of information into lower vector space. The randomly generated key is used to set initial conditions and control parameters of logistic map. Subsequently, compressed image is encrypted by substituting and scrambling of pixel sequences using key stream sequences generated from logistic map.The proposed algorithms are experimentally tested over five standard grayscale images. Compression and encryption efficiency of proposed algorithms are evaluated and analyzed based on peak signal to noise ratio(PSNR), mean square error(MSE), structural similarity index metrics(SSIM) and statistical,differential, entropy analysis respectively. Simulation results show that proposed algorithms provide high quality reconstructed images with excellent levels of security during transmission..
文摘Digital image encryption based on Joseph circle and Chaotic system has become a hot spot in the research of image encryption. An encryption algorithm based on improved Josephus loop and logistic mapping is proposed to scrambling blocks in this paper. At first, the original image is scrambled by using logistic mapping to obtain the encrypted image, and then the encrypted image is divided into many blocks. Finally, the position of the blocked image is scrambled by using the improved Josephus ring to get the encrypted image. According to the experiments, the information entropy of the encrypted image reaches 7.99 and the adjacent correlations in three directions are within ±0.1. The experimental results show that the proposed algorithm has advantages of large key space, high key sensitivity and can effectively resist the attacks of statistical analysis and gray value analysis. It has good encryption effect on digital image encryption.
