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
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
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
Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of...This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.展开更多
The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity differ...The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity difference between the receiver （carrier） and the transmittal （carrier plus signal）, several signals can be encoded into a single pulse. If one signal contains several binary bits, two-dimensional messages in the form of a matrix can be encoded and transmitted on a single pulse. With these improvements in secure communications using chaotic multi-mode lasers, not only the transmission rate can be increased but also the privacy can be enhanced greatly.展开更多
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
We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynami...We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.展开更多
We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of...We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.展开更多
The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The e...The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.展开更多
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
Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although ...Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization(IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.展开更多
Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived sol...Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.展开更多
This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a...This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.展开更多
In order to solve the problem of patient information security protection in medical images,whilst also taking into consideration the unchangeable particularity of medical images to the lesion area and the need for med...In order to solve the problem of patient information security protection in medical images,whilst also taking into consideration the unchangeable particularity of medical images to the lesion area and the need for medical images themselves to be protected,a novel robust watermarking algorithm for encrypted medical images based on dual-tree complex wavelet transform and discrete cosine transform(DTCWT-DCT)and chaotic map is proposed in this paper.First,DTCWT-DCT transformation was performed on medical images,and dot product was per-formed in relation to the transformation matrix and logistic map.Inverse transformation was undertaken to obtain encrypted medical images.Then,in the low-frequency part of the DTCWT-DCT transformation coefficient of the encrypted medical image,a set of 32 bits visual feature vectors that can effectively resist geometric attacks are found to be the feature vector of the encrypted medical image by using perceptual hashing.After that,different logistic initial values and growth parameters were set to encrypt the watermark,and zero-watermark technology was used to embed and extract the encrypted medical images by combining cryptography and third-party concepts.The proposed watermarking algorithm does not change the region of interest of medical images thus it does not affect the judgment of doctors.Additionally,the security of the algorithm is enhanced by using chaotic mapping,which is sensitive to the initial value in order to encrypt the medical image and the watermark.The simulation results show that the pro-posed algorithm has good homomorphism,which can not only protect the original medical image and the watermark information,but can also embed and extract the watermark directly in the encrypted image,eliminating the potential risk of decrypting the embedded watermark and extracting watermark.Compared with the recent related research,the proposed algorithm solves the contradiction between robustness and invisibility of the watermarking algorithm for encrypted medical images,and it has good results against both conventional attacks and geometric attacks.Under geometric attacks in particular,the proposed algorithm performs much better than existing algorithms.展开更多
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
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
A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach ...A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.展开更多
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
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funded by Deanship of Research and Graduate Studies at King Khalid University.The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Group Project under grant number(RGP.2/556/45).
文摘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.
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.
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11672257, 11772306, 11972173, and 12172340)the 5th 333 High-level Personnel Training Project of Jiangsu Province of China (Grant No. BRA2018324)。
文摘This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China （Grant No BK2001138）.
文摘The digital communication of two-dimensional messages is investigated when two solid state multi-mode chaotic lasers are employed in a master-slave configuration. By introducing the time derivative of intensity difference between the receiver （carrier） and the transmittal （carrier plus signal）, several signals can be encoded into a single pulse. If one signal contains several binary bits, two-dimensional messages in the form of a matrix can be encoded and transmitted on a single pulse. With these improvements in secure communications using chaotic multi-mode lasers, not only the transmission rate can be increased but also the privacy can be enhanced greatly.
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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11972173 and 12172340)。
文摘We present a class of two-dimensional memristive maps with a cosine memristor. The memristive maps do not have any fixed points, so they belong to the category of nonlinear maps with hidden attractors. The rich dynamical behaviors of these maps are studied and investigated using different numerical tools, including phase portrait, basins of attraction,bifurcation diagram, and Lyapunov exponents. The two-parameter bifurcation analysis of the memristive map is carried out to reveal the bifurcation mechanism of its dynamical behaviors. Based on our extensive simulation studies, the proposed memristive maps can produce hidden periodic, chaotic, and hyper-chaotic attractors, exhibiting extremely hidden multistability, namely the coexistence of infinite hidden attractors, which was rarely observed in memristive maps. Potentially,this work can be used for some real applications in secure communication, such as data and image encryptions.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574011)Natural Science Foundation of Heilongjiang Province,China (Grant No A200506)
文摘We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.
基金supported by National Natural Science Foundation of China under Grant No.60872065Open Foundation of State Key Laboratory for Novel Software Technology at Nanjing University under Grant No.KFKT2010B17
文摘The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61001099 and 10971120)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200444)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61161006 and 61573383)the Key Innovation Project of Graduate of Central South University(Grant No.2018ZZTS009)the Postdoctoral Innovative Talents Support Program(Grant No.BX20180386)。
文摘Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization(IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.
基金浙江省自然科学基金，Foundation of New Century "151 Talent Engineering" of Zhejiang Province，丽水学院校科研和教改项目，the Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.
文摘This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.
基金supported by the Key Research Project of Hainan Province[ZDYF2018129]the Higher Education Research Project of Hainan Province(Hnky2019-73)+3 种基金the National Natural Science Foundation of China[61762033]the Natural Science Foundation of Hainan[617175]the Special Scientific Research Project of Philosophy and Social Sciences of Chongqing Medical University[201703]the Key Research Project of Haikou College of Economics[HJKZ18-01].
文摘In order to solve the problem of patient information security protection in medical images,whilst also taking into consideration the unchangeable particularity of medical images to the lesion area and the need for medical images themselves to be protected,a novel robust watermarking algorithm for encrypted medical images based on dual-tree complex wavelet transform and discrete cosine transform(DTCWT-DCT)and chaotic map is proposed in this paper.First,DTCWT-DCT transformation was performed on medical images,and dot product was per-formed in relation to the transformation matrix and logistic map.Inverse transformation was undertaken to obtain encrypted medical images.Then,in the low-frequency part of the DTCWT-DCT transformation coefficient of the encrypted medical image,a set of 32 bits visual feature vectors that can effectively resist geometric attacks are found to be the feature vector of the encrypted medical image by using perceptual hashing.After that,different logistic initial values and growth parameters were set to encrypt the watermark,and zero-watermark technology was used to embed and extract the encrypted medical images by combining cryptography and third-party concepts.The proposed watermarking algorithm does not change the region of interest of medical images thus it does not affect the judgment of doctors.Additionally,the security of the algorithm is enhanced by using chaotic mapping,which is sensitive to the initial value in order to encrypt the medical image and the watermark.The simulation results show that the pro-posed algorithm has good homomorphism,which can not only protect the original medical image and the watermark information,but can also embed and extract the watermark directly in the encrypted image,eliminating the potential risk of decrypting the embedded watermark and extracting watermark.Compared with the recent related research,the proposed algorithm solves the contradiction between robustness and invisibility of the watermarking algorithm for encrypted medical images,and it has good results against both conventional attacks and geometric attacks.Under geometric attacks in particular,the proposed algorithm performs much better than existing algorithms.
基金Supported by the National Natural Science Foundation of China (60973162)the Natural Science Foundation of Shandong Province of China (ZR2009GM037)+2 种基金the Science and Technology Project of Shandong Province,China (2010GGX10132,2012GGX10110)the Key Natural Science Foundation of Shan-dong Province of China (Z2006G01)the Soft Science Project of Shangdong Province of China (2012RKA10009)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61173183, 60973152, and 60573172)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No. 20070141014)+2 种基金the Program for Excellent Talents in Universities of Liaoning Province, China (Grant No. LR2012003)the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165)the Fundamental Research Funds for the Central Universities of China (Grant No. DUT12JB06)
文摘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.
文摘A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.
基金This research work was partially funded by the Chiang Mai University.
文摘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).
