The field of medical images has been rapidly evolving since the advent of the digital medical information era.However,medical data is susceptible to leaks and hacks during transmission.This paper proposed a robust mul...The field of medical images has been rapidly evolving since the advent of the digital medical information era.However,medical data is susceptible to leaks and hacks during transmission.This paper proposed a robust multi-watermarking algorithm for medical images based on GoogLeNet transfer learning to protect the privacy of patient data during transmission and storage,as well as to increase the resistance to geometric attacks and the capacity of embedded watermarks of watermarking algorithms.First,a pre-trained GoogLeNet network is used in this paper,based on which the parameters of several previous layers of the network are fixed and the network is fine-tuned for the constructed medical dataset,so that the pre-trained network can further learn the deep convolutional features in the medical dataset,and then the trained network is used to extract the stable feature vectors of medical images.Then,a two-dimensional Henon chaos encryption technique,which is more sensitive to initial values,is used to encrypt multiple different types of watermarked private information.Finally,the feature vector of the image is logically operated with the encrypted multiple watermark information,and the obtained key is stored in a third party,thus achieving zero watermark embedding and blind extraction.The experimental results confirmthe robustness of the algorithm from the perspective ofmultiple types of watermarks,while also demonstrating the successful embedding ofmultiple watermarks for medical images,and show that the algorithm is more resistant to geometric attacks than some conventional watermarking algorithms.展开更多
This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The propos...This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.展开更多
A new method to design parity-check matrix based on Henon chaos model is presented. The designed parity-check matrix is with rather random behavior. Simulation results show that the proposed method makes an improvemen...A new method to design parity-check matrix based on Henon chaos model is presented. The designed parity-check matrix is with rather random behavior. Simulation results show that the proposed method makes an improvement in bit error rate （BER） performance by 0.4 dB compared with that of Luby for AWGN channel. The proposed method decreases the complexity of decoding significantly, and improves the error correcting performance of LDPC codes. It has been shown that Henon chaotic model is a powerful tool for construction of good LDPC codes, which make it possible to apply the LDPC code in real communication systems.展开更多
A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map...A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended.展开更多
The Henon map forms one of the most-studied two-dimensional discrete-time dynamical systems that exhibits chaotic behavior.The Henon map takes a point(Xn,Yn)in the plane and maps it to a new point(Xn+1,Yn+1).In this p...The Henon map forms one of the most-studied two-dimensional discrete-time dynamical systems that exhibits chaotic behavior.The Henon map takes a point(Xn,Yn)in the plane and maps it to a new point(Xn+1,Yn+1).In this paper,a chaotic pulse generator based on the chaotic Henon map is proposed.It consists of a Henon map function subcircuit to realize the Henon map and another subcircuit to perform the iterative operation.The Henon map subcircuit comprises operational amplifiers,multipliers,delay elements and resistors,whereas,the iterative subcircuit is implemented with a simple design that comprises of an edge forming circuit followed by a monostable multivibrator and a voltage controlled switch without the use of any clock control.The proposed design can be used to realize the Henon map and also to generate a chaotic pulse train,with a controllable time interval and pulse position.The proposed circuit is implemented and simulated using Multisim 13.0 and MATLAB R2019b.The chaotic nature of the generated pulse train and also the time interval between the consecutive pulses is verified by the calculation of its Lyapunov exponents.展开更多
A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control ...A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.展开更多
We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.
A new method to design interleaver based on Henon chaos model is presented. The designed interleaver is with rather random behavior. Experimental results show that the proposed S-henon interleaver make a magnitude of ...A new method to design interleaver based on Henon chaos model is presented. The designed interleaver is with rather random behavior. Experimental results show that the proposed S-henon interleaver make a magnitude of im provement in bit error rate （BER） performance by 0.4 dB compared with the S-random interleaver for AWGN channel respectively. The S-henon interleaver may be adapted to 3G mobile communication systems.展开更多
Chaotic sequences are basically ergodic random sequences. By improving correlativity of a chaotic signal, the chaotic dynamic system can be controlled to converge to its equilibrium point and, more significantly, to i...Chaotic sequences are basically ergodic random sequences. By improving correlativity of a chaotic signal, the chaotic dynamic system can be controlled to converge to its equilibrium point and, more significantly, to its multi-periodic orbits. Mathematical theory analysis is carried out and some computer simulation results are provided to support such controllability of the chaotic Henon system and the discrete coupled map lattice.展开更多
By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to sol...By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the generalized Henon map. First, move the decimal point of elements in the sequence to the fight; then, cut off the integer; and finally, quantify it into a binary sequence. Statistical test, security analysis, and the application of image encryption have strongly supported the good random statistical characteristics, high linear complexity, large key space, and great sensitivity of the binary sequence.展开更多
This paper presents a theoretical framework for parallelizing the FD3 algorithm,which estimates the capacity,information,and correlation dimensions of chaotic time series using the box-counting method.We propose a hyb...This paper presents a theoretical framework for parallelizing the FD3 algorithm,which estimates the capacity,information,and correlation dimensions of chaotic time series using the box-counting method.We propose a hybrid parallel implementation leveraging MPI as well as OpenMP to achieve scalable performance on modern high-performance computing architectures.The serial FD3 algorithm is analyzed in detail,followed by a comprehensive parallelization strategy for its key phases,including data retrieval,trajectory reconstruction,sorting,and dimension estimation.Theoretical models based on Amdahl’s and Gustafson’s Laws predict significant speedup,supported by complexity analysis and communication cost models.While experimental validation is planned as future work,this study provides a robust foundation for parallel fractal dimension estimation,with potential applications in chaotic system analysis and computational physics.The motivation for this research is that,although the FD3 algorithm is relatively old and more advanced and efficient algorithms have since been developed,its structure and operation allow for parallelization,which,by providing significant acceleration,could render it competitive once again and suitable for efficient use.展开更多
To improve the security of the color image encryption scheme,a color image encryption scheme based on chaotic systems is proposed. Firstly, the proposed scheme sets the color image as a three-dimensional matrix which ...To improve the security of the color image encryption scheme,a color image encryption scheme based on chaotic systems is proposed. Firstly, the proposed scheme sets the color image as a three-dimensional matrix which is scrambled by affine transformation. Second, the Logistic chaotic sequence applied to generate the control parameter and auxiliary key is used to encrypt the three-dimensionaL matrix. Here, we mainly focus on two methods for encryption processes. One is to generate a chaotic sequence by Logistic map and Henon map, which is used to perform XOR operation with the scrambled components R＇, G＇, B＇ respectively. The other one is to adopt a binary Logistic sequence to select the pixel position for the scrambled components R＇, G＇, B＇ image, and then applying the Henon map and Logistic map with the auxiliary key to perform the replacement encryption. Based on this, an encrypted image is synthesized. Simulation results show that the proposed image encryption scheme can implement better encryption and achieve higher security performance.展开更多
An important problem in a given dynamical system is to determine the existence of a homoclinic orbit. We improve the results of Qin and Xiao [Nonlinearity, 20 （2007）, 2305-2317], who present some sufficient conditio...An important problem in a given dynamical system is to determine the existence of a homoclinic orbit. We improve the results of Qin and Xiao [Nonlinearity, 20 （2007）, 2305-2317], who present some sufficient conditions for the existence of a homoclinic/heteroclinic orbit for the generalized H@non map. Moreover, an algorithm is presented to locate these homoclinic orbits.展开更多
基金supported in part by the Natural Science Foundation of China under Grants 62063004the Key Research Project of Hainan Province under Grant ZDYF2021SHF Z093+1 种基金the Hainan Provincial Natural Science Foundation of China under Grants 2019RC018 and 619QN246the postdoctor research from Zhejiang Province under Grant ZJ2021028.
文摘The field of medical images has been rapidly evolving since the advent of the digital medical information era.However,medical data is susceptible to leaks and hacks during transmission.This paper proposed a robust multi-watermarking algorithm for medical images based on GoogLeNet transfer learning to protect the privacy of patient data during transmission and storage,as well as to increase the resistance to geometric attacks and the capacity of embedded watermarks of watermarking algorithms.First,a pre-trained GoogLeNet network is used in this paper,based on which the parameters of several previous layers of the network are fixed and the network is fine-tuned for the constructed medical dataset,so that the pre-trained network can further learn the deep convolutional features in the medical dataset,and then the trained network is used to extract the stable feature vectors of medical images.Then,a two-dimensional Henon chaos encryption technique,which is more sensitive to initial values,is used to encrypt multiple different types of watermarked private information.Finally,the feature vector of the image is logically operated with the encrypted multiple watermark information,and the obtained key is stored in a third party,thus achieving zero watermark embedding and blind extraction.The experimental results confirmthe robustness of the algorithm from the perspective ofmultiple types of watermarks,while also demonstrating the successful embedding ofmultiple watermarks for medical images,and show that the algorithm is more resistant to geometric attacks than some conventional watermarking algorithms.
基金This research was funded by Deanship of Scientific Research,Taif University Researches Supporting Project number(TURSP-2020/216),Taif University,Taif,Saudi Arabia.
文摘This paper introduces an efficient image cryptography system.The pro-posed image cryptography system is based on employing the two-dimensional(2D)chaotic henon map(CHM)in the Discrete Fourier Transform(DFT).The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures.In the proposed DFT-based CHM image cryptography,the confusion is employed using the CHM while the diffu-sion is realized using the DFT.So,the proposed DFT-based CHM image crypto-graphy achieves both confusion and diffusion characteristics.The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the final-ly encrypted image.The decryption procedure follows the inverse procedure of encryption.The proposed DFT-based CHM image cryptography system is exam-ined using a set of security tests like statistical tests,entropy tests,differential tests,and sensitivity tests.The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system.These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.
基金Supported by the National High Technology Research and Development Program of China (2001AA123053)
文摘A new method to design parity-check matrix based on Henon chaos model is presented. The designed parity-check matrix is with rather random behavior. Simulation results show that the proposed method makes an improvement in bit error rate （BER） performance by 0.4 dB compared with that of Luby for AWGN channel. The proposed method decreases the complexity of decoding significantly, and improves the error correcting performance of LDPC codes. It has been shown that Henon chaotic model is a powerful tool for construction of good LDPC codes, which make it possible to apply the LDPC code in real communication systems.
基金supported by the National Natural Science Foundation of China (Grant No 60372061)
文摘A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended.
文摘The Henon map forms one of the most-studied two-dimensional discrete-time dynamical systems that exhibits chaotic behavior.The Henon map takes a point(Xn,Yn)in the plane and maps it to a new point(Xn+1,Yn+1).In this paper,a chaotic pulse generator based on the chaotic Henon map is proposed.It consists of a Henon map function subcircuit to realize the Henon map and another subcircuit to perform the iterative operation.The Henon map subcircuit comprises operational amplifiers,multipliers,delay elements and resistors,whereas,the iterative subcircuit is implemented with a simple design that comprises of an edge forming circuit followed by a monostable multivibrator and a voltage controlled switch without the use of any clock control.The proposed design can be used to realize the Henon map and also to generate a chaotic pulse train,with a controllable time interval and pulse position.The proposed circuit is implemented and simulated using Multisim 13.0 and MATLAB R2019b.The chaotic nature of the generated pulse train and also the time interval between the consecutive pulses is verified by the calculation of its Lyapunov exponents.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60874009 and 10971120)a foundation for the author of National Excellent Doctoral Dissertation of China (FANEDD) (Grant No. 200444)
文摘A visualization of Julia sets of the complex Henon map system with two complex variables is introduced in this paper. With this method, the optimal control function method is introduced to this system and the control and synchronization of its Julia sets are achieved. Control and synchronization of generalized Julia sets are also achieved with this optimal control method. The simulations illustrate the efficacy of this method.
基金Supported by NSF of China (10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese Scholarsthe Scientific Research Foundation of Ministry of Human and Resources and Social Security of China for Returned Overseas Scholars
文摘We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O（1/√n）.
基金Supported by the National High Technology Re-search and Development Program of China(2001AA123053)
文摘A new method to design interleaver based on Henon chaos model is presented. The designed interleaver is with rather random behavior. Experimental results show that the proposed S-henon interleaver make a magnitude of im provement in bit error rate （BER） performance by 0.4 dB compared with the S-random interleaver for AWGN channel respectively. The S-henon interleaver may be adapted to 3G mobile communication systems.
基金Supported by the National Natural Science Foundation of China (No.60172065)
文摘Chaotic sequences are basically ergodic random sequences. By improving correlativity of a chaotic signal, the chaotic dynamic system can be controlled to converge to its equilibrium point and, more significantly, to its multi-periodic orbits. Mathematical theory analysis is carried out and some computer simulation results are provided to support such controllability of the chaotic Henon system and the discrete coupled map lattice.
基金the National Natural Science Foundation of China (60372061)
文摘By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the generalized Henon map. First, move the decimal point of elements in the sequence to the fight; then, cut off the integer; and finally, quantify it into a binary sequence. Statistical test, security analysis, and the application of image encryption have strongly supported the good random statistical characteristics, high linear complexity, large key space, and great sensitivity of the binary sequence.
文摘This paper presents a theoretical framework for parallelizing the FD3 algorithm,which estimates the capacity,information,and correlation dimensions of chaotic time series using the box-counting method.We propose a hybrid parallel implementation leveraging MPI as well as OpenMP to achieve scalable performance on modern high-performance computing architectures.The serial FD3 algorithm is analyzed in detail,followed by a comprehensive parallelization strategy for its key phases,including data retrieval,trajectory reconstruction,sorting,and dimension estimation.Theoretical models based on Amdahl’s and Gustafson’s Laws predict significant speedup,supported by complexity analysis and communication cost models.While experimental validation is planned as future work,this study provides a robust foundation for parallel fractal dimension estimation,with potential applications in chaotic system analysis and computational physics.The motivation for this research is that,although the FD3 algorithm is relatively old and more advanced and efficient algorithms have since been developed,its structure and operation allow for parallelization,which,by providing significant acceleration,could render it competitive once again and suitable for efficient use.
基金supported by the National Natural Science Foundation of China(61301091)the Natural Science Basic Research Plan in Shaanxi Province of China(2015JQ6262)+1 种基金the Open Foundation of State Key Laboratory of Information Security(2015-MS-14)the New Star Team of Xi’an University of Posts and Telecommunications
文摘To improve the security of the color image encryption scheme,a color image encryption scheme based on chaotic systems is proposed. Firstly, the proposed scheme sets the color image as a three-dimensional matrix which is scrambled by affine transformation. Second, the Logistic chaotic sequence applied to generate the control parameter and auxiliary key is used to encrypt the three-dimensionaL matrix. Here, we mainly focus on two methods for encryption processes. One is to generate a chaotic sequence by Logistic map and Henon map, which is used to perform XOR operation with the scrambled components R＇, G＇, B＇ respectively. The other one is to adopt a binary Logistic sequence to select the pixel position for the scrambled components R＇, G＇, B＇ image, and then applying the Henon map and Logistic map with the auxiliary key to perform the replacement encryption. Based on this, an encrypted image is synthesized. Simulation results show that the proposed image encryption scheme can implement better encryption and achieve higher security performance.
基金Supported by NSFC(11101295,11301256)SCED(13ZB0005,14TD0026)
文摘An important problem in a given dynamical system is to determine the existence of a homoclinic orbit. We improve the results of Qin and Xiao [Nonlinearity, 20 （2007）, 2305-2317], who present some sufficient conditions for the existence of a homoclinic/heteroclinic orbit for the generalized H@non map. Moreover, an algorithm is presented to locate these homoclinic orbits.
