To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different bloc...To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.展开更多
A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem： multivariate quadratic equations over fini...A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem： multivariate quadratic equations over finite fields. This problem has been shown to be NP-complete and can＇t be solved with polynomial time algorithm.展开更多
By using the minimal polynomial of ergodic matrix and the property of polynomial over finite field,we present a polynomial time algorithm for the two-side exponentiation problem about ergodic matrices over finite fie...By using the minimal polynomial of ergodic matrix and the property of polynomial over finite field,we present a polynomial time algorithm for the two-side exponentiation problem about ergodic matrices over finite field （TSEPEM）,and analyze the time and space complexity of the algorithm.According to this algorithm,the public key scheme based on TSEPEM is not secure.展开更多
Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they...Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they did not provide a rigorous security proof for their KE protocols. In this paper, applying the properties of ergodic matrix, we first present a polynomial time algorithm to solve the TEP problem using O(n^6) arithmetic operations in the finite field, where n is the security parameter. Then, applying this polynomial time algorithm, we generate a common shared key for two TEP-based KE constructions, respectively. In addition, we also provide a polynomial time algorithm with O(n^6) arithmetic operations that directly recovers the plaintext from a ciphertext for the KE-based encryption scheme. Thus, the TEP-based KE protocols and their corresponding encryption schemes are insecure.展开更多
The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant qua...The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.U0735004 and 60972133)the Natural Science Foundation of Guangdong Province,China(Grant No.05006593)+2 种基金the Project Team for Natural Science Foundation of Guangdong Province,China(Grant No.9351064101000003)Energy Technology Key Laboratory Project of Guangdong Province,China(Grant No.2008A060301002)the Fundamental Research Funds for the Central Universities,China(Grant No.X2dXD2116370)
文摘To ensure the security of a digital image, a new self-adapting encryption algorithm based on the spatiotemporal chaos and ergodic matrix is proposed in this paper. First, the plain-image is divided into different blocks of the same size, and each block is sorted in ascending order to obtain the corresponding standard ergodic matrix. Then each block is encrypted by the spatiotemporal chaotic system and shuffled according to the standard ergodic matrix. Finally, all modules are rearranged to acquire the final encrypted image. In particular, the plain-image information is used in the initial conditions of the spatiotemporal chaos and the ergodic matrices, so different plain-images will be encrypted to obtain different cipherimages. Theoretical analysis and simulation results indicate that the performance and security of the proposed encryption scheme can encrypt the image effectively and resist various typical attacks.
基金Supported bythe Specialized Research Fundfor the Doctoral Programof Higher Education of China (20050183032) the Science Foundation Project of Jilin Province Education Office(2005180 ,2005181)
文摘A new public key encryption scheme is proposed in this paper, which is based on a hard problem over ergodic matrices. The security of this scheme is equal to the MQ-problem： multivariate quadratic equations over finite fields. This problem has been shown to be NP-complete and can＇t be solved with polynomial time algorithm.
基金Supported by the National Natural Science Foundation of China (70671096)Jiangsu Teachers University of Technology (KYY08004,KYQ09002)
文摘By using the minimal polynomial of ergodic matrix and the property of polynomial over finite field,we present a polynomial time algorithm for the two-side exponentiation problem about ergodic matrices over finite field （TSEPEM）,and analyze the time and space complexity of the algorithm.According to this algorithm,the public key scheme based on TSEPEM is not secure.
基金supported by the National Natural Science Foundation of China(No.61672270,61602216,61702236)the Qing Lan Project for Young Researchers of Jiangsu Province of China(No.KYQ14004)+1 种基金the Open Fund of State Key Laboratory of Information Security,Institute of Information Engineering,Chinese Academy of Sciences(No.2015-MSB-10)Jiangsu Overseas Research&Training Program for University Prominent Young&Middle-aged Teachers and Presidents,Changzhou Sci&Tech Program,(Grant No.CJ20179027)
文摘Recently, Mao, Zhang, Wu et al. constructed two key exchange(KE) protocols based on tensor ergodic problem(TEP). Although they conjectured that these constructions can potentially resist quantum computing attack, they did not provide a rigorous security proof for their KE protocols. In this paper, applying the properties of ergodic matrix, we first present a polynomial time algorithm to solve the TEP problem using O(n^6) arithmetic operations in the finite field, where n is the security parameter. Then, applying this polynomial time algorithm, we generate a common shared key for two TEP-based KE constructions, respectively. In addition, we also provide a polynomial time algorithm with O(n^6) arithmetic operations that directly recovers the plaintext from a ciphertext for the KE-based encryption scheme. Thus, the TEP-based KE protocols and their corresponding encryption schemes are insecure.
基金the National Natural Science Foundation of China，the State Key Program of National Natural Science of China，the Major Research Plan of the National Natural Science Foundation of China，Major State Basic Research Development Program of China (973 Program)，the Hubei Natural Science Foundation of China
文摘The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and eneryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security,security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.
