The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing....The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.展开更多
Tensor complementarity problem (TCP) is a special kind of nonlinear complementarity problem (NCP). In this paper, we introduce a new class of structure tensor and give some examples. By transforming the TCP to the sys...Tensor complementarity problem (TCP) is a special kind of nonlinear complementarity problem (NCP). In this paper, we introduce a new class of structure tensor and give some examples. By transforming the TCP to the system of nonsmooth equations, we develop a semismooth Newton method for the tensor complementarity problem. We prove the monotone convergence theorem for the proposed method under proper conditions.展开更多
The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusio...The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images.展开更多
The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical info...The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor provides, its gauge independence sounds reasonable. Moreover, its original construction was made by looking for this gauge independence. The aim of this paper, however, is to prove that the quantum metric tensor does depend on the gauge. In addition, a real gauge invariant quantum metric tensor is introduced. A related concept is the quantum fidelity, which is also shown to depend on the gauge in this paper. The gauge dependences are explicitly shown by computing the quantum metric tensor and the quantum fidelity of the Landau problem in different gauges. Then, a real gauge independent metric tensor is proposed and computed for the same Landau problem. Since the gauge dependences have not been observed before, the results of this paper might lead to a new study of topics that are believed to be completely understood.展开更多
The tensor complementarity problem is a special instance in the class of nonlinear complementarity problems, which has many applications in multi-person noncooperative games, hypergraph clustering problems and traffic...The tensor complementarity problem is a special instance in the class of nonlinear complementarity problems, which has many applications in multi-person noncooperative games, hypergraph clustering problems and traffic equilibrium problems. Two most important research issues are how to identify the solvability and how to solve such a problem via analyzing the structure of the involved tensor. In this paper, based on the concept of monotone mappings, we introduce a new class of structured tensors and the corresponding monotone tensor complementarity problem. We show that the solution set of the monotone tensor complementarity problem is nonempty and compact under the feasibility assumption. Moreover, a necessary and sufficient condition for ensuring the feasibility is given via analyzing the structure of the involved tensor. Based on the Huber function,we propose a regularized smoothing Newton method to solve the monotone tensor complementarity problem and establish its global convergence. Under some mild assumptions, we show that the proposed algorithm is superlinearly convergent. Preliminary numerical results indicate that the proposed algorithm is very promising.展开更多
In the framework of continuum mechanics, one of possible consistent definitions of deformable permanent magnets is introduced and explored. Similar model can be used for ferroelectric substances. Based on the suggeste...In the framework of continuum mechanics, one of possible consistent definitions of deformable permanent magnets is introduced and explored. Similar model can be used for ferroelectric substances. Based on the suggested definition, we establish the key kinematic relationship for the deformable permanent magnet and suggest the simplest master system, allowing to analyze behavior of such substances.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.61303212,61170080,61202386)the State Key Program of National Natural Science of China(Grant Nos.61332019,U1135004)+2 种基金the Major Research Plan of the National Natural Science Foundation of China(Grant No.91018008)Major State Basic Research Development Program of China(973 Program)(No.2014CB340600)the Hubei Natural Science Foundation of China(Grant No.2011CDB453,2014CFB440)
文摘The hardness of tensor decomposition problem has many achievements, but limited applications in cryptography, and the tensor decomposition problem has been considered to have the potential to resist quantum computing. In this paper, we firstly proposed a new variant of tensor decomposition problem, then two one-way functions are proposed based on the hard problem. Secondly we propose a key exchange protocol based on the one-way functions, then the security analysis, efficiency, recommended parameters and etc. are also given. The analyses show that our scheme has the following characteristics: easy to implement in software and hardware, security can be reduced to hard problems, and it has the potential to resist quantum computing.Besides the new key exchange can be as an alternative comparing with other classical key protocols.
文摘Tensor complementarity problem (TCP) is a special kind of nonlinear complementarity problem (NCP). In this paper, we introduce a new class of structure tensor and give some examples. By transforming the TCP to the system of nonsmooth equations, we develop a semismooth Newton method for the tensor complementarity problem. We prove the monotone convergence theorem for the proposed method under proper conditions.
基金supported by NSFC under grant No.11471331partially supported by National Center for Mathematics and Interdisciplinary Sciences
文摘The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images.
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
文摘The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor provides, its gauge independence sounds reasonable. Moreover, its original construction was made by looking for this gauge independence. The aim of this paper, however, is to prove that the quantum metric tensor does depend on the gauge. In addition, a real gauge invariant quantum metric tensor is introduced. A related concept is the quantum fidelity, which is also shown to depend on the gauge in this paper. The gauge dependences are explicitly shown by computing the quantum metric tensor and the quantum fidelity of the Landau problem in different gauges. Then, a real gauge independent metric tensor is proposed and computed for the same Landau problem. Since the gauge dependences have not been observed before, the results of this paper might lead to a new study of topics that are believed to be completely understood.
基金supported by National Natural Science Foundation of China(Grant No.12171271)。
文摘The tensor complementarity problem is a special instance in the class of nonlinear complementarity problems, which has many applications in multi-person noncooperative games, hypergraph clustering problems and traffic equilibrium problems. Two most important research issues are how to identify the solvability and how to solve such a problem via analyzing the structure of the involved tensor. In this paper, based on the concept of monotone mappings, we introduce a new class of structured tensors and the corresponding monotone tensor complementarity problem. We show that the solution set of the monotone tensor complementarity problem is nonempty and compact under the feasibility assumption. Moreover, a necessary and sufficient condition for ensuring the feasibility is given via analyzing the structure of the involved tensor. Based on the Huber function,we propose a regularized smoothing Newton method to solve the monotone tensor complementarity problem and establish its global convergence. Under some mild assumptions, we show that the proposed algorithm is superlinearly convergent. Preliminary numerical results indicate that the proposed algorithm is very promising.
文摘In the framework of continuum mechanics, one of possible consistent definitions of deformable permanent magnets is introduced and explored. Similar model can be used for ferroelectric substances. Based on the suggested definition, we establish the key kinematic relationship for the deformable permanent magnet and suggest the simplest master system, allowing to analyze behavior of such substances.
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.
