A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is...To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is constructed for the system.The new variable introduced can be separated from the difference scheme to obtain another difference scheme containing only the original variable.The energy method is applied to the theoretical analysis of the difference scheme.Results show that the difference scheme is uniquely solvable and satisfies the energy conservation law corresponding to the original problem.Moreover,the difference scheme converges when the step ratio satisfies a constraint condition,and the temporal and spatial convergence orders are both two.Numerical examples verify the convergence order and the invariant of the difference scheme.Furthermore,the step ratio constraint is unnecessary for the convergence of the difference scheme.Compared with a known two-level nonlinear difference scheme,the proposed difference scheme has more advantages in numerical calculation.展开更多
A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify h...A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid share.Another does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.展开更多
In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we part...In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.展开更多
In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique...In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.展开更多
Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing i...Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational(e.g.,pitching)excitations.To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks,a variational domain-decomposition scheme is proposed.This scheme includes three steps:(i)dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles(i.e.,using the baffle as part of the boundaries of the sub-domain)by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces;(ii)expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients,and expressing the auxiliary normal fluid velocity functions on the artificial in terfaces as Fourier-type series with undetermined coefficients;(iii)solving the undetermined coefficients by the Trefftz method and the proposed variational formulations.The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method(FEM),and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation.The present semi-analytical result is compared with that given by computational fluid dynamics(CFD)software or literature.展开更多
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g...In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.展开更多
Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every lin...Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.展开更多
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi...In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform c...We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.展开更多
Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and give...Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and gives more freedom in designing controllers in order to achieve some desired performance.With the aid of Lyapunov stability theorem and partial stability theory,two cases were presented:1) Chaos synchronization of the system without perturbation or with vanishing perturbations;2) The boundness of the error state for the system with nonvanishing perturbations satisfying some conditions.Finally,several simulations for Lorenz system were provided to verify the effectiveness and feasibility of our method.Compared numerically with the existing results of linear feedback control scheme,the results are sharper than the existing ones.展开更多
This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference s...This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference scheme on a uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed.展开更多
We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is ...We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.展开更多
Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay e...Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay exactly faster than . The system contains a dynamic compensator with another state v in the feedback loop, and consists of two states u and v. This problem entirely differs from the one with static feedback scheme in which the system consists only of a single state u. To show the essential difference, some specific property of the spectral subspaces associated with our control system is studied.展开更多
Cloud-based services have powerful storage functions and can provide accurate computation.However,the question of how to guarantee cloud-based services access control and achieve data sharing security has always been ...Cloud-based services have powerful storage functions and can provide accurate computation.However,the question of how to guarantee cloud-based services access control and achieve data sharing security has always been a research highlight.Although the attribute-based proxy re-encryption(ABPRE)schemes based on number theory can solve this problem,it is still difficult to resist quantum attacks and have limited expression capabilities.To address these issues,we present a novel linear secret sharing schemes(LSSS)matrix-based ABPRE scheme with the fine-grained policy on the lattice in the research.Additionally,to detect the activities of illegal proxies,homomorphic signature(HS)technology is introduced to realize the verifiability of re-encryption.Moreover,the non-interactivity,unidirectionality,proxy transparency,multi-use,and anti-quantum attack characteristics of our system are all advantageous.Besides,it can efficiently prevent the loss of processing power brought on by repetitive authorisation and can enable precise and safe data sharing in the cloud.Furthermore,under the standard model,the proposed learning with errors(LWE)-based scheme was proven to be IND-sCPA secure.展开更多
We analyze mimetic properties of a conservative finite-volume (FV) scheme on polygonal meshes used for modeling solute transport on a surface with variable elevation. Polygonal meshes not only provide enormous mesh ge...We analyze mimetic properties of a conservative finite-volume (FV) scheme on polygonal meshes used for modeling solute transport on a surface with variable elevation. Polygonal meshes not only provide enormous mesh generation flexibility, but also tend to improve stability properties of numerical schemes and reduce bias towards any particular mesh direction. The mathematical model is given by a system of weakly coupled shallow water and linear transport equations. The equations are discretized using different explicit cell-centered FV schemes for flow and transport subsystems with different time steps. The discrete shallow water scheme is well balanced and preserves the positivity of the water depth. We provide a rigorous estimate of a stable time step for the shallow water and transport scheme and prove a bounds-preserving property of the solute concentration. The scheme is second-order accurate over fully wet regions and first-order accurate over partially wet or dry regions. Theoretical results are verified with numerical experiments on rectangular, triangular, and polygonal meshes.展开更多
This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpola...This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
基金The National Natural Science Foundation of China(No.11671081).
文摘To numerically solve the initial-boundary value problem of the Korteweg-de Vries equation,an equivalent coupled system of nonlinear equations is obtained by the method of reduction of order.Then,a difference scheme is constructed for the system.The new variable introduced can be separated from the difference scheme to obtain another difference scheme containing only the original variable.The energy method is applied to the theoretical analysis of the difference scheme.Results show that the difference scheme is uniquely solvable and satisfies the energy conservation law corresponding to the original problem.Moreover,the difference scheme converges when the step ratio satisfies a constraint condition,and the temporal and spatial convergence orders are both two.Numerical examples verify the convergence order and the invariant of the difference scheme.Furthermore,the step ratio constraint is unnecessary for the convergence of the difference scheme.Compared with a known two-level nonlinear difference scheme,the proposed difference scheme has more advantages in numerical calculation.
文摘A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid share.Another does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.
基金Supported by the National Natural Science Foundation of China (11271237)
文摘In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.
基金National Natural Science Foundation of China(No.11571373)
文摘In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.
基金the National Natural Science Foundation of China(Grant Nos.11572018 and 11772020).
文摘Sloshing-induced force and moment may affect the dynamic property of the liquid-contained system.Analytically presented linear Stokes-Joukowski potentials of fluid are usually needed for analytical study of sloshing in liquid-filled tank under rotational(e.g.,pitching)excitations.To obtain the analytically approximate linear Stokes-Joukowski potentials of fluid in the rigid baffled tanks,a variational domain-decomposition scheme is proposed.This scheme includes three steps:(i)dividing the hydrostatic baffled fluid domain into simple sub-domains based on the positions of the baffles(i.e.,using the baffle as part of the boundaries of the sub-domain)by introducing artificial interfaces and densities of fluids in the different sub-domains or auxiliary normal fluid velocity functions on the artificial interfaces;(ii)expressing the solution for linear Stokes-Joukowski potential of each sub-domain as a linear combination of a class of harmonic functions with undetermined coefficients,and expressing the auxiliary normal fluid velocity functions on the artificial in terfaces as Fourier-type series with undetermined coefficients;(iii)solving the undetermined coefficients by the Trefftz method and the proposed variational formulations.The obtained semi-analytical linear Stokes-Joukowski potential agrees well with that published in literature or given by finite element method(FEM),and its applicability to study nonlinear sloshing problem is verified by applying it to a two-dimensional partially fluid-filled rectangular tank with a T-shaped baffle under pitching excitation.The present semi-analytical result is compared with that given by computational fluid dynamics(CFD)software or literature.
基金supported by the Simons Foundation:Collaboration Grantssupported by the AFOSR grant FA9550-18-1-0383.
文摘In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.
文摘Secret sharing is an important topic in cryptography and has applications in information security. The coding theory has been an important role in the constructing of secret sharing schemes. It is known that every linear code can be used to construct secret sharing schemes. So, we use the parity-check matrix of a linear code to construct secret sharing schemes based on linear codes. We also describe some techniques to recover the secret and determine the access structure of the new scheme. In this paper, we use the Massey＇s secret sharing scheme.
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
文摘In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
文摘We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.
基金Projects(61075065,60774045,U1134108) supported by the National Natural Science Foundation of ChinaProject(20110162110041) supported by the Ph.D Programs Foundation of Ministry of Education of ChinaProject(CX2011B086) supported by Hunan Provincial Innovation Foundation For Postgraduate,China
文摘Chaos synchronization of systems with perturbations was investigated.A generic nonlinear control scheme to realize chaos synchronization of systems was proposed.This control scheme is flexible and practicable,and gives more freedom in designing controllers in order to achieve some desired performance.With the aid of Lyapunov stability theorem and partial stability theory,two cases were presented:1) Chaos synchronization of the system without perturbation or with vanishing perturbations;2) The boundness of the error state for the system with nonvanishing perturbations satisfying some conditions.Finally,several simulations for Lorenz system were provided to verify the effectiveness and feasibility of our method.Compared numerically with the existing results of linear feedback control scheme,the results are sharper than the existing ones.
文摘This paper is concerned with the numerical solution for singular perturbation system of two coupled second ordinary differential equations with initial and boundary conditions, respectively. Fitted finite difference scheme on a uniform mesh, whose solution converges pointwise independently of the singular perturbation parameter is constructed and analyzed.
基金supported by the National Natural Science Foundation of China(Nos.12132001 and 52192632)。
文摘We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.
文摘Unlike regular stabilizations, we construct in the paper a specific feedback control system such that u(t) decays exponentially with the designated decay rate, and that some non-trivial linear functionals of u decay exactly faster than . The system contains a dynamic compensator with another state v in the feedback loop, and consists of two states u and v. This problem entirely differs from the one with static feedback scheme in which the system consists only of a single state u. To show the essential difference, some specific property of the spectral subspaces associated with our control system is studied.
基金The project is provided funding by the Natural Science Foundation of China(Nos.62272124,2022YFB2701400)the Science and Technology Program of Guizhou Province(No.[2020]5017)+3 种基金the Research Project of Guizhou University for Talent Introduction(No.[2020]61)the Cultivation Project of Guizhou University(No.[2019]56)the Open Fund of Key Laboratory of Advanced Manufacturing Technology,Ministry of Education,GZUAMT2021KF[01]the Postgraduate Innovation Program in Guizhou Province(No.YJSKYJJ[2021]028).
文摘Cloud-based services have powerful storage functions and can provide accurate computation.However,the question of how to guarantee cloud-based services access control and achieve data sharing security has always been a research highlight.Although the attribute-based proxy re-encryption(ABPRE)schemes based on number theory can solve this problem,it is still difficult to resist quantum attacks and have limited expression capabilities.To address these issues,we present a novel linear secret sharing schemes(LSSS)matrix-based ABPRE scheme with the fine-grained policy on the lattice in the research.Additionally,to detect the activities of illegal proxies,homomorphic signature(HS)technology is introduced to realize the verifiability of re-encryption.Moreover,the non-interactivity,unidirectionality,proxy transparency,multi-use,and anti-quantum attack characteristics of our system are all advantageous.Besides,it can efficiently prevent the loss of processing power brought on by repetitive authorisation and can enable precise and safe data sharing in the cloud.Furthermore,under the standard model,the proposed learning with errors(LWE)-based scheme was proven to be IND-sCPA secure.
基金This work was carried out under the auspices of the National Nuclear Security Administration of the U.S.Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396The Los Alamos unlimited release number is LA-UR-22-30864.
文摘We analyze mimetic properties of a conservative finite-volume (FV) scheme on polygonal meshes used for modeling solute transport on a surface with variable elevation. Polygonal meshes not only provide enormous mesh generation flexibility, but also tend to improve stability properties of numerical schemes and reduce bias towards any particular mesh direction. The mathematical model is given by a system of weakly coupled shallow water and linear transport equations. The equations are discretized using different explicit cell-centered FV schemes for flow and transport subsystems with different time steps. The discrete shallow water scheme is well balanced and preserves the positivity of the water depth. We provide a rigorous estimate of a stable time step for the shallow water and transport scheme and prove a bounds-preserving property of the solute concentration. The scheme is second-order accurate over fully wet regions and first-order accurate over partially wet or dry regions. Theoretical results are verified with numerical experiments on rectangular, triangular, and polygonal meshes.
文摘This paper presents a study on the development and implementation of a second derivative method for the solution of stiff first order initial value problems of ordinary differential equations using method of interpolation and collocation of polynomial approximate solution. The results of this paper bring some useful information. The constructed methods are A-stable up to order 8. As it is shown in the numerical examples, the new methods are superior for stiff systems.
