In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value pr...In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.展开更多
In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism ...In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.展开更多
In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function...In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functi...In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.展开更多
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinit...Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinitely many common commuting conserved functions. Further, infinite conservation laws of the hierarchy are presented.展开更多
In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the ex...In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the existence of infinitely many conservation laws for this two hierarchies and obtain the formulae of the corresponding conserved densities and associated fluxes.展开更多
Let T 〉 1 be an integer, T = {0, 1,2,... ,T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems △u（t） - a（t）u（t） =λu（t） ＋ f（u...Let T 〉 1 be an integer, T = {0, 1,2,... ,T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems △u（t） - a（t）u（t） =λu（t） ＋ f（u（t -τ（t））） - h（t）, t ∈T, u（O） = u（T）, = where △u（t）=u（t＋1）-u（t）,a：T→R and satisfies ∏ （T-1） t=0 （1＋a（t））=1,τ：T→Z t-τ（t）∈T for t ∈T,f：R→R is continuous and satisfies Landesman-Lazer type condition and h ： T → R. The proofs of our main results are based on the Rabinowitz＇s global bifurcation theorem and Leray-Schauder degree.展开更多
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curv...In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.展开更多
A class of geometric asynchronous parallel algorithms for solving large-scale discrete PDE eigenvalues has been studied by the author (Sun in Sci China Math 41(8): 701–725, 2011;Sun in Math Numer Sin 34(1): 1–24, 20...A class of geometric asynchronous parallel algorithms for solving large-scale discrete PDE eigenvalues has been studied by the author (Sun in Sci China Math 41(8): 701–725, 2011;Sun in Math Numer Sin 34(1): 1–24, 2012;Sun in J Numer Methods Comput Appl 42(2): 104–125, 2021;Sun in Math Numer Sin 44(4): 433–465, 2022;Sun in Sci China Math 53(6): 859–894, 2023;Sun et al. in Chin Ann Math Ser B 44(5): 735–752, 2023). Different from traditional preconditioning algorithm with the discrete matrix directly, our geometric pre-processing algorithm (GPA) algorithm is based on so-called intrinsic geometric invariance, i.e., commutativity between the stiff matrix A and the grid mesh matrix G:AG=GA, Thus, the large-scale system solvers can be replaced with a much smaller block-solver as a pretreatment. In this paper, we study a sole PDE and assume G satisfies a periodic condition G^(m)=I,m<<dim(G). Four special cases have been studied in this paper: two-point ODE eigen-problem, Laplace eigen-problems over L-shaped region, square ring, and 3D hexahedron. Two conclusions that “the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron” and “commutativity of grid mesh matrix and mass matrix is the essential condition for the GPA algorithm” have been obtained.展开更多
Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equatio...Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equations with multiple right-hand sides.However,little is known about the behavior of these methods when they are applied to the solution of linear discrete ill-posed problems with multiple right-hand sides contaminated by errors.In this paper,the regularizing properties of the block GMERR method and the simpler block GMERR method are examined.Both a regularized block GMERR method and a regularized simpler block GMERR method are developed for solving large-scale linear discrete ill-posed problems with multiple right-hand sides.Numerical experiments on typical test matrices show the efficiency of the proposed methods.展开更多
In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mat...In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.展开更多
Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi...Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi- cient way. Certificateless signcryption and pro- xy signcryption in identity-based cryptography were proposed for different applications. Most of these schemes are constructed by bilinear pairings from elliptic curves. However, some schemes were recently presented without pai- rings. In this paper, we present a certificateless proxy identity-based signcryption scheme with- out bilinear pairings, which is efficient and secure.展开更多
A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the s...A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the signer can not make a linkage between the blind signature and the identity of the requester. Proxy signature and blind signature are used widely in electronic commerce. With satisfying the security properties of both two signatures, a new proxy blind signature scheme based on discrete logarithm problem is proposed.展开更多
A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ...A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ensure the scheme's security. However,we show by formulating an attack that their CLAS scheme cannot defend against Type I adversary. Furthermore, we point out an error that exists in the signature simulation of their security proof.After that we give a correct signature simulation for the security proof. Finally, to resist the Type I attack, we present two methods for improving Qu et al's CLAS scheme. Moreover, the second improving method can elevate the trust level of Qu et al's CLAS scheme to the highest trust level: Level 3.展开更多
Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-f...Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-fold Darboux transformation(DT) and conservation laws for the lattice Burgers equation are constructed based on its Lax pair.N-soliton solutions in the form of Vandermonde-like determinant are derived via the resulting DT with symbolic computation,structures of which are shown graphically.Coexistence of the elastic-inelastic interaction among the three solitons is firstly reported for the lattice Burgers equation,even if the similar phenomenon for certern continuous systems is known.Results in this paper might be helpful for understanding some ecological problems describing the evolution of competing species and the propagation of nonlinear waves in fluids.展开更多
Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic ...Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.展开更多
In this paper we establish the existence of single and multiple positive solutions to the following singular discrete boundary value problem {△[Ф△x（i-1））]＋q1（i）f1（i,x（i）,y（i））=0,i∈{1,2,…,T}△[Ф△x（...In this paper we establish the existence of single and multiple positive solutions to the following singular discrete boundary value problem {△[Ф△x（i-1））]＋q1（i）f1（i,x（i）,y（i））=0,i∈{1,2,…,T}△[Ф△x（i-1））]＋q1（i）f2（i,x（i）,y（i））=0,x（0）=x（T＋1）=y（T＋1）=y（0）=y（T＋1）=0,whereФ（s）=｜s｜^p-2s,p〉1 and the nonlinear terms fk（i,x,y）（k=1,2）may be singular at （x,y）=（0,0）.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12361040)the Department of Education University Innovation Fund of Gansu Province(Grant No.2021A-006)。
文摘In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1236104012461035)+1 种基金the Outstanding Youth Fund of Gansu Province(Grant No.24JRRA121)the Scientific Research Ability Improvement Program for Young Teachers of Northwest Normal University(Grant No.NWNU-LKQN2021-17)。
文摘In this paper,we consider the discrete boundary value problem of the type{∆u1=0=∆un-1,∇(t_(k)^(N-1))φ(∆uk))+t_(k)^(N-1)fk(t_(k),u_(k),∆_(uk))=0,2≤k≤n-1,whereφ:(-a,a)→R,0<a<∞,is an increasing homeomorphism withφ(0)=0,such aφis called singular,N≥1,n≥3 are integers,tk are the grid points,uk:=u(tk),k=1,2,...,n,∇is the backward difference operator defined by∆uk=uk-uk-1,△is the forward difference operator defined by△uk=uk+1-uk,fk(2≤k≤n-1)are continuous functions.We prove the existence of solutions to this problem by employing the sign condition,the continuation lemma and the upper and lower solutions,respectively.On this basis,we also establish the Ambrosetti-Prodi type results for it.
基金Supported by the National Natural Science Foundation of China(50 1 740 51 )
文摘In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C 1.The paper deals with this problem by means of taking the place of maximum entropy function with adjustable entropy function.By constructing an interval extension of adjustable entropy function an d some region deletion test rules,a new interval algorithm is presented.The rele vant properties are proven.The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum entropy algorithm.Both theoretical and numerica l results show that the method is reliable and efficient.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88（4） （2009）, pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金The authors are supported by National Natural Sciences Foundation of China(11961060,11671322)the Key Project of Natural Sciences Foundation of Gansu Province(18JR3RA084).
文摘In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.
文摘This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
基金the State Key Basic Research Project of China under Grant No.2004CB318000National Natural Science Foundation of China under Grant No.10371023
文摘Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinitely many common commuting conserved functions. Further, infinite conservation laws of the hierarchy are presented.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1412800the Innovation Program of Shanghai Municipal Education Commission under Grant No.10ZZ131
文摘In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the existence of infinitely many conservation laws for this two hierarchies and obtain the formulae of the corresponding conserved densities and associated fluxes.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1132612711101335)+1 种基金the Science Research Project of Gansu University(Grant No.2013A-001)NWNU-LKQN-11-23
文摘Let T 〉 1 be an integer, T = {0, 1,2,... ,T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems △u（t） - a（t）u（t） =λu（t） ＋ f（u（t -τ（t））） - h（t）, t ∈T, u（O） = u（T）, = where △u（t）=u（t＋1）-u（t）,a：T→R and satisfies ∏ （T-1） t=0 （1＋a（t））=1,τ：T→Z t-τ（t）∈T for t ∈T,f：R→R is continuous and satisfies Landesman-Lazer type condition and h ： T → R. The proofs of our main results are based on the Rabinowitz＇s global bifurcation theorem and Leray-Schauder degree.
基金Supported by the National Science Foundation of China under Grant No.11371244the Applied Mathematical Subject of SSPU under Grant No.XXKPY1604
文摘In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.
基金supported by the Basic Research Plan on High Performance Computing of Institute of Software(No.ISCAS-PYFX-202302).
文摘A class of geometric asynchronous parallel algorithms for solving large-scale discrete PDE eigenvalues has been studied by the author (Sun in Sci China Math 41(8): 701–725, 2011;Sun in Math Numer Sin 34(1): 1–24, 2012;Sun in J Numer Methods Comput Appl 42(2): 104–125, 2021;Sun in Math Numer Sin 44(4): 433–465, 2022;Sun in Sci China Math 53(6): 859–894, 2023;Sun et al. in Chin Ann Math Ser B 44(5): 735–752, 2023). Different from traditional preconditioning algorithm with the discrete matrix directly, our geometric pre-processing algorithm (GPA) algorithm is based on so-called intrinsic geometric invariance, i.e., commutativity between the stiff matrix A and the grid mesh matrix G:AG=GA, Thus, the large-scale system solvers can be replaced with a much smaller block-solver as a pretreatment. In this paper, we study a sole PDE and assume G satisfies a periodic condition G^(m)=I,m<<dim(G). Four special cases have been studied in this paper: two-point ODE eigen-problem, Laplace eigen-problems over L-shaped region, square ring, and 3D hexahedron. Two conclusions that “the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron” and “commutativity of grid mesh matrix and mass matrix is the essential condition for the GPA algorithm” have been obtained.
基金National Natural Science Foundation of China under Grant No.11571171the anonymous referees for their useful comments and suggestions which greatly improved the representation of this paper.
文摘Based on the block Arnoldi process and minimizing the Frobenius norm of the error,the block generalized minimal error(GMERR)method and its simpler version are proposed for solving large-scale linear systems of equations with multiple right-hand sides.However,little is known about the behavior of these methods when they are applied to the solution of linear discrete ill-posed problems with multiple right-hand sides contaminated by errors.In this paper,the regularizing properties of the block GMERR method and the simpler block GMERR method are examined.Both a regularized block GMERR method and a regularized simpler block GMERR method are developed for solving large-scale linear discrete ill-posed problems with multiple right-hand sides.Numerical experiments on typical test matrices show the efficiency of the proposed methods.
基金The National Natural Science Foundation of China(No60402019)the Science Research Program of Education Bureau of Hubei Province (NoQ200629001)
文摘In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.
基金supported by the National Natural Science Foundation of China under Grants No.61272499,No.10990011
文摘Signcryption, which was introduced by ZHEN~ is a cryptographic primitive that fulfils the functions of both digital signature and encryption and guarantees confidentiality, integrity and non-repudiation in a more effi- cient way. Certificateless signcryption and pro- xy signcryption in identity-based cryptography were proposed for different applications. Most of these schemes are constructed by bilinear pairings from elliptic curves. However, some schemes were recently presented without pai- rings. In this paper, we present a certificateless proxy identity-based signcryption scheme with- out bilinear pairings, which is efficient and secure.
基金Supported by the National High Technology Research and Development Program of China (2004AA001021), the Anhui Province Educa-tion Department Project (G2006jq1011) and Hefei University of Technology Project (G061105F)
文摘A proxy signature scheme allows an original signer to delegate his signing capability to a proxy signer who can sign on behalf of the original signer. A blind signature is the concept with a salient feature that the signer can not make a linkage between the blind signature and the identity of the requester. Proxy signature and blind signature are used widely in electronic commerce. With satisfying the security properties of both two signatures, a new proxy blind signature scheme based on discrete logarithm problem is proposed.
基金Supported by the National Natural Science Foundation of China(61373140,61170246)the Program for Innovative Research Team in Science and Technology in Fujian Province University and 2018 Scientific Research and Innovation Special Project of Putian University(2018ZP11,2018ZP12)+1 种基金the Opening Project of Key Laboratory of Financial Mathematics of Fujian Province University(Putian University)(JR201806)Educational Research Projects of Young and Middle-aged Teachers in Fujian Education Department(JT180487)。
文摘A Certificateless Aggregate Signature(CLAS) scheme was proposed by Qu and Mu recently, which was published in "Int J. Electronic Security and Digital Forensics, 2018, 10(2)". They used discrete logarithm to ensure the scheme's security. However,we show by formulating an attack that their CLAS scheme cannot defend against Type I adversary. Furthermore, we point out an error that exists in the signature simulation of their security proof.After that we give a correct signature simulation for the security proof. Finally, to resist the Type I attack, we present two methods for improving Qu et al's CLAS scheme. Moreover, the second improving method can elevate the trust level of Qu et al's CLAS scheme to the highest trust level: Level 3.
基金Supported by the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-2012ZX-10,Beijing University of Aeronautics and Astronauticsthe Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02+2 种基金the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications)the Specialized Research Fund for the Doctoral Program of Higher Education (No. 200800130006),Chinese Ministry of Educationthe Scientific Research Common Program of Beijing Municipal Commission of Education under Grant No. KM201010772020
文摘Burgers-type equations can describe some phenomena in fluids,plasmas,gas dynamics,traffic,etc.In this paper,an integrable hierarchy covering the lattice Burgers equation is derived from a discrete spectral problem.N-fold Darboux transformation(DT) and conservation laws for the lattice Burgers equation are constructed based on its Lax pair.N-soliton solutions in the form of Vandermonde-like determinant are derived via the resulting DT with symbolic computation,structures of which are shown graphically.Coexistence of the elastic-inelastic interaction among the three solitons is firstly reported for the lattice Burgers equation,even if the similar phenomenon for certern continuous systems is known.Results in this paper might be helpful for understanding some ecological problems describing the evolution of competing species and the propagation of nonlinear waves in fluids.
文摘Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.
基金Supported by the XJZDXK of China(Grant No.XJZDXK2011004)the National Natural Science Foundation of China(Grant No.10971021)
文摘In this paper we establish the existence of single and multiple positive solutions to the following singular discrete boundary value problem {△[Ф△x（i-1））]＋q1（i）f1（i,x（i）,y（i））=0,i∈{1,2,…,T}△[Ф△x（i-1））]＋q1（i）f2（i,x（i）,y（i））=0,x（0）=x（T＋1）=y（T＋1）=y（0）=y（T＋1）=0,whereФ（s）=｜s｜^p-2s,p〉1 and the nonlinear terms fk（i,x,y）（k=1,2）may be singular at （x,y）=（0,0）.
