For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This ...Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class...This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.展开更多
To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation o...To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.展开更多
Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equatio...Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.展开更多
In this paper, we give the algebraic independence measures for the values ofMahler type functions in complex number field and p-adic number field, respectively.
Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the la...Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theore...The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 cont...In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.展开更多
Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated.Examples show that the results are sharp.
The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the ap...The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.展开更多
Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new cr...Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].展开更多
In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the correspon...In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. （Yuan W J, Xiao B, Zhang J J. The general theorem of Gol＇dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58：1788 1791）. Meanwhile, we also take some examples to show that our estimate is sharp.展开更多
As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the a...As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems. In this paper, we first introduces general theories of Clifford algebra. Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane. Thus we extend some results of plane problem-la three dimensions or high dimensions. Obviously, it is very important for elastic and fluid mechanics. But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions. The left problems are yet to be found out.展开更多
This letter proposes algebraic attacks on two kinds of nonlinear filter generators with symmetric Boolean functions as the filter fimctions. Different fxom the classical algebraic attacks, the proposed attacks take th...This letter proposes algebraic attacks on two kinds of nonlinear filter generators with symmetric Boolean functions as the filter fimctions. Different fxom the classical algebraic attacks, the proposed attacks take the advantage of the combinational property of a linear feedback shift register （LFSR） and the symmetric Boolean function to obtain a tow-degree algebraic relation, and hence the complexities of the proposed attacks are independent of the algebraic immunity （AI） of the filter functions. It is shown that improper combining of the LFSR with the filter function can make the filter generator suffer from algebraic attacks. As a result, the bits of the LFSR must be selected properly to input the filter function with large AI in order to withstand the proposed algebraic attacks.展开更多
In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed ext...In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.展开更多
基金Supported by the National Natural Science Foundation of China ( 60603012)the Foundation of Hubei Provincial Department of Education, China (D200610004)
文摘For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
基金Supported by the National Natural Science Foundation of China(61272434)the Natural Science Foundation of Shandong Province(ZR 2012FM004,ZR2013FQ021)the Foundation of Science and Technology on Information Assume Laboratory(KJ-13-004)
文摘Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金by Basic and Advanced Research Project of CQCSTC(cstc2019jcyj-msxmX0107)Fundamental Research Funds of Chongqing University of Posts and Telecommunications(CQUPT:A2018-125).
文摘This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.
基金This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215 the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003 and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
文摘To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.
基金Supported by the National Natural Science Foundation of China（10471065） Supported by the Natural Science Foundation of Guangdong Province（04010474）
文摘Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.
基金Supported by the Natural Science Foundation of Henan University（05ZDZR001）
文摘In this paper, we give the algebraic independence measures for the values ofMahler type functions in complex number field and p-adic number field, respectively.
文摘Here we complete our work on the asymptotics of Hankel determinants studying the case wherein the entries are “ultrarapidly”-varying functions in the sense that their logarithms are rapidly varying. Moreover, the last results in the paper highlight analogies between algebraic identities for Hankelians with special entries and asymptotic relations valid for large classes of entries.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
基金Supported by Guangdong Natural Science Foundation(2015A030313628,S2012010010376)Training plan for Distinguished Young Teachers in Higher Education of Guangdong(Yqgdufe1405)+1 种基金Guangdong Education Science Planning Project(2014GXJK091,GDJG20142304)the National Natural Science Foundation of China(11301140,11101096)
文摘The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金Supported by the National Key Basic Research Project of China (No. 2004CB318000)the NSF of China(No. 60533060/60872095)+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (No.20060358055)the Subject Foundation in Ningbo University(No. xkl09046)
文摘In this paper we propose a construction method of the planar cubic algebraic splinecurve with endpoint interpolation conditions and a specific analysis of its properties. Thepiecewise cubic algebraic curve has G2 continuous contact with the control polygon at twoendpoints and is G2 continuous between each segments of itself. The process of this method issimple and clear, and provides a new way of thinking to design implicit curves.
文摘Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated.Examples show that the results are sharp.
文摘The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function.
文摘Algebraic attack was applied to attack Filter-Combintr model keystreamgenerators. We proposed the technique of function composition to improve the model, and the improvedmodel can resist the algebraic attack. A new criterion for designing Filter-Combiner model was alsoproposed: the total length I. of Linear Finite State Machines used in the model should be largeenough and the degree d of Filter-Combiner function should be approximate [L/2].
基金The NSF(10471065)of Chinathe Foundation(2011SQRL172)of the Education Department of Anhui Province for Outstanding Young Teachers in Universitythe Foundation(2012xq26)of the Huaibei Normal University for Young Teachers
文摘In this paper, we give an estimate result of Gol＇dberg＇s theorem concern- ing the growth of meromorphic solutions of Mgebraic differential equations by using Zalcman Lemma. It is an extending result of the corresponding theorem by Yuan et al. （Yuan W J, Xiao B, Zhang J J. The general theorem of Gol＇dberg concerning the growth of meromorphic solutions of algebraic differential equations. Comput. Math. Appl., 2009, 58：1788 1791）. Meanwhile, we also take some examples to show that our estimate is sharp.
基金This is a comprehensive report at the Second National Symposium on Modern Mathematics and MechanicsProject Supported by the Science Foundation of the Chinese Academy of Sciences
文摘As is Wellknown in both elastic mechanics andfluid mechanics, the plane problems are more convenient than space problems. One of the causes is that there has been a complete theory about the complex Junction and the analytic junction, hut in space problems, the case is quite different.We have no effective method to deal with these problems. In this paper, we first introduces general theories of Clifford algebra. Then we emphatically explain Clifford algebra in three dimensions and establish theories of regular Junction in three dimensions analogically to analytic function in plane. Thus we extend some results of plane problem-la three dimensions or high dimensions. Obviously, it is very important for elastic and fluid mechanics. But because Clifford algebra is not a commutative algebra, we can't simply extend the results of two dimensions to high dimensions. The left problems are yet to be found out.
基金Supported by the National Basic Research Program of China （No. 2007CB311201）, the National Natural Science Foundation of China （No.60833008 No.60803149）, and the Foundation of Guangxi Key Laboratory of Information and Communication （No.20902）.
文摘This letter proposes algebraic attacks on two kinds of nonlinear filter generators with symmetric Boolean functions as the filter fimctions. Different fxom the classical algebraic attacks, the proposed attacks take the advantage of the combinational property of a linear feedback shift register （LFSR） and the symmetric Boolean function to obtain a tow-degree algebraic relation, and hence the complexities of the proposed attacks are independent of the algebraic immunity （AI） of the filter functions. It is shown that improper combining of the LFSR with the filter function can make the filter generator suffer from algebraic attacks. As a result, the bits of the LFSR must be selected properly to input the filter function with large AI in order to withstand the proposed algebraic attacks.
文摘In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.
