The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independe...The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.展开更多
In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent function...In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.展开更多
Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions ...Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions of semi-bent and bent functions are special cases of the new construction.展开更多
Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit...Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit element increases.A subarray-based space-time coding(sub-STC)radar is explored to alleviate the range resolution reduction.For the proposed radar configuration,an identical waveform is transmitted and it introduces a small time offset in different subarrays.The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range,Doppler,angle and probing direction.Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage,resolution performance and low sidelobes are also given.Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.展开更多
By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no...By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no homogeneous bent functions ofdegree in in n=2mvariables for m>3.展开更多
A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that th...A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that the algebraic degrees of the new semi-bent functions attain the maximum values.展开更多
This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the res...This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6展开更多
Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardwa...Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.展开更多
基金the General Research Fund of the University of Kansas.
文摘The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) the Doctorate Foundation ofInstitute of Information Engineering (YP20014401)HenanInno-vation Project for University Prominent Research Talents(2003KJCX008)
文摘In this paper, the definition of multl-output partially Bent functions is presented and some properties are discussed. Then the relationship between multi-output partially Bent functions and multi-output Bent functions is given in Theorem 4, which includes Walsh spectrum expression and function expression. This shows that multi-output partially Bent functions and multi-output Bent functions can define each other in principle. So we obtain the general method to construct multi-output partially Bent functions from multi-output Bent functions.
基金The Starting Research Projects for Young Teachers of Southwest Jiaotong University (No.2007Q090)
文摘Based on the theory of quadratic forms over finite fields, a new construction of semi-bent and bent functions is presented. The proposed construction has a cascaded characteristic. Some previously known constructions of semi-bent and bent functions are special cases of the new construction.
基金supported by the National Key Research and Development Program of China(2016YFE0200400)the Key R&D Program of Shaanxi Province(2017KW-ZD-12)+1 种基金the Postdoctoral Science Foundation of Shaanxi Provincethe Nature Science Foundation of Shaanxi Province
文摘Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit element increases.A subarray-based space-time coding(sub-STC)radar is explored to alleviate the range resolution reduction.For the proposed radar configuration,an identical waveform is transmitted and it introduces a small time offset in different subarrays.The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range,Doppler,angle and probing direction.Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage,resolution performance and low sidelobes are also given.Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.
基金Supported by the National Natura1 Science Founda—tion of China(60373087,60473023,66973034)the National High-Technology Research and Development Plan of China(2002AA41051)the Ph D Programs Foundation of Ministry of Education of China(20020486046)
文摘By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions,and by the Hamming weight of homogenousBoolean function,it is proved that there exist no homogeneous bent functions ofdegree in in n=2mvariables for m>3.
基金Supported by the National Natural Science Foundation of China (60773002)the National High Technology Research and Development Program of China (863 Program) (2007AA01Z472)
文摘A class of semi-bent functions with an even number of variables is constructed by using the values of Kloosterman sums.These semi-bent functions are Boolean functions with four trace terms.Moreover,it is shown that the algebraic degrees of the new semi-bent functions attain the maximum values.
文摘This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6
文摘Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.
