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
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
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
First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the ...First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF（2）2k are discussed.展开更多
Several new results on the non-existence of some generalized bent functions are proved by using properties of the decomposition law of primes in cyclotomic fields and properties of the solutions of some special Diopha...Several new results on the non-existence of some generalized bent functions are proved by using properties of the decomposition law of primes in cyclotomic fields and properties of the solutions of some special Diophantine equations.展开更多
In this paper, the ranks of a special family of Maiorana-McFarland bent functions are discussed. The upper and lower bounds of the ranks are given and those bent functions whose ranks achieve these bounds are determin...In this paper, the ranks of a special family of Maiorana-McFarland bent functions are discussed. The upper and lower bounds of the ranks are given and those bent functions whose ranks achieve these bounds are determined. As a consequence, the inequivalence of some bent functions are derived. Furthermore, the ranks of the functions of this family are calculated when t 6.展开更多
This paper presents a construction of infinite classes of binary and p-ary hyperbent functions of polynomial trace form,based on finding a zero of a Kloosterman sum.
Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, an...Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, and examples satisfying our results are given.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
This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptog...This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St^nic~ and Maitra （2008）. Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li （2006）, and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky （1994）.展开更多
Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-e...Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.展开更多
Three classes of Boolean functions with four-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from Bent functions of the MaioranaMc Farland and Dillon PS ap ty...Three classes of Boolean functions with four-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from Bent functions of the MaioranaMc Farland and Dillon PS ap types and of the monomial form Tr1^2m（λx^r（2^m-1）） by complementing the values of the Bent functions at two points.展开更多
This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above B...This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.展开更多
Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then sh...Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.展开更多
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Returned Overseas Student,Foundation of Shanxi Province of China and by Fund of Nanjing University of Information Science and Technology
文摘First, this paper discusses and sums up some properties of a pair of functions p（x）, q（x） that makes （y ＋ 1）p（x） ＋ yq（x） into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF（2）2k are discussed.
文摘Several new results on the non-existence of some generalized bent functions are proved by using properties of the decomposition law of primes in cyclotomic fields and properties of the solutions of some special Diophantine equations.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10571005, 60473019)863 Project (Grant No. 2006AA01Z434)NKBRPC (Grant No. 2004CB318000)
文摘In this paper, the ranks of a special family of Maiorana-McFarland bent functions are discussed. The upper and lower bounds of the ranks are given and those bent functions whose ranks achieve these bounds are determined. As a consequence, the inequivalence of some bent functions are derived. Furthermore, the ranks of the functions of this family are calculated when t 6.
基金supported by National Natural Science Foundation of China (Grant Nos. 10971250 and 10990011)
文摘This paper presents a construction of infinite classes of binary and p-ary hyperbent functions of polynomial trace form,based on finding a zero of a Kloosterman sum.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10771100, 10971250）
文摘Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, and examples satisfying our results are given.
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.
基金supported by the National Natural Science Foundation of China under Grant Nos.11071285 and 61121062973 Project under Grant No.2011CB302401the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences
文摘This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St^nic~ and Maitra （2008）. Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li （2006）, and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky （1994）.
基金supported by the National Natural Science Foundation of China(No.60373059)the National Research Foundation for the Doctoral Program of Higher Education of China(No.20040013007)the Research Foundation of the State Key Laboratory of Information Security.
文摘Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.
基金supported by the National Key Basic Research Program of China under Grant No.2013CB834203the National Natural Science Foundation of China under Grant No.61472417+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA06010702the State Key Laboratory of Information Security,Chinese Academy of Sciences
文摘Three classes of Boolean functions with four-valued Walsh spectra are presented and their Walsh spectrum distributions are determined. They are derived from Bent functions of the MaioranaMc Farland and Dillon PS ap types and of the monomial form Tr1^2m（λx^r（2^m-1）） by complementing the values of the Bent functions at two points.
基金supported by the National Basic Research Program of China under Grant No.2011CB302400
文摘This paper first proposes an infinite class of 2k-variable Boolean functions with high nonlinearity and high algebraic degree. Then an infinite class of balanced Boolean functions are proposed by modifying the above Boolean functions. This class of balanced Boolean functions have optimal algebraic degree and high nonlinearity. Both classes have optimal algebraic immunity based on a general combinatorial conjecture.
基金supported by National Basic Research Program of China under Grant No.2011CB302400
文摘Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums.
