Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is ...Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.展开更多
The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this ...The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.展开更多
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
Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonl...Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.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
Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions.In this paper,we study∑d-1 i=0(ni)-weight Boolean functions with algebraic immunity achiev-ing the minim...Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions.In this paper,we study∑d-1 i=0(ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n-d+1,which is highest for the functions.We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity.In addition,we prove that their algebraic degrees are not less than the maximum of d and n-d+1,and for d=n1+2 their nonlinearities equalthe minimum of∑d-1 i=0(ni)and∑d-1 i=0(ni).Lastly,we identify two classes of such functions,one having algebraic degree of n or n-1.展开更多
基金Acknowledgments This work was supported in part by 973 Project of China （No. 2007CB311201）, the Notional Natural Science Foundation（No. 60833008, 60803149）, and the Foundation of Guangxi Key Laboratory of Information and Communication（No. 20902）.
文摘Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.
文摘The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.
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This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 61373008, 11201359, 61562069）, the Natural Science Basic Research Plan in Shaanxi Province of China （Grant No. 2012JM8013）, the 111 Project （Grant No. B08038）, and the Science and Technology on Communication Security Laboratory （Grant No. 9140C110203140C11049）.
文摘Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.
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 National Natural Science Foundation of China(Grant Nos.10971246,60970152)
文摘Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions.In this paper,we study∑d-1 i=0(ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n-d+1,which is highest for the functions.We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity.In addition,we prove that their algebraic degrees are not less than the maximum of d and n-d+1,and for d=n1+2 their nonlinearities equalthe minimum of∑d-1 i=0(ni)and∑d-1 i=0(ni).Lastly,we identify two classes of such functions,one having algebraic degree of n or n-1.
