This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in assoc...This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided.展开更多
The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtaine...The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.展开更多
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 two main results to find balanced Boolean functions with maximum algebraic immunity. Through swapping the values of two bits, and then generalizing the result to swap some pairs of bits of the symmetric Boolean function constructed by Dalai, a new class of Boolean functions with maximum algebraic immunity are constructed. Enumeration of such functions is also n given. For a given function p（x） with deg（p（x）） 〈 [n/2], we give a method to construct functions in the form p（x）＋q（x） which achieve the maximum algebraic immunity, where every term with nonzero coefficient in the ANF of q（x） has degree no less than [n/2].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
Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we ge...Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.展开更多
To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immuni...To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented,here N is a factor of 2^n-1,where n is an integer.The case is more complicated when the period is even.In this paper,we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k-error linear complexity algorithm.Then,an algorithm for spectral immunity of binary sequence with period N=2^n is obtained.Furthermore,the time complexity of this algorithm is proved to be O（n）.展开更多
Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary fini...Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary finite fields. In this paper, the results of Ref. [25] are generalized to arbitrary finite fields. We obtain vector-valued functions over arbitrary finite fields such that their algebraic immunities can reach the upper bounds. Furthermore, all the component functions, together with their some nonzero linear combinations, of vector-valued Boolean functions achieved by this construction have optimal algebraic immunities simultaneously.展开更多
基金supported by the National Natural Science Foundations of China under Grant Nos. 60903200,61003299
文摘This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided.
基金Supported by the National Natural Science Foundation of China(Grant No.60573028)the Open Founds of Key Lab of Fujian Province University Network Security and Cryptology(Grant No. 07A003)the Basic Research Foundation of National University of Defense Technology(Grant No.JC07-02-03)
文摘The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.
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 (Grant No. 60673068)the Natural Science Foundation of Shandong Province (Grant Nos. Y2007G16, Y2008G01)
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 two main results to find balanced Boolean functions with maximum algebraic immunity. Through swapping the values of two bits, and then generalizing the result to swap some pairs of bits of the symmetric Boolean function constructed by Dalai, a new class of Boolean functions with maximum algebraic immunity are constructed. Enumeration of such functions is also n given. For a given function p（x） with deg（p（x）） 〈 [n/2], we give a method to construct functions in the form p（x）＋q（x） which achieve the maximum algebraic immunity, where every term with nonzero coefficient in the ANF of q（x） has degree no less than [n/2].
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supported by the National Natural Science Foundation of China (61102093, 61170270, 61121061)The Fundamental Research for the Central Universities (BUPT 2012RC0710)
文摘Algebraic immunity is an important cryptographic property of Boolean functions. In this paper, odd-variable balanced Boolean functions with optimal algebraic immunity are obtained by m-sequence and consequently, we get bases with special constructions of vector space. Furthermore, through swapping some vectors of these two bases, we establish all kinds of odd-variable balanced Boolean functions with optimal algebraic immunity.
基金Supported by the National Natural Science Foundation of China(61300181,61272057,61202434,61170270,61100203,61121061)
文摘To resist the fast algebraic attack and fast selective discrete Fourier transform attacks,spectral immunity of a sequence or a Boolean function was proposed.At the same time,an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented,here N is a factor of 2^n-1,where n is an integer.The case is more complicated when the period is even.In this paper,we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k-error linear complexity algorithm.Then,an algorithm for spectral immunity of binary sequence with period N=2^n is obtained.Furthermore,the time complexity of this algorithm is proved to be O（n）.
基金supported by National Natural Science Foundation of China(60873191,60903152,61003286,60821001)
文摘Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary finite fields. In this paper, the results of Ref. [25] are generalized to arbitrary finite fields. We obtain vector-valued functions over arbitrary finite fields such that their algebraic immunities can reach the upper bounds. Furthermore, all the component functions, together with their some nonzero linear combinations, of vector-valued Boolean functions achieved by this construction have optimal algebraic immunities simultaneously.
