In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to...In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.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
基金the National Natural Science Foundation of China (Grant No. 60673081)the "863" project (Grant No. 2006AA01Z417)
文摘In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity. We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally, we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.
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.
