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 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.
