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
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.
