Avalanche Properties Of Boolean Functions

Let f(x) be a boolean function on Vn . In this paper , the set Rf of the vectors satisfying the propagation criteria is discussed. If deg f(x) = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in (?)f is discussed and the structure and properties of f(x) are discussed when |(?)f|= 1 ,2,3,4. wherethe sequence of the linear function (?)ai = . Furthermore a simple proof oftheorem is given and several conclusions from this theorem aregot. The construction of functions which satisfy propagation criteria of degree 2 is given.