On the $\Delta$-equivalence of Boolean functions

A new equivalence relation on the set of Boolean functions is introduced: functions are declared to be $\Delta$-equivalent if their autocorrelation functions are equal. It turns out that this classification agrees well with the cryptographic properties of Boolean functions: for functions belonging to the same $\Delta $-equivalence class a number of their cryptographic characteristics do coincide. For example, all bent-functions (of a fixed number of variables) make up one class.