Matrix Description on Cryphographic Properties of Plateaued Functions

In this paper, the cryptographic properties of the Plateaued functions such as propagation criterion, linear structures are studied by a new method, which is denoted by the dot product matrix. The upper and lower bounds of the correlation coefficient when the element is not in the linear structures set are presented. The count of the nonzero correlation coefficient set of the Plateaued functions on different conditions is given. Finally, the degeneracy of the Plateaued functions is discussed and we present the distribution of the linear structures.