Walsh Distribution of Multiplied by Constant Operation on Modulo 2n

Multiplied by constant on modulo 2n operation(y=cx mod 2n), is widely used in the ciphers like Sosemanuk, RC6, MARS, and so on. This operation is recognized as a permutation with considerable diffusion, confusion and fine realization efficiency, where the constant c is odd. The operation can be viewed as a vector Boolean function, which vector Walsh spectrum character is not analyzed in published paper. In this paper, the property of the vector Walsh spectrum distribution of the operation is studied, the structure and counting formulas of input and output linear masks and the constant are given for the first time, where the Walsh spectrum of the operation is to be 1. It is proved that there is not input and output linear masks which Walsh spectrum is to be -1.