Paper 2015/201

Statistical Properties of Multiplication mod $2^n$

A. Mahmoodi Rishakani and S. M. Dehnavi and M. R. Mirzaee Shamsabad and Hamidreza Maimani and Einollah Pasha

Abstract

In this paper, we investigate some statistical properties of multiplication mod $2^n$ for cryptographic use. For this purpose, we introduce a family of T-functions similar to modular multiplication, which we call M-functions as vectorial Boolean functions. At first, we determine the joint probability distribution of arbitrary number of the output of an M-function component bits. Then, we obtain the probability distribution of the component Boolean functions of combination of a linear transformation with an M-function. After that, using a new measure for computing the imbalance of maps, we show that the restriction of the output of an M-function to its upper bits is asymptotically balanced.