Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / Modular multiplication, Boolean function, Joint probability distribution, T-function, Symmetric cryptography

Date: received 4 Mar 2015, last revised 5 Mar 2015

Contact author: std_dehnavism at khu ac ir

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Version: 20150306:132127 (All versions of this report)

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