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.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Modular multiplicationBoolean functionJoint probability distributionT-functionSymmetric cryptography
- Contact author(s)
- std_dehnavism @ khu ac ir
- History
- 2015-03-06: received
- Short URL
- https://ia.cr/2015/201
- License
-
CC BY