Paper 2015/201 Original: eprint.iacr.org/2015/201 ↗
Statistical Properties of Multiplication mod $2^n$
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)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2015-03-06: last updated
- 2015-03-06: published
- Short URL
- https://ia.cr/2015/201
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2015/201,
author = {A. Mahmoodi Rishakani and S. M. Dehnavi and M. R. Mirzaee Shamsabad and Hamidreza Maimani and Einollah Pasha},
title = {Statistical Properties of Multiplication mod $2^n$},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/201},
year = {2015},
url = {https://eprint.iacr.org/2015/201}
}