Statistical Properties of Multiplication mod $2^n$

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

Paper 2015/201

Statistical Properties of Multiplication mod $2^n$

A. Mahmoodi Rishakani, S. M. Dehnavi, M. R. Mirzaee Shamsabad, 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): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: Modular multiplication Boolean function Joint probability distribution T-function Symmetric cryptography
Contact author(s): std_dehnavism @ khu ac ir
History: 2015-03-06: received
Short URL: https://ia.cr/2015/201
License: CC BY

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}
}