Paper 2015/201

Statistical Properties of Multiplication mod 2n

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 2n 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 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
Creative Commons Attribution
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}
}
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