Statistical Properties of the Square Map Modulo a Power of Two

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

Paper 2014/789

Statistical Properties of the Square Map Modulo a Power of Two

S. M. Dehnavi, A. Mahmoodi Rishakani, M. R. Mirzaee Shamsabad, and Einollah Pasha

Abstract

The square map is one of the functions that is used in cryptography. For instance, the square map is used in Rabin encryption scheme, block cipher RC6 and stream cipher Rabbit, in different forms. In this paper we study a special case of the square map, namely the square function modulo a power of two. We obtain probability distribution of the output of this map as a vectorial Boolean function. We find probability distribution of the component Boolean functions of this map. We present the joint probability distribution of the component Boolean functions of this function. We introduce a new function which is similar to the function that is used in Rabbit cipher and we compute the probability distribution of the component Boolean functions of this new map.

Note: This paper is an English version of a paper in Persian, which was presented in ISCISC'14

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. ISCISC'14
Keywords: Square map modulo a power of two Vectorial Boolean function Component Boolean function Rabbit cipher
Contact author(s): std_dehnavism @ khu ac ir
History: 2015-04-14: last of 3 revisions; 2014-10-07: received; See all versions
Short URL: https://ia.cr/2014/789
License: CC BY

BibTeX

@misc{cryptoeprint:2014/789,
      author = {S.  M.  Dehnavi and A.  Mahmoodi Rishakani and M.  R.  Mirzaee Shamsabad and Einollah Pasha},
      title = {Statistical Properties of the Square Map Modulo a Power of Two},
      howpublished = {Cryptology ePrint Archive, Paper 2014/789},
      year = {2014},
      note = {\url{https://eprint.iacr.org/2014/789}},
      url = {https://eprint.iacr.org/2014/789}
}