**Statistical Properties of the Square Map Modulo a Power of Two**

*S. M. Dehnavi and A. Mahmoodi Rishakani and 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.

**Category / Keywords: **foundations / Square map modulo a power of two, Vectorial Boolean function, Component Boolean function, Rabbit cipher

**Original Publication**** (in the same form): **ISCISC'14

**Date: **received 3 Oct 2014, last revised 14 Apr 2015

**Contact author: **std_dehnavism at khu ac ir

**Available format(s): **PDF | BibTeX Citation

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

**Version: **20150414:145311 (All versions of this report)

**Short URL: **ia.cr/2014/789

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