International Association
for Cryptologic Research

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.