the square map is one of the functions 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 statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

For $a \neq 1$ and $p$ a prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) numbers. example, $75 = 3 \cdot 25$; $108 36$; $45 5 9$. These are listed in OEIS as A228056. We study properties these numbers, their distribution/density, also develop few claims on distribution/density. rely computer programs verify some conjectures up large

Burgess (1991) has proposed a new index of subtest scatter for the WAIS-R which uses a test statistic, the Mahalanobis Distance (MD). When used with the WAIS-R, MD scores should be distributed as chi square with 11 degrees of freedom. The suitability of the MD index for UK clinical practice was assessed by examining its psychometric properties in a sample of 200 healthy subjects. The sample, wh...