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....

in this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. next, some numerical solutions are considered for the cases of unavailable closed form of solutions. finally, these methods are illustrated via some numerical examples.

Distributions have several different types of associated functions. The most familiar is the density function. Figure 1A and 1D show density functions for the normal distribution and gamma distribution, respectively. Density functions are related to histograms in that if enough data are collected then the histogram and density share the same shape. Hence, density functions serve as a first-orde...

The droplet size distribution in the column is usually represented as the average volume to surface area, known as the Sauter mean drop diameter. It is a key variable in the extraction column design. A study of the drop size distribution and Sauter-mean drop diameter for a liquid-liquid extraction column has been presented for a range of operating conditions and three different liquid-liquid sy...

The rock masses in a construction site of underground cavern are generally not continuous, due to the presence of discontinuities, such as bedding, joints, faults, and fractures. The performance of an underground cavern is principally ruled by the mechanical behaviors of the discontinuities in the vicinity of the cavern. During underground excavation, many surrounding rock failures have close r...

Given a probability distribution on a totally ordered set, we define for each n ≥ 1 a related distribution on the symmetric group Sn, called the QS-distribution. It is a generalization of the q-shuffle distribution considered by Bayer, Diaconis, and Fulman. The QS-distribution is closely related to the theory of quasisymmetric functions and symmetric functions. We obtain explicit formulas in te...