This work is dedicated to the construction and evaluation of random number generators used in cryptography. The critical element on which the security of information is based is the cryptographic key (usually a binary sequence). In order to be resistant to brute force attacks it is necessary that it be made up of random variables with a certain degree of randomness and independence. Formally, this comes back to generate the cryptographic key through the systems which ensures a certain minimum level of entropy. The observer has access to a sample, of a certain size, and based on it he will estimate the minimum value of the entropy, in the situations in which the variables resulting from the measurement process are independent. In the situation where these variables are not independent, complex mathematical procedures also allow estimation of the minimum entropy. This article is a review of how mathematical entropy can be estimated and evaluated, of the construction mode (from technologies based on analogue procedures: thermal noise in a transistor to modern procedures: quantum devices), as well as to evaluate the security of binary sequence generators used for generating cryptographic keys or critical security parameters related to new technologies based on quantum principles. The techniques and methods used to generate binary random values as well as the methods of statistical and informational validation (Shannon entropy) are exemplified in this paper.

Energy service techniques for public lighting systems are briefly discussed. Proposals for energy savings and a product conception are then made. Voltage regulation principle proves to be an efficient way of bringing quality and economies in the administration of public lighting. Behavior and experimental results of the proposed voltage chopper are next evaluated.

The partitions in which the parts of size n can come in n different colors are known as n-color partitions. For $r\in \{0,1\}$, let $Q{L}_r\left(n\right)$ be the number of n-color partitions of n into distinct parts which have a number of parts congruent to r modulo 2. In this paper, we consider specializations of complete and elementary symmetric functions in order to establish two kinds of formulas for $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$ as sums over partitions of n in terms of binomial coefficients. The first kind of formulas only involve partitions in which the parts of size n appear at most n times, while the second kind of formulas involve unrestricted partitions. Similar results are obtained for the first differences of $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$ and the partial sums of $Q{L}_0\left(n\right)\pm Q{L}_1\left(n\right)$.