In today's modern world everything is at reach of a couple of mouse clicks, but our security has become compromised. Privacy is often violated and personal information is used without authorization in various criminal purposes. In order to prevent that, cryptography is increasingly being used: a new branch of science that is constantly evolving along with technology. Cryptography enables data protection by using digital signatures and certificates; by encryption of emails and documents that are sent via insecure communication channels; in electronic payment, and in many other ways. Various data encrypting algorithms have been developed to make data transfer through the Internet as safe as possible. These algorithms require encryption keys, which are composed of random numbers. Random Number Generator is a computer or a physical system designed to generate a series of numbers that appear randomly. True random numbers are difficult to obtain, because the computers that generate random numbers work in a deterministic mode. In everyday life, true random numbers appear only in natural phenomena and in situations that are impossible to predict. Using computers, only pseudorandom numbers can be obtained. Their main feature is being as similar to real random numbers as possible. In order to obtain a satisfactory set of numbers, the pseudorandom number generators are used. Each generator has a matching algorithm. Here are mentioned the most commonly used LCG, RSA, ANSI X9.17 and BBS algorithms. To check the coincidence obtained, a series of standardized tests are used. Some of the most common ones are described here, such as Chi-square test, Kolmogorov – Smirnov test, a set of empirical tests, and specially designed sets of tests DIEHARD and NIST. These tests eliminate the bad and confirm potentially good algorithms for generating pseudorandom numbers that will be later used as encryption keys in cryptography