The article is about generators of random numbers (GPN) constructed on points of an elliptic curve and algorithms of development irreducible polynomials over prime fields. It describes their advantages and main features. The authors analyzes the algorithm of development GPN constructed on points of an elliptic curve with using irreducible polynomials of degree three over finite fields. In this approach, calculations were made in the system of residual classes. According to the results of computer simulation shows the advantages of algorithm in speed and security of a cryptosystem.

Keywords: the generator of pseudo-random numbers, elliptic curve, system of residual classes, cryptographic security, irreducible polynomials