A new Pseudo random number generator based on generalized Newton complex map with dynamic key

Abstract

In recent years, the chaotic systems in engineering applications attracted many researchers. One of the most important applications of chaos theory is the production of pseudo random numbers that can be used in different areas of cryptography, signal processing, and a variety of other fields. In production of pseudo random numbers generators the chaotic maps are the source of entropy for producing randomness. Most chaotic map based techniques have been easily attacked in recent years by using non-linear prediction as well as phase space analyze on the map. In this paper a new generalized map based on Newton complex map is proposed. The proposed map has appropriate statistical characteristics and the map phase space is completely random, which makes it impossible to predict in practice. The proposed map is capable of generating pseudo random numbers in both integer and complex domain, and it can be used in hardware implementations due to its low dimension. The generalized Newton complex map has dynamic key length, which is the main feature of the map. This feature is due to the existence of an additional Order parameter in map structure. This parameter controls the polynomial length and the β control parameter of map is dependent on it. Generating hexadecimal pseudo random numbers, large key space, high randomness and unpredictability are the main features of the proposed pseudo random number generator. To evaluate the pseudo random number generator, a set of statistical tests include NIST, DIEHARD, ENT, and TESTU01 as well as various performance and security measures, have been used to show the high performance of the proposed generator.