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.

近年来，工程应用中的混沌系统吸引了许多研究人员。混沌理论最重要的应用之一是伪随机数的产生，该伪随机数可用于密码学，信号处理以及其他各种领域的不同领域。在产生伪随机数发生器中，混沌图是产生随机性的熵源。近年来，通过使用非线性预测以及在地图上进行相空间分析，大多数基于混沌地图的技术都容易受到攻击。本文提出了一种基于牛顿复图的广义广义图。所提出的地图具有适当的统计特性，并且地图相空间是完全随机的，这使得在实践中无法进行预测。所提出的映射能够在整数域和复数域中生成伪随机数，并且由于其尺寸小，可以在硬件实现中使用。广义牛顿复杂图具有动态键长，这是该图的主要特征。此功能是由于存在附加功能地图结构中的订单参数。此参数控制多项式长度，并且映射的β控制参数与其相关。生成十六进制伪随机数，较大的密钥空间，较高的随机性和不可预测性是所提出的伪随机数生成器的主要特征。为了评估伪随机数生成器，已使用一组统计测试（包括NIST，DIEHARD，ENT和TESTU01）以及各种性能和安全性措施来证明所提出的生成器的高性能。