A Digital Random Number Generator Based on Four Regional Examination of Double Scroll Chaos

Abstract

This paper presents the design of a novel random number generator (RNG) based on a new method. Digital Double scroll chaos is used as an RNG production source. Design is performed based on the regional examination of regular samples from a double scroll chaos system. The digital double scroll chaos used in this study is implemented by exploiting the nonlinearity of the sawtooth wave in a 3rd order ordinary differential equation (ODE). By analyzing the distributions of the chaotic state variables $x, y, z$ in 3-dimensions, it has been observed that they have an underlying distribution. The double scroll chaos is divided into four regions by preserving the characteristics of the underlying distributions, and binary data is obtained using each one of these four regions. These binary data are combined through a xor operation to generate the RNG output and a robust RNG is obtained. The proposed RNG is implemented using the Verilog hardware description language and is prototyped on the KCU105 Evaluation Board Xilinx FPGA. The proposed RNG is demonstrated to provide data throughput up to 13.25 Mbps. The RNG output satisfies all statistical randomness tests in the NIST 800-22 and TestU01 packages without post-processing.