Logistic Map Pseudo Random Number Generator in FPGA

TL;DR

This paper presents an FPGA implementation of a pseudo-random number generator based on the logistic map, producing Gaussian-distributed outputs verified through real-time visualization and histogram analysis.

Contribution

It introduces a novel FPGA-based PRNG using the logistic map with integrated modules for real-time interaction and distribution verification.

Findings

Successful FPGA implementation of logistic map PRNG

Generated Gaussian-distributed pseudo-random numbers

Real-time visualization and histogram analysis capability

Abstract

This project develops a pseudo-random number generator (PRNG) using the logistic map, implemented in Verilog HDL on an FPGA and processes its output through a Central Limit Theorem (CLT) function to achieve a Gaussian distribution. The system integrates additional FPGA modules for real-time interaction and visualisation, including a clock generator, UART interface, XADC, and a 7-segment display driver. These components facilitate the direct display of PRNG values on the FPGA and the transmission of data to a laptop for histogram analysis, verifying the Gaussian nature of the output. This approach demonstrates the practical application of chaotic systems for generating Gaussian-distributed pseudo-random numbers in digital hardware, highlighting the logistic map's potential in PRNG design.