Design and Implementation of a Chaotic Pendulum-based Pseudo-Random Number Generator on FPGA

Core Concepts

A pseudo-random number generator is designed and implemented on an FPGA board using the chaotic dynamics of a double pendulum system, leveraging environmental sensor data as the seed.

Abstract

The paper presents the design and implementation of a pseudo-random number generator (pRNG) using a double pendulum system on an FPGA board. The key highlights are:

The pRNG algorithm is derived from the chaotic dynamics of a double pendulum, which exhibits strong sensitivity to initial conditions. Environmental sensor data, including magnetic field, sound, light, and temperature/humidity, are used as the seed to initialize the algorithm.

To handle the complex mathematical operations required by the double pendulum equations, custom functions for basic arithmetic (addition, subtraction, multiplication, division) and trigonometric (sine, cosine) operations are developed in Verilog HDL. These functions can handle signed integers with decimal values.

The hardware implementation on the CMOD A7 35t FPGA board includes modules for interfacing with the environmental sensors, performing analog-to-digital conversion, and transmitting the generated random numbers to an Arduino Nano for display on an LCD screen.

Experimental results demonstrate that the generated random numbers exhibit no discernible pattern, with a period of over 1 million cycles and over 1 billion possible combinations for the 10-digit output.

The authors showcase a novel approach to designing a pRNG by leveraging the inherent randomness in a chaotic physical system, implemented on an FPGA platform. The work highlights the challenges in translating the complex mathematical model to hardware and the solutions developed to address them.

Stats

The following sentences contain key metrics or important figures used to support the author's key logics:
The pRNG generates a 10 digits number, with over 1 billion possible combinations.
A histogram of 1,048,575 random numbers generated shows no discernible pattern.
The period for the random number generator does not repeat before a million cycles.

Quotes

"The double pendulum is categorized as a dynamic chaotic system [1]."
"The environmental data are used to set the conditions (pRNG seed) such as weight, length, and gravitational acceleration onto a double pendulum (chaotic pendulum) algorithm to generate the random numbers."
"The project will focus on interfacing the sensors with the FPGA and developing suitable algorithms to ensure the generated numbers exhibit strong randomness properties."

Key Insights Distilled From

Hardware Implementation of Double Pendulum Pseudo Random Number Generator

by Jarrod Lim,T... at arxiv.org 04-26-2024

https://arxiv.org/pdf/2404.16504.pdf

Deeper Inquiries

How can the performance and efficiency of the pRNG be further improved, such as through hardware optimization or alternative chaotic system models?

To enhance the performance and efficiency of the pRNG based on the chaotic pendulum model, several strategies can be implemented:

Hardware Optimization:

Utilize more advanced FPGA boards with higher processing capabilities to speed up the random number generation process.
Implement parallel processing techniques to generate random numbers concurrently, thereby increasing throughput.
Optimize the Verilog HDL code to reduce resource consumption and improve the speed of calculations.

Algorithmic Improvements:

Explore more efficient mathematical approximations for trigonometric functions to reduce computation complexity.
Fine-tune the parameters of the double pendulum model to maximize randomness while minimizing computational overhead.
Implement hardware accelerators for specific mathematical operations to offload the FPGA's main processing unit.

Alternative Chaotic System Models:

Investigate other chaotic systems beyond the double pendulum that may offer better randomness properties and faster generation speeds.
Experiment with different initial conditions and system configurations to find the optimal setup for random number generation.
Consider hybrid models that combine multiple chaotic systems to enhance the unpredictability of the generated numbers.

By implementing these strategies, the performance and efficiency of the pRNG can be significantly improved, leading to faster and more reliable random number generation.

What are the potential security applications of this chaotic pendulum-based pRNG, and how does it compare to other hardware-based random number generators?

The chaotic pendulum-based pRNG offers several security applications due to its inherent unpredictability and sensitivity to initial conditions. Some potential applications include:

Cryptography: The random numbers generated by the chaotic pendulum pRNG can be used for encryption keys, ensuring secure communication and data protection.

Secure Authentication: Random numbers from the pRNG can be utilized for secure authentication processes, such as two-factor authentication or password generation.

Secure Transactions: In financial systems, the pRNG can provide random values for secure transaction verification and fraud prevention.

Secure IoT Communication: Random numbers can be used in IoT devices for secure communication and data exchange, safeguarding against unauthorized access.

Compared to other hardware-based random number generators, the chaotic pendulum pRNG offers a unique advantage in terms of its inherent chaotic nature, which enhances randomness and unpredictability. Traditional hardware RNGs may rely on physical phenomena like thermal noise or radioactive decay, but the chaotic pendulum model provides a novel approach that can potentially offer higher levels of security and randomness.

Could the principles of this work be extended to generate random numbers from other types of physical, chemical, or biological chaotic systems, and what are the challenges in doing so?

The principles of utilizing chaotic systems for random number generation can indeed be extended to various other domains, including physical, chemical, and biological systems. Some potential systems for generating random numbers include:

Chemical Reactions: Chaotic reactions in chemical systems can produce random patterns that may be harnessed for RNG applications.

Biological Systems: Biological processes like neural activity or genetic mutations exhibit chaotic behavior that could be leveraged for random number generation.

Fluid Dynamics: Turbulent flow in fluids is another example of a chaotic system that can be explored for generating random numbers.

Challenges in extending these principles to other systems include:

Modeling Complexity: Different systems have unique dynamics, and accurately modeling their chaotic behavior can be challenging.
Measurement and Sensing: Obtaining precise data from physical, chemical, or biological systems for RNG purposes may require sophisticated sensing and measurement techniques.
Noise and Interference: External factors and noise in these systems can introduce biases or inaccuracies in the generated random numbers.
Validation and Testing: Ensuring the randomness and statistical properties of the generated numbers from diverse chaotic systems would require extensive validation and testing procedures.
Despite these challenges, exploring random number generation from various chaotic systems can lead to novel RNG approaches with diverse applications in security, cryptography, and scientific research.