Tian-Gaussian Distribution Simulator

This project implements a novel approach to generating Gaussian-like random numbers using Ethereum-style Keccak-256 hashing. It's designed to explore the distribution of bit counts in hash-generated bitfields for analysis of their properties in relation to Gaussian distributions.

The original idea is Simon Tian's[1] and his Solidity implementation can be found here: https://github.com/simontianx/OnChainRNG/tree/main/GaussianRNG [2]

Key Concepts

1. Bitfields: Generated from Keccak-256 hashes of seeds.
2. Bit Counting: Using Brian Kernighan's algorithm to count set bits in bitfields.

Installation

Prerequisites

• Python 3.x
• pycryptodome library

Instructions

1. Clone the repository:

   git clone https://github.com/tcotten-scrypted/tian-gaussian-distribution-simulator.git

2. Navigate to the project directory:

   cd tian-gaussian-distribution-simulator

3. Install the required packages:

   pip install -r requirements.txt

Usage

Running the Simulation

To run the simulation, use the following command:

python gaussian.py [-b BITFIELD_SIZE] [-n NUM_TRIALS] [-s SEED]

Command-Line Arguments

• -b, --bitfield-size: Size of bitfield (default: 32)
• -n, --num-trials: Number of trials (default: 1000)
• -s, --seed: Seed value (default: 42)

Example Usage

python gaussian.py -b 16 -n 10000 -s 42

Expected output:

Bit count distribution:
1: 4
2: 15
3: 85
4: 314
5: 649
6: 1214
7: 1744
8: 2015
9: 1738
10: 1174
11: 653
12: 296
13: 83
14: 15
15: 1

Interpretation of Results

The output shows the distribution of bit counts across the trials. In a Gaussian-like distribution:

• The counts should be roughly symmetrical around the mean.
• The mean should be close to half the bitfield size.
• The distribution should resemble a bell curve.

Key Features

1. Ethereum-Compatible Hashing: Uses Keccak-256, the same hash function as Ethereum.
2. Configurable Bitfield Size: Allows exploration of different-sized bitfields.
3. Multiple Trials: Supports running multiple trials for statistical analysis.
4. Efficient Bit Counting: Utilizes Kernighan's algorithm for fast bit counting.

Limitations and Considerations

• The generated distribution is discrete, unlike a true Gaussian distribution.
• The statistical properties may vary based on bitfield size and number of trials.
• This method is experimental and may not perfectly mimic a true Gaussian distribution.

Citations

1. S. Tian, "On-chain Gaussian Randomness is Now Made Available," Medium, Aug. 12, 2021. [Online]. Available: https://medium.com/@maxareo/on-chain-gaussianity-is-available-now-1409c7f14cbe. [Accessed: Jul. 18, 2024].

2. S. Tian, "OnChainRNG," GitHub repository, 2021. [Online]. Available: https://github.com/simontianx/OnChainRNG/tree/main/GaussianRNG. [Accessed: Jul. 18, 2024].

AI Attribution

This content was generated in whole or part with the assistance of an AI model - see the AI.md file for details.

License

This project is licensed under the MIT License - see the LICENSE file for details.