Zero-Knowledge Proof (ZKP) Learning Path

This repository is a curated learning path for understanding Zero-Knowledge Proofs (ZKPs). It provides a structured collection of resources, tutorials, and implementation in Python to guide learners from the fundamentals of zero-knowledge concepts to advanced applications, including cryptographic implementations, zk-SNARKs, and zk-STARKs.

Getting Started

Prerequisites

This project requires Python 3.7+ and Jupyter Notebook/Lab.

Installation

Option 1: Using Dev Container (Recommended)

The easiest way to get started with a consistent development environment and automatic port forwarding.

Prerequisites:

• Docker Desktop installed and running
• VS Code or Cursor IDE with the "Dev Containers" extension

Steps:

1. Clone the repository:

git clone <repository-url>
cd zeroknowledge

2. Open the project in VS Code/Cursor:

code .  # For VS Code
# or
cursor . # For Cursor IDE

3. When prompted, click "Reopen in Container", or manually:

   • Press Cmd/Ctrl + Shift + P
   • Select "Dev Containers: Reopen in Container"

4. Wait for the container to build (first time only)

Option 2: Local Installation

1. Clone the repository:

git clone <repository-url>
cd zeroknowledge

2. Create a virtual environment (recommended):

python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

3. Install dependencies:

pip install -r requirements.txt

Locked Dependencies (see requirements.txt):

• numpy==2.4.6
• sympy==1.14.0
• galois==0.4.11
• matplotlib==3.10.9
• jupyter==1.1.1
• notebook==7.3.3
• merkle (custom module included in this repository as merkle.py)

Running the Notebooks

zkSTARK.ipynb

This notebook demonstrates the implementation of a zk-STARK (Zero-Knowledge Scalable Transparent Argument of Knowledge) proof system. It includes step-by-step examples of:

• Finite field arithmetic
• Polynomial constraints
• FRI (Fast Reed-Solomon Interactive Oracle Proof of Proximity) protocol
• Merkle tree commitments

To run:

jupyter notebook zkSTARK.ipynb

circleSTARK.ipynb

This notebook implements Circle STARK, a variant of the standard STARK proof system that uses the circle group over a prime field instead of a multiplicative subgroup. It demonstrates:

• Circle group arithmetic over finite fields
• Using Mersenne primes (like M₃₁) for efficient FFT domains
• Circle STARK protocol implementation

To run:

jupyter notebook circleSTARK.ipynb

Running Jupyter in Dev Container

If using the Dev Container, Jupyter is already configured. You can:

1. Open notebooks directly in VS Code/Cursor:

   • Simply click on any .ipynb file, and it will open with Jupyter support

2. Start Jupyter Notebook server:

   jupyter notebook --ip=0.0.0.0 --port=8888 --no-browser

   The port 8888 is automatically forwarded, so you can access it at http://localhost:8888