Cryptofinance

A comprehensive study of Bitcoin mining strategies, blockchain consensus mechanisms, and cryptographic hash functions.

📋 Project Overview

This project implements and analyzes various aspects of cryptocurrency mining, including statistical analysis of hash functions, mining strategy simulations, and blockchain security thresholds. The work is based on practical exercises in cryptofinance and blockchain technology.

🗂️ Repository Structure

Cryptofinance/
├── statistics/              # Statistical analysis of hash functions and proof-of-work
├── mining-strategy/         # Mining strategy simulations and optimizations
├── bitcoin-thresholds/      # Bitcoin security thresholds analysis (NEW ✨)
├── docs/                    # Documentation and theoretical analysis
└── README.md                # This file

📚 Completed Sections

1. Statistics ✅

• 1.1 Hash Function Distribution: Analysis of hash function uniformity using statistical tests
• 1.2 Proof-of-Work Duration: Empirical validation of exponential distribution in mining times

2. Mining Strategies ✅

• 2.1 Strategy 1+2 Simulation: Numerical evaluation and comparison with theoretical formulas
• 2.2 Selfish Mining: Performance analysis with parameters (q, γ) representing hashing power and connectivity
• 2.3 Optimal Selfish Mining: Dynamic decision-making based on fork states (a, h)

3. Bitcoin Thresholds ✅ [NEW]

• 3.1 Orphan Block Mining: Determination of profitability thresholds for mining on orphan blocks
  • Theoretical threshold: √2 - 1 ≈ 0.4142 (41.42%)
  • Visualization of yield curves and profitability zones
• 3.2 Block Withholding (γ=0): Analysis of rational miner behavior with zero connectivity
  • Numerical verification of threshold using scipy.optimize
  • Comparative analysis with orphan mining strategy
  • Security implications for Bitcoin network

Key Finding (Section 3)

Both strategies share the same profitability threshold: a miner with more than 41.42% of network hash power has economic incentive to deviate from honest mining. This reveals a fundamental security threshold in Bitcoin's consensus mechanism.

🚧 Work in Progress

4. Advanced Topics (Bonus)

• 4.1 Double-Spending Attacks: Framework for repeated attack scenarios
• 4.2 Ethereum Commitment Attacks: Implementation of research from arXiv:2407.19479

🛠️ Technologies Used

• Python 3.x: Main programming language
• Jupyter Notebook: Interactive development and visualization
• NumPy/SciPy: Statistical analysis and numerical computations
• Matplotlib: Data visualization and plotting

📊 Key Concepts Explored

• Hash Functions: Uniformity testing and cryptographic properties
• Proof-of-Work: Mining difficulty and solution distribution
• Selfish Mining: Strategic blockchain manipulation
• Game Theory: Rational miner behavior and incentive structures
• Blockchain Security: Attack vectors and defense mechanisms
• Economic Thresholds: Profitability analysis of deviation strategies

🔬 Methodology

Each section combines:

1. Theoretical Analysis: Mathematical foundations and formulas
2. Simulation: Numerical experiments and Monte Carlo methods
3. Visualization: Graphs and plots for result interpretation
4. Comparison: Empirical results vs. theoretical predictions

📈 Results and Findings

Detailed results and analysis are available in the Jupyter notebooks within each respective directory. Key findings include:

• Validation of exponential distribution in proof-of-work mining times
• Identification of profitability thresholds for selfish mining strategies
• Analysis of connectivity impact on mining strategy effectiveness
• Discovery of critical security threshold at √2 - 1 ≈ 41.42% hash power
• Equivalence between orphan mining and block withholding strategies

🎯 Running the Notebooks

Local Setup

# Clone the repository
git clone https://github.com/alineuh/Cryptofinance.git
cd Cryptofinance

# Install dependencies
pip install numpy scipy matplotlib jupyter

# Launch Jupyter
jupyter notebook

Google Colab

1. Open Google Colab
2. Upload any .ipynb file from the repository
3. Run all cells

All notebooks are self-contained and include necessary imports.

🤝 Collaboration

This project was developed as part of a cryptofinance course, with collaborative work on the foundational implementations and individual extensions for advanced topics.

📖 References

• Bitcoin Whitepaper: Nakamoto, S. (2008). "Bitcoin: A Peer-to-Peer Electronic Cash System"
• Selfish Mining: Eyal, I., & Sirer, E. G. (2014). "Majority is not Enough: Bitcoin Mining is Vulnerable"
• Optimal Selfish Mining: Sapirshtein, A., Sompolinsky, Y., & Zohar, A. (2016). "Optimal Selfish Mining Strategies in Bitcoin"
• Mining Strategy Analysis: Various blockchain security and game theory research papers

🔒 Security Implications

Our analysis in Section 3 reveals critical insights:

• Bitcoin's security relies on no miner controlling >41.42% of hash power
• Economic incentives for centralization exist above this threshold
• Network connectivity (γ) plays a crucial role in strategy profitability
• Current Bitcoin mining pool distribution maintains safe margins

📝 License

This project is for educational purposes as part of academic coursework.

👤 Authors

Aya - GitHub Profile Aline - GitHub Profile Lina - GitHub Profile

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Last updated: January 2026 Section 3 completed: Bitcoin Thresholds Analysis