Geometric Cryptanalysis Framework

A production-ready ECDSA vulnerability detection framework that identifies cryptographic implementation flaws through geometric signal analysis of public signature data.

Quick Demo

Analyze ECDSA signatures for vulnerabilities in seconds:

python src/tools/analyze.py --input signatures.csv

Detects known vulnerabilities:

PS3 Nonce Reuse ❌

Android RNG Bias (CVE-2013-4254) ❌

Zero false positives on secure implementations ✅

Overview

This framework provides rigorous detection of ECDSA implementation vulnerabilities using only publicly observable signature data. The system successfully identifies known vulnerabilities (PS3 nonce reuse, Android CVE-2013-4254) while maintaining zero false positives on secure implementations.

Quick Start

# Install dependencies and run full analysis
make setup
make repro

# Run vulnerability detection
python src/tools/analyze.py --input signatures.csv

# Run falsification tests
make falsify

Key Features

Vulnerability Detection

• PS3 Nonce Reuse: Detects duplicate r-values across signatures
• Android RNG Bias (CVE-2013-4254): Identifies low-entropy nonce generation
• Zero False Positives: Rigorous falsification framework ensures no spurious detections

Analysis Techniques

• Geometric signal analysis in (r,s) space
• Entropy measurements across multiple projections
• Statistical clustering detection
• Comparative analysis against null distributions

Example Detection Results

PS3 Nonce Reuse (Detected ❌)

Geometric visualization showing nonce reuse pattern - identical r-values across multiple signatures.

Android CVE-2013-4254 (Detected ❌)

Statistical clustering reveals biased random number generator - non-uniform distribution in signature space.

Vulnerability Comparison

Comparative analysis: PS3 (red) vs. Android (orange) vs. Secure baseline (green)

Output Artifacts

• vulnerability_visualizations/*.png - Visual analysis results
• secp256k1_analysis/comprehensive_report.json - Full analysis report
• falsification_results/ - Falsification test results

Technical Architecture

src/
├── diagnostics/          # Core analysis framework (API v1.0.0)
│   ├── secp256k1_analyzer.py    # Main vulnerability detector
│   ├── falsification.py         # Falsification testing
│   └── signal_explorer.py       # Signal gradient analysis
├── tools/                # Command-line utilities
└── lib/                  # Supporting libraries

tests/                    # Comprehensive test suite
├── test_known_vulnerable.py     # Positive controls
└── test_*_baseline.py           # Negative controls

Verification Methodology

The framework employs a falsification-first approach:

1. Negative Controls: Verify no false positives on secure signatures
2. Positive Controls: Confirm detection of known vulnerabilities
3. Cross-Validation: Multiple independent detection techniques
4. Statistical Rigor: Significance testing against null distributions

Usage Examples

Basic Analysis

from src.diagnostics import SECP256K1Analyzer

analyzer = SECP256K1Analyzer()
analyzer.load_signatures_from_file('signatures.csv')
report = analyzer.run_full_analysis()

if report['summary']['verdict'] == 'FAIL':
    print("Vulnerabilities detected")

Command Line

# Analyze signature file
python src/tools/analyze.py --input signatures.csv --output report.json

# Run comparative vulnerability demo
python src/tools/vulnerability_demo.py

Expected Output

Vulnerable Signature Set (PS3 Nonce Reuse):

=== SECP256K1 VULNERABILITY ANALYSIS ===
Verdict: FAIL ❌
Reason: Nonce reuse detected (duplicate r-values)
Affected signatures: 15/200 (7.5%)
Confidence: 100% (mathematical certainty)
Recommendation: IMMEDIATE ACTION REQUIRED - Private key compromise possible

Secure Signature Set:

=== SECP256K1 VULNERABILITY ANALYSIS ===
Verdict: PASS ✅
Status: No vulnerabilities detected
Distribution: Uniform (as expected for secure ECDSA)
All statistical tests passed
Recommendation: Signatures conform to security standards

Comparison with Other Tools

Feature	geometric-cryptanalysis	lattice-attack	ecdsa-nonce-reuse	mini_ecdsa
Nonce Reuse Detection	✅ Duplicate r-values	❌	✅	✅
RNG Bias Detection	✅ CVE-2013-4254	❌	❌	❌
Lattice Attacks	❌	✅ Partial k recovery	❌	❌
Falsification Framework	✅ Negative controls	❌	❌	❌
Public-Key-Only	✅ Strict	⚠️ Partial	✅	⚠️ Mixed
Visualization Suite	✅ 3D PCA/t-SNE	❌	❌	❌
Production Ready	✅ API v1.0.0	⚠️ Research	⚠️ Research	❌ Educational
CI/CD Testing	✅ Python+Rust+JS	❌	⚠️ Basic	❌
Documentation	✅ Comprehensive	⚠️ Basic	⚠️ Basic	⚠️ Basic

Unique Strengths:

• Only tool with rigorous falsification framework (negative/positive controls)
• Detects multiple vulnerability classes, not just nonce reuse
• Production-grade with frozen API (v1.0.0) and semantic versioning
• Comprehensive geometric visualization suite (PCA, t-SNE, clustering)
• Zero false positives guaranteed through statistical rigor

Academic References

This framework builds on research in ECDSA vulnerability detection and cryptanalysis:

Nonce Reuse & Implementation Vulnerabilities

• PS3 ECDSA Bug (2010) - fail0verflow team, 27th Chaos Communication Congress
  • Private Key Recovery from PlayStation 3
• Android RNG Vulnerability (CVE-2013-4254) - Bitcoin.org Security Advisory
  • Android SecureRandom Weakness
• Nguyen & Shparlinski (2002) - "The Insecurity of the Digital Signature Algorithm with Partially Known Nonces"
  • Journal of Cryptology, Vol. 15, pp. 151-176

Lattice-Based Cryptanalysis

• Howgrave-Graham & Smart (2001) - "Lattice Attacks on Digital Signature Schemes"
  • Designs, Codes and Cryptography, Vol. 23, pp. 283-290
• Brumley & Tuveri (2011) - "Remote Timing Attacks are Still Practical"
  • USENIX Security Symposium

Geometric Analysis Techniques

• Principal Component Analysis - Applied to signature distribution analysis
• t-SNE Dimensionality Reduction - Visualization of high-dimensional signature space
• DBSCAN Clustering - Detection of non-uniform distributions

Note: This tool focuses on detection of implementation vulnerabilities using public data only. It does not perform lattice-based private key recovery or signature forgery.

Documentation

• docs/API.md - Complete API reference
• docs/FRAMEWORK.md - Architecture documentation
• docs/FALSIFICATION_FRAMEWORK.md - Testing methodology
• docs/DETECTION_FRAMEWORK.md - Detection algorithms

Requirements

• Python 3.8+
• NumPy, SciPy, scikit-learn, matplotlib
• See requirements.txt for full dependencies

Installation

pip install -r requirements.txt
# Or install as package
pip install -e .

Contributing

This project maintains high standards for code quality and mathematical rigor. Contributions must include appropriate tests and documentation. See docs/COLLABORATION.md for guidelines.

Security Considerations

• This framework analyzes signatures only - it cannot forge or create signatures
• Only analyzes publicly available signature data
• Follow responsible disclosure for any vulnerabilities discovered
• See SECURITY.md for security policy

License

Apache License 2.0 - See LICENSE file for details.

Acknowledgments

• FastNear team for initial exploratory discussions
• Security research community for vulnerability disclosures
• Open source cryptography libraries

Status

• Version: 1.0.0 (Frozen API)
• Status: Production-ready
• Last Updated: November 2025