cd dual-ec-drbg

# One command to setup and run
./run.sh

cd dual-ec-drbg

# Set local Python version with pyenv
pyenv local 3.12.12

# Create virtual environment
python3 -m venv venv
source venv/bin/activate

# Install dependencies
pip install --upgrade pip
pip install -r requirements.txt

# Launch Jupyter
jupyter notebook dual_ec_drbg_backdoor_poc.ipynb

cd dual-ec-drbg
pip install --user -r requirements.txt
jupyter notebook dual_ec_drbg_backdoor_poc.ipynb

Dual_EC_DRBG State Update:    s_{i+1} = φ(s_i · P)
Dual_EC_DRBG Output:          r_i = φ(s_i · Q)     [truncated]

Backdoor Relationship:        Q = d · P

Attack (knowing d):
1. Observe r_i (30+ bytes of output)
2. Reconstruct candidate R where x(R) ≈ r_i  
3. Compute: s_{i+1} = φ(d⁻¹ · R) = φ(s_i · P)
4. Predict ALL future output!

Time Complexity: O(1) - milliseconds on a laptop
Data Required: 32 bytes of observed output

# Extract code cells to a Python script
jupyter nbconvert --to script dual_ec_drbg_backdoor_poc.ipynb

# Run the script
python dual_ec_drbg_backdoor_poc.py

[=== HONEST Dual_EC_DRBG ===]
[+] DRBG initialized
    Mode: HONEST
    P = (6b17d1f2e12c4247..., 4fe342e2fe1a7f9b...)
    Q = (a53a7f9b2e1c4247..., 7fe342e2fe1a7f9b...)

[=== BACKDOORED Dual_EC_DRBG ===]
[+] DRBG initialized
    Mode: BACKDOORED
    P = (6b17d1f2e12c4247..., 4fe342e2fe1a7f9b...)
    Q = (b23d7c9a3f8e5156..., 9ab456d3c7e2f1a8...)
    Secret d = 0x4f3e2d1c0b9a8f7e...

[=== ATTACK EXECUTION ===]
[+] Observed output: a1b2c3d4e5f6...
[+] Found 2 candidate points on curve
...
[OK] PERFECT MATCH - All future output predicted!