Blind Threshold Signatures over Lattices

This repository accompanies the academic paper:
Lattice-based Threshold Blind Signatures Sebastian Faller, Guilhem Niot, Michael Reichle

This repository extends the original Plover code to build a threshold blind signature scheme over lattices.

Overview

This codebase provides a Python implementation of a threshold blind signature scheme based on the Plover signature scheme, with additional components for threshold and blind signing.

Disclaimer

This code is for academic and research purposes only and is not production-ready. It may not be constant time or have security vulnerabilities. Do not use this code in production environments without thorough review, testing, and security audits.

Setup & Testing on Ubuntu

To get started on a fresh Ubuntu system, follow these steps:

1. Install Prerequisites

sudo apt update
sudo apt install -y python3-pip python3.12-venv unzip libgmp-dev libmpfr-dev cmake

2. Python Environment

Create and activate a virtual environment in the repository root:

python3 -m venv .
source bin/activate

Upgrade setuptools and install Python dependencies:

pip install --upgrade setuptools
pip install requests cffi

3. Build Dependencies

Initialize git submodules:

git submodule update --init --recursive

Build the LaZer library and Python bindings:

cd lazer/
make
cd python/
make
cd ../..

Install Python requirements for the threshold blind signature code:

pip install -r requirements.txt

Build proof components:

cd proof/
make
cd ..

4. Running Tests

After setup, you can run tests:

python threshold_party.py --help

If you encounter issues, ensure all dependencies are installed and submodules are up to date.

Alternative Testing Method

To run the test in plover_api.py:

1. Ensure dependencies are built (follow steps 3 above)

2. Run the test

   python3 plover_api.py

Using Threshold Blind Signatures

The threshold_party.py script implements a T-out-of-N threshold blind signature scheme using JSON-RPC communication between parties.

Basic Usage

To run a threshold blind signature protocol, you need:

• 1 User party (who wants to get a message signed)
• T Signer parties (who collectively sign the message)

Starting Signer Parties

First, start the required number of signer parties (each in a separate terminal):

# Terminal 1: Start signer 1
python3 threshold_party.py --party-id 1 --party-type signer

# Terminal 2: Start signer 2
python3 threshold_party.py --party-id 2 --party-type signer

# Terminal 3: Start signer 3
python3 threshold_party.py --party-id 3 --party-type signer

Each signer will start a JSON-RPC server on port 8000 + party_id (e.g., signer 1 on port 8001, signer 2 on port 8002, etc.).

Starting the User Party

Once all signers are running, start the user party:

# Terminal 4: For a 2-out-of-3 threshold scheme
python3 threshold_party.py --party-id 0 --party-type user --threshold 2 --total-parties 3

Command Line Options

• --party-id: Unique integer ID for the party
• --party-type: Either "user" or "signer"
• --threshold: Number of signers required (T) - required for user party
• --total-parties: Total number of signer parties (N) - required for user party
• --user-port: Base port number (default: 8000)
• --signer-hosts: List of signer hosts for user party (format: host1:port1 host2:port2 ...)
• --signer-host: Host address for signer party (default: localhost)
• --signer-port: Port for signer party (defaults to 8000 + party-id)
• --runs: Number of signing runs for averaging measurements (default: 1)

Protocol Flow

1. Setup: Signers start and wait for connections
2. Key Generation: User generates threshold keys and distributes shares to signers
3. Round 1: User collects commitments from signers
4. Round 2: User distributes commitments and collects witness values
5. Round 3: User distributes witnesses and collects final responses
6. Completion: User aggregates responses to create the final blind signature

Example: 2-out-of-3 Threshold Signature

# Terminal 1: Start signer 1
python3 threshold_party.py --party-id 1 --party-type signer

# Terminal 2: Start signer 2
python3 threshold_party.py --party-id 2 --party-type signer

# Terminal 3: Start signer 3
python3 threshold_party.py --party-id 3 --party-type signer

# Terminal 4: Start user (will use signers 1 and 2 for threshold=2)
python3 threshold_party.py --party-id 0 --party-type user --threshold 2 --total-parties 3

The protocol will automatically select the first T signers that are available to participate in the signing.

Performance Measurement

To get reliable performance measurements, run multiple signing iterations:

# Run 10 iterations and average the measurements
python3 threshold_party.py --party-id 0 --party-type user --threshold 2 --total-parties 3 --runs 10

This will perform key generation once, then execute the 3-round signing protocol 10 times and report averaged timing measurements with standard deviations.

Using Different Hosts

You can run signers on different machines by specifying custom hosts and ports:

# On machine 192.168.1.10: Start signer 1
python3 threshold_party.py --party-id 1 --party-type signer --signer-host 192.168.1.10 --signer-port 9001

# On machine 192.168.1.11: Start signer 2
python3 threshold_party.py --party-id 2 --party-type signer --signer-host 192.168.1.11 --signer-port 9002

# On user machine: Start user with custom signer locations
python3 threshold_party.py --party-id 0 --party-type user --threshold 2 --total-parties 2 \
    --signer-hosts 192.168.1.10:9001 192.168.1.11:9002

Project Structure

├── lazer/                 LaZer zero-knowledge proof library
├── Makefile               Clean target
├── polyr.py               Polynomial ring arithmetic + NTT code
├── plover_api.py          Serialization/deserialization, NIST functions, tests
├── plover_core.py         Plover signature scheme core algorithm
├── README.md              This file
├── requirements.txt       Python dependencies
├── test_ntt.py            Basic NTT tests
├── threshold_party.py     T-out-of-N threshold blind signature with JSON-RPC
└── proof/                 NIZK proof components

Note:
This repository extends the original Plover code to support threshold and blind signature features. Please refer to the code and comments for details on the new functionalities.