Thresholdized UOV Signature Scheme with MPyC

This project implements a thresholdized version of the Unbalanced Oil and Vinegar (UOV) digital signature scheme using the MPyC secure multi-party computation (MPC) framework. UOV is a multivariate quadratic (MQ) signature protocol and a candidate in the NIST Post-Quantum Cryptography Standardization process.

This implementation is based on the paper Share the MAYO: thresholdizing MAYO by Sofia Celi, Daniel Escudero, and Guilhem Niot

Features

• Thresholdized UOV: The signing key is distributed among multiple parties; a threshold of parties must collaborate to generate a valid signature.
• Secure Multi-Party Computation: Built on MPyC, enabling distributed trust and privacy-preserving computation.
• Post-Quantum Security: UOV is designed to resist attacks from quantum computers.
• Flexible Parameters: Easily configure the number of parties, threshold, and UOV parameters.

Stack

• MPyC (Multi-Party Computation in Python)
• numpy (matrix and vector operations)
• gmpy2 (arbitrary precision arithmetic)
• implicit-globals (for field context management)
• uvloop (optional, for faster event loops on non-Windows)

Installation

With Nix (recommended for Nix/NixOS users)

nix develop

This will provide a shell with all dependencies available.

With uv

pip install uv
uv venv
uv pip install .

Or, using plain pip:

python3 -m venv .venv
source .venv/bin/activate
pip install .

Usage

Single-Party (Demo)

python3 -m src.main

Multi-Party (MPC) Usage

To run with N parties, open N shells and run in each:

python3 -m src.main -M<N> -I<id>

where <N> is the number of parties and <id> is the party index (0 to N-1).

Example (N=3):

python3 -m src.main -M3 -I0
python3 -m src.main -M3 -I1
python3 -m src.main -M3 -I2

Threshold Option

You can set the threshold t (number of parties required to sign) with the -T<t> flag:

python3 -m src.main -M5 -T2 -I0

where 0 <= t < n/2.

Developer Notes

• The src/mp-spdz/ folder contains an early attempt at implementing the protocol using the MP-SPDZ framework. This approach was discontinued in favor of MPyC, which offers a more Pythonic and flexible library interface, making development and experimentation easier.
• The main protocol logic is in src/main.py and supporting modules in src/.

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For more technical/developer details, see DEVELOPER.md.