TNO PET Lab - secure Multi-Party Computation (MPC) - Encryption Schemes - Shamir

Implementation of the Shamir Secret Sharing scheme.

PET Lab

The TNO PET Lab consists of generic software components, procedures, and functionalities developed and maintained on a regular basis to facilitate and aid in the development of PET solutions. The lab is a cross-project initiative allowing us to integrate and reuse previously developed PET functionalities to boost the development of new protocols and solutions.

The package tno.mpc.encryption_schemes.shamir is part of the TNO Python Toolbox.

Limitations in (end-)use: the content of this software package may solely be used for applications that comply with international export control laws.
This implementation of cryptographic software has not been audited. Use at your own risk.

Documentation

Documentation of the tno.mpc.encryption_schemes.shamir package can be found here.

Install

Easily install the tno.mpc.encryption_schemes.shamir package using pip:

$ python -m pip install tno.mpc.encryption_schemes.shamir

Note: If you are cloning the repository and wish to edit the source code, be sure to install the package in editable mode:

$ python -m pip install -e 'tno.mpc.encryption_schemes.shamir'

If you wish to run the tests you can use:

$ python -m pip install 'tno.mpc.encryption_schemes.shamir[tests]'

Note: A significant performance improvement can be achieved by installing the GMPY2 library.

$ python -m pip install 'tno.mpc.encryption_schemes.shamir[gmpy]'

Usage

The shamir secret sharing module can be used as follows:

from tno.mpc.encryption_schemes.shamir import ShamirSecretSharingScheme, ShamirShares

# Initialize a three-out-of-five secrect sharing scheme with prime 10657
# Note: the polynomial degree is one less than the number of parties needed for reconstruction
shamir_scheme = ShamirSecretSharingScheme(10657, 5, 2)
# Share a secret integer
sharing = shamir_scheme.share_secret(42)
# When receiving shares a reconstructor can be created as follows
reconstructor = ShamirShares(
    shamir_scheme, {1: sharing.shares[1], 2: sharing.shares[2], 3: sharing.shares[3]}
)
# Reconstruct the secret and check if it is the expected result
assert 42 == sharing.reconstruct_secret() == reconstructor.reconstruct_secret()

For the performance it is important to bear in mind the following information: Both ShamirSecretSharingScheme and ShamirSecretSharingIntegers make use of a VanderMonde matrix when sharing a secret. The size of this matrix grows exponentially with the number of parties. This matrix is constructed on-the-fly, which means that the first time the property van_der_monde is called, this matrix is constructed. This generally happens during the secret_share operation. If you would like to initialize this in an earlier stage, you can put the following piece of code wherever you want the initialization to take place:

# scheme is initialized
scheme = ShamirSecretSharingScheme(...)

# VanderMonde matrix is initialized
_ = scheme.van_der_monde