Building block: MPyC exponentiation

A generic extension to MPyC that allows you to securely compute \(`a^{[x]}`\), where \(`a`\) is a non-negative, plain-text base (floating point or integer) and \(`x`\) is a secure number (SecFxp or SecInt).

This building block is included in the TNO MPC Python Toolbox.

Install

Install the tno.mpc.mpyc.exponentiation package using one of the following options.

  • Personal access token

  • Deploy tokens

  • Cloning this repo (developer mode)

Personal access token

  1. Generate a personal access token with read_api scope. Instruction are found here.

  2. Install

    python -m pip install tno.mpc.mpyc.exponentiation --extra-index-url https://__token__:<personal_access_token>@ci.tno.nl/gitlab/api/v4/projects/5977/packages/pypi/simple

Deploy tokens

  1. Generate a deploy token with read_package_registry scope. Instruction are found here.

  2. Install

    python -m pip install tno.mpc.mpyc.exponentiation --extra-index-url https://<GITLAB_DEPLOY_TOKEN>:<GITLAB_DEPLOY_PASSWORD>@ci.tno.nl/gitlab/api/v4/projects/5977/packages/pypi/simple

Dockerfile

FROM python:3.8

ARG GITLAB_DEPLOY_TOKEN
ARG GITLAB_DEPLOY_PASSWORD

RUN python -m pip install tno.mpc.mpyc.exponentiation --extra-index-url https://$GITLAB_DEPLOY_TOKEN:$GITLAB_DEPLOY_PASSWORD@ci.tno.nl/gitlab/api/v4/projects/5977/packages/pypi/simple

Usage

Minimal example

scripts/example_usage.py

from mpyc.runtime import mpc
from tno.mpc.mpyc.exponentiation import secure_pow
import math


async def main(base=math.e, x=[-1.5, 2.3, 4.5]):
    async with mpc:
        stype = mpc.SecFxp()
        sec_x = [stype(xx, integral=False) for xx in x] if isinstance(x, list) else stype(x)
        result = secure_pow(base, sec_x)
        revealed_result = await mpc.output(result)
    plain_result = [base ** xx for xx in x] if isinstance(x, list) else base ** x
    print(f"Result of secure exponentiation is {revealed_result}")
    print(f"In the plain we would have gotten  {plain_result}")
    diff = (
        [abs(sec - plain) for sec, plain in zip(revealed_result, plain_result)]
        if isinstance(x, list)
        else abs(revealed_result - plain_result)
    )
    print(f"The absolute difference is {diff}")


if __name__ == "__main__":
    mpc.run(main())

Indices and tables