TNO PET Lab - secure Multi-Party Computation (MPC) - MPyC - Floating Point

Implementation of secure computations on floating-points using the MPyC framework. It serves as an alternative to the SecureFloat class that was introduced in MPyC v0.8. A key difference between the two implementations is that we represent the significand of a secure floating-point by a SecureInteger, whereas MPyC's SecureFloat represents the significand by a (signed) SecureFixedPoint. Furthermore, our implementation contains the following functionality:

• More efficient bit length protocol.
• Optimized protocols for performing multiple additions or multiplications (see here).
• Cached attributes for speeding up sequential operations.

Also, there are initial protocols for computing

1. the secure square root and
2. the logarithm

of a secure floating-point. We should note that the accuracy of those protocols is up for improvement. For example, inaccuracies may occur in the logarithm of input that is close to zero or one.

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.mpyc.floating_point 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.

Install

Easily install the tno.mpc.mpyc.floating_point package using pip:

console $ python -m pip install tno.mpc.mpyc.floating_point

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

console $ python -m pip install -e 'tno.mpc.mpyc.floating_point'

If you wish to run the tests you can use:

console $ python -m pip install 'tno.mpc.mpyc.floating_point[tests]'

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

console $ python -m pip install 'tno.mpc.mpyc.floating_point[gmpy]'

Basic usage

The following code snippet shows how secure floating points can be initialized and used.

```python """ Example usage. This script can be executed with multiple parties as follows:

$ python example.py -M3

or, in separate terminals,

$ python example.py -M3 -I0 $ python example.py -M3 -I1 $ python example.py -M3 -I2 """

from math import log2, sqrt

from mpyc.runtime import mpc from mpyc.sectypes import SecFxp

from tno.mpc.mpyc.floatingpoint import SecFlp, logflp, sqrt_flp

async def main(): # start the MPyC framework async with mpc: # create a secure floating point type secflptype = SecFlp(significandbitlength=32, exponentbitlength=16)

    val_1 = 2**15
    val_2 = 1 / 2**10
    # create two (placeholder) secure floating points
    if mpc.pid == 0:
        sec_val_1 = sec_flp_type(val_1)
        sec_val_2 = sec_flp_type(val_2)
    else:
        sec_val_1 = sec_flp_type(None)
        sec_val_2 = sec_flp_type(None)

    # secret-share floating points
    sec_val_1 = mpc.input(sec_val_1, senders=0)
    sec_val_2 = mpc.input(sec_val_2, senders=0)

    # apply regular computation for comparison
    regular_results = [
        val_1 + val_2,  # addition
        val_2 - val_1,  # subtraction
        val_1 / val_2,  # division
        val_1 * val_2,  # multiplication
        sqrt(val_2),  # square root
        log2(val_1),  # logarithm base 2
    ]

    # create a secure fixed point type to use in certain subroutines
    # if the bit length is too small, the subroutines might produce wrong answers
    sec_fxp_type = SecFxp(96)

    # apply secure computations
    sec_results = [
        sec_val_1 + sec_val_2,  # addition
        sec_val_2 - sec_val_1,  # subtraction
        sec_val_1 / sec_val_2,  # division
        sec_val_1 * sec_val_2,  # multiplication
        sqrt_flp(sec_val_2, secfxp_type=sec_fxp_type),  # square root
        log_flp(sec_val_1, secfxp_type=sec_fxp_type),  # logarithm base 2
    ]

    # reconstruct the secret shares
    revealed_results = await mpc.output(sec_results)

# print the results
print(regular_results)
print(revealed_results)

if name == "main": # if a custom mpyc runtime rt is created, it can be set with tno.mpc.mpyc.floatingpoint.setruntime(rt) mpc.run(main()) ```

The output of this code snippet is:

commandline $ python example.py -M 3 2023-11-02 10:28:07,647 Start MPyC runtime v0.8 2023-11-02 10:28:07,752 All 3 parties connected. 2023-11-02 10:28:09,055 Stop MPyC runtime -- elapsed time: 0:00:01.407784 [32768.0009765625, -32767.9990234375, 33554432.0, 32.0, 0.03125, 15.0] [32768.0009765625, -32767.9990234375, 33554432.0, 32.0, 0.03125576677848585, 15.000011652708054]