Less Than Comparison

Here we demonstrate comparing two secret-shared arrays elementwise to see which values from the first are less than those from the second. The resulting secret shared array will be the same shape as the input, containing \(1\) where the first input is less than the second, and \(0\) where it is not. Note that we use the Boolean encoding when we reveal the output because the default FixedPoint encoding would produce unexpected results.

In this example, we compare \(2 < 3.5\), with the revealed result indicating that the comparison is, indeed true:

[1]:

import logging

import numpy

from cicada.additive import AdditiveProtocolSuite
from cicada.communicator import SocketCommunicator
from cicada.encoding import Boolean
from cicada.logging import Logger

logging.basicConfig(level=logging.INFO)

def main(communicator):
    log = Logger(logging.getLogger(), communicator)
    protocol = AdditiveProtocolSuite(communicator)

    a = numpy.array(2) if communicator.rank == 1 else None
    b = numpy.array(3.5) if communicator.rank == 2 else None

    log.info(f"Player {communicator.rank} secret: {a}", src=1)
    log.info(f"Player {communicator.rank} secret: {b}", src=2)

    a_share = protocol.share(src=1, secret=a, shape=())
    b_share = protocol.share(src=2, secret=b, shape=())
    less_than_share = protocol.less(a_share, b_share)
    less_than = protocol.reveal(less_than_share, encoding=Boolean())

    log.info(f"Player {communicator.rank} result: {less_than}")

SocketCommunicator.run(world_size=3, fn=main);

INFO:root:Player 1 secret: 2
INFO:root:Player 2 secret: 3.5
INFO:root:Player 0 result: True
INFO:root:Player 1 result: True
INFO:root:Player 2 result: True