Implementation of secure comparison protocol as given in https://eprint.iacr.org/2018/1100.pdf
Project description
TNO MPC Lab - Protocols - Secure Comparison
The TNO MPC lab consists of generic software components, procedures, and functionalities developed and maintained on a regular basis to facilitate and aid in the development of MPC solutions. The lab is a cross-project initiative allowing us to integrate and reuse previously developed MPC functionalities to boost the development of new protocols and solutions.
The package tno.mpc.protocols.secure_comparison is part of the TNO Python Toolbox.
Remark: This cryptography software may not be used in applications that violate international export control legislations.
This implementation of cryptographic software has not been audited. Use at your own risk.
Documentation
Documentation of the tno.mpc.protocols.secure_comparison package can be found here.
Install
Easily install the tno.mpc.protocols.secure_comparison package using pip:
$ python -m pip install tno.mpc.protocols.secure_comparison
Note:
A significant performance improvement for some algorithms can be achieved by installing the GMPY2 library.
$ python -m pip install tno.mpc.protocols.secure_comparison[gmpy]
Usage
import asyncio
from tno.mpc.communication import Pool
from tno.mpc.encryption_schemes.dgk import DGK
from tno.mpc.encryption_schemes.paillier import Paillier
from tno.mpc.encryption_schemes.utils import next_prime
from tno.mpc.protocols.secure_comparison import Initiator, KeyHolder
async def run_protocol():
taskA = asyncio.create_task(alice.perform_secure_comparison(x_enc, y_enc))
taskB = asyncio.create_task(bob.perform_secure_comparison())
x_leq_y_enc, _ = await asyncio.gather(*[taskA, taskB])
x_leq_y = scheme_paillier.decrypt(x_leq_y_enc)
assert x_leq_y == 1
if __name__ == "__main__":
# Set maximum bit length
l = 16
# Setup the Paillier scheme
scheme_paillier = Paillier.from_security_parameter(key_length=2048)
# Setup the DGK scheme
u = next_prime((1 << (l + 2)))
scheme_dgk = DGK.from_security_parameter(
v_bits=160, n_bits=2048, u=u, full_decryption=False
)
# Setup communication pools
pool_alice = Pool()
pool_alice.add_http_server(8040)
pool_alice.add_http_client("keyholder", "localhost", 8041)
pool_bob = Pool()
pool_bob.add_http_server(8041)
pool_bob.add_http_client("initiator", "localhost", 8040)
# Encrypt two numbers (x,y) for the protocol and set the maximum bit_length (l)
x = 23
y = 42
x_enc = scheme_paillier.encrypt(x)
y_enc = scheme_paillier.encrypt(y)
alice = Initiator(l, communicator=pool_alice, other_party="keyholder")
bob = KeyHolder(
l,
communicator=pool_bob,
other_party="initiator",
scheme_paillier=scheme_paillier,
scheme_dgk=scheme_dgk,
)
# Run entire protocol interactively:
loop = asyncio.get_event_loop()
loop.run_until_complete(run_protocol())
# Or execute the protocol steps without interaction
z_enc, r = alice.step_1(x_enc, y_enc, l, scheme_paillier)
z, beta = bob.step_2(z_enc, l, scheme_paillier)
alpha = alice.step_3(r, l)
d_enc = bob.step_4a(z, scheme_dgk, scheme_paillier, l)
beta_is_enc = bob.step_4b(beta, l, scheme_dgk)
d_enc = alice.step_4c(d_enc, r, scheme_dgk, scheme_paillier)
alpha_is_xor_beta_is_enc = alice.step_4d(alpha, beta_is_enc)
w_is_enc, alpha_tilde = alice.step_4e(
r, alpha, alpha_is_xor_beta_is_enc, d_enc, scheme_paillier
)
w_is_enc = alice.step_4f(w_is_enc)
s, delta_a = alice.step_4g()
c_is_enc = alice.step_4h(
s, alpha, alpha_tilde, d_enc, beta_is_enc, w_is_enc, delta_a, scheme_dgk
)
c_is_enc = alice.step_4i(c_is_enc, scheme_dgk)
delta_b = bob.step_4j(c_is_enc, scheme_dgk)
zeta_1_enc, zeta_2_enc, delta_b_enc = bob.step_5(z, l, delta_b, scheme_paillier)
beta_lt_alpha_enc = alice.step_6(delta_a, delta_b_enc)
x_leq_y_enc = alice.step_7(
zeta_1_enc, zeta_2_enc, r, l, beta_lt_alpha_enc, scheme_paillier
)
x_leq_y = scheme_paillier.decrypt(x_leq_y_enc)
assert x_leq_y == 1
The communicator object is required only when the protocol is ran through perform_secure_comparison
. In that case, one may choose to pass any communicator object that adheres to the tno.mpc.protocols.secure_comparison.Communicator
protocol. An example can be found in the unit tests.
! SAFETY NOTICE ! ENSURE CIPHERTEXTS ARE RANDOMIZED
Since version 2.0.0 of tno.mpc.encryption_schemes.paillier
and tno.mpc.encryption_schemes.dgk
, it is possible to (potentially) make protocols more efficient by delaying randomization of ciphertexts. This library always operates in this 'expert' mode and therefore several protocol steps yield non-randomized ciphertext outputs. As a consequence, if the user chooses to perform the secure comparison steps manually, she needs to make sure that the resulting ciphertexts are randomized before they are communicated. If the tno.mpc.communication
library is used (or more specifically, the Paillier and DGK serialize methods), then this will be done automatically for you (but warnings might be raised).
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