mpc-secret-shares 0.1.0

MPC primitives over Shamir secret shares, implemented from the SoK paper

mpc-secret-shares

A pure-Python library for Secure Multiparty Computation (MPC) over Secret Shares.

Implements the protocols described in:

SoK: Secure Computation over Secret Shares

All protocols operate over a prime finite field Z_p using Shamir's (t,n)-secret sharing: any t out of n parties can reconstruct a secret; fewer than t parties learn nothing.

---

Installation

pip install mpc-secret-shares

Or install directly from source:

git clone https://github.com/yourusername/mpc-secret-shares.git
cd mpc-secret-shares/mpc_project
pip install .

---

Quick Start

import random
from mpc_secret_shares import (
    protocol_1_share,
    protocol_2_reconstruct,
    protocol_4_secure_mult,
    protocol_5_secure_compare,
    protocol_10_is_zero,
)

random.seed(42)

# --- MPC parameters ---
p = 11   # prime field  Z_11
n = 3    # three parties
t = 2    # any 2 shares reconstruct the secret

# --- Share two secrets ---
shares_u = protocol_1_share(S=4, n=n, t=t, P=p)
shares_v = protocol_1_share(S=5, n=n, t=t, P=p)

# --- Secure multiplication: 4 * 5 = 20 ≡ 9 (mod 11) ---
shares_w = protocol_4_secure_mult(shares_u, shares_v, n=n, t=t, P=p)
w = protocol_2_reconstruct(shares_w[:t], p)
print(f"4 × 5 mod 11 = {w}")   # → 9

# --- Secure comparison: 4 < 5 ? ---
shares_cmp = protocol_5_secure_compare(shares_u, shares_v, n=n, t=t, p=p)
cmp_result = protocol_2_reconstruct(shares_cmp[:t], p)
print(f"4 < 5 → {bool(cmp_result)}")   # → True

# --- IsZero test ---
shares_zero = protocol_1_share(S=0, n=n, t=t, P=p)
shares_iz = protocol_10_is_zero(shares_zero, n=n, t=t, p=p)
print(f"IsZero(0) = {protocol_2_reconstruct(shares_iz[:t], p)}")  # → 1

---

Implemented Protocols

Module	Protocol	Description
protocol1	Share	Shamir secret sharing
protocol2	Reconstruct	Lagrange interpolation
protocol3	RNG	Shared random number generation
protocol4	SecureMult	Secure multiplication
protocol5_secure_compare	SecureCompare	Secure 1_{u < v}
protocol6_less_than_half_p	LessThan_Half_P	Secure 1_{a < p/2}
protocol7_lsb	LSB	Secure least-significant-bit extraction
protocol8_gen_rnd_bit_sharing	GenRndBitSharing	Random bit generation
protocol9_bitwise_less_than	Bitwise_LessThan	Bitwise comparison
protocol10	IsZero	Secure equality to zero
protocol12	BinaryLongDiv	Cleartext binary long division
protocol13_secure_division	SecureDivision	Secure floor division
algorithm14_bitwise_sqrt	BitwiseSqrt	Cleartext integer square root
protocol15_secure_sqrt	SecureSqrt	Secure integer square root
protocol16_mary_or	m-ary OR	Secure OR via polynomial evaluation
protocol17_improved_mary_or	Improved OR	Communication-efficient OR
algorithm18_kth_ranked	KthRanked	Cleartext k-th ranked element
affine_combinations	AffineCombo	Local α + β·u + γ·v
share_utils	—	Local share arithmetic helpers
secure_inv	SecureInv	Secure modular inverse

---

Running the Tests

cd mpc_project
pip install pytest
pytest tests/ -v

---

License

MIT — see LICENSE.