Multiparty Computation (MPC) in Rust

This repository provides two Rust-based implementations of secret sharing techniques for secure Multiparty Computation (MPC): Shamir's Secret Sharing and Additive Secret Sharing. These methods allow multiple parties to compute functions over shared data without revealing their individual inputs.

Overview

Multiparty Computation (MPC) enables secure computation where multiple participants jointly compute a function over their private inputs while keeping those inputs hidden.

This project includes two primary modules:

1. Shamir's Secret Sharing:

   • Uses polynomial-based secret sharing to distribute a secret among n participants.
   • Requires a threshold of participants to reconstruct the secret.
   • Supports addition and multiplication operations on shared secrets.

2. Additive Secret Sharing:

   • Distributes a secret as the sum of random shares.
   • Simple and efficient, ideal for addition-based computations.

---

Code Structure

Modules

1. shamir_sharing.rs Implements Shamir's Secret Sharing.

   Key Functions:

   • calc_mod: Computes the modular value while handling negative numbers.
   • polynomial_eval: Evaluates a polynomial at a given point.
   • polynomial_multiply: Multiplies two polynomials.
   • share: Generates shares of a secret using random polynomial coefficients.
   • plot: Simulates visualization of shares and polynomials.
   • shamir_sharing: Demonstrates addition and multiplication operations on shared secrets.

2. addictive_sharing.rs Implements Additive Secret Sharing.

   Key Functions:

   • calc_mod: Computes the modular value while handling negative numbers.
   • share: Distributes a secret as random shares summing to the original secret.
   • open: Reconstructs the secret by summing shares.
   • sum_received_shares: Computes the sum of received shares.
   • addictive_sharing: Demonstrates secure addition of inputs using additive sharing.

Main File

The main.rs file imports both modules and serves as the entry point to run demonstrations of the two secret sharing techniques.

---

Getting Started

Prerequisites

• Rust installed on your system.

Running the Code

1. Clone the repository:

   git clone https://github.com/obah/rust_mpc.git
   cd rust_mpc

2. Run:

   cargo run

---

Examples

Shamir's Secret Sharing

• Distributes a secret using a polynomial and reconstructs it from shares.
• Supports secure addition and multiplication of shared secrets.

Sample Output:

Polynomial 1: 5 + 12 x^1 + 8 x^2
Polynomial 2: 2 + 4 x^1 + 11 x^2
Combined Polynomial: 7 + 16 x^1 + 19 x^2
Total sum: 12

Additive Secret Sharing

• Distributes a secret into additive shares.
• Reconstructs the secret by summing all shares.

Sample Output:

Input from: Alice = [3, -5, 22], Bob = [-1, 4, 12], Chris = [20, -7, -3]
Total received shares: Alice = 22, Bob = 12, Chris = 30
Total sum: 64

---

Key Features

1. Modular Arithmetic: Ensures all operations are performed within a finite field defined by a prime number.
2. Secure Sharing: Secrets are split into shares that reveal no information when viewed individually.
3. Flexible Computations: Supports both addition and multiplication for shared secrets.
4. Visualization (Simulated): Demonstrates the relationship between shares and their underlying polynomials.

---

Enjoy secure computation with Rust!