Secret Sharing and Verifiable Secret Sharing in Rust

This repository implements Shamir's Secret Sharing (SSS) and Feldman's Verifiable Secret Sharing (VSS) in Rust. These cryptographic schemes are used to securely split secrets into shares, distribute them to participants, and reconstruct the original secret from a subset of shares. The VSS implementation also ensures that shares are verifiable against commitments, preventing tampering.

Features

• Shamir's Secret Sharing:
  • Split a secret into shares using polynomial interpolation.
  • Reconstruct the original secret from a minimum threshold of shares.
• Feldman's Verifiable Secret Sharing:
  • Create shares with cryptographic commitments.
  • Verify the integrity of shares.
  • Reconstruct the secret from valid shares.

---

Getting Started

Prerequisites

• Rust: Ensure you have Rust installed. If not, install it from rust-lang.org.

Dependencies

This project uses the following crates:

• num-bigint: For handling arbitrarily large integers.
• rand: For generating random numbers.

Install dependencies by running:

cargo build

Running the Code

Execute the project with:

cargo run

This will demonstrate both SSS and VSS workflows.

---

Code Overview

Directory Structure

src/
├── main.rs       # Demonstrates SSS and VSS workflows
├── sss.rs        # Implements Shamir's Secret Sharing
├── vss.rs        # Implements Feldman's Verifiable Secret Sharing

Key Components

main.rs

This file contains the entry point for the program and demonstrates the following workflows:

1. Shamir's Secret Sharing:
   • Splits a secret into shares.
   • Reconstructs the secret using the minimum required shares.
2. Verifiable Secret Sharing:
   • Splits a secret into verifiable shares with cryptographic commitments.
   • Verifies shares and reconstructs the secret.

sss.rs

Implements Shamir's Secret Sharing:

• SecretSharer struct:
  • new: Initializes with a prime modulus, threshold, and total shares.
  • split_secret: Splits a secret into shares using a random polynomial.
  • reconstruct_secret: Reconstructs the secret using Lagrange interpolation.

vss.rs

Implements Feldman's Verifiable Secret Sharing:

• FeldmanVSS struct:
  • new: Initializes with prime parameters, threshold, and total shares.
  • split_secret: Splits a secret into shares and generates commitments.
  • verify_share: Verifies a share against commitments.
  • reconstruct_secret: Reconstructs the secret using valid shares.

---

Usage Examples

Shamir's Secret Sharing

let secret = 22773311u64.to_biguint().unwrap();
let sharer = SecretSharer::new(3, 5);

let shares = sharer.split_secret(&secret);
assert_eq!(shares.len(), 5);

let reconstructed = sharer.reconstruct_secret(&shares[0..3]).unwrap();
assert_eq!(reconstructed, secret);

Verifiable Secret Sharing

let p = BigUint::parse_bytes(b"115792089237316195423570985008687907853269984665640564039457584007908834671663", 10).unwrap();
let q = BigUint::parse_bytes(b"115792089237316195423570985008687907852837564279074904382605163141518161494337", 10).unwrap();
let g = BigUint::from(2u32);
let mut vss = FeldmanVSS::new(p, q, g, 3, 5);

let secret = 123456789u64.to_biguint().unwrap();
let (shares, commitments) = vss.split_secret(&secret).unwrap();

assert!(shares.iter().all(|share| vss.verify_share(share, &commitments)));
let reconstructed = vss.reconstruct_secret(&shares[0..3]).unwrap();
assert_eq!(reconstructed, secret);

---

Best Practices

• Prime Selection: Use secure prime numbers for production environments (e.g., 256-bit or higher).
• Threshold: Ensure the threshold value matches the security and redundancy requirements of your application.
• Testing: Thoroughly test with various configurations of thresholds and share counts.

---

Common Pitfalls

• Insufficient Shares: Ensure you provide at least the threshold number of shares for reconstruction.
• Parameter Validation: Check that secret < q and threshold <= total_shares in VSS to avoid runtime errors.
• Randomness: Use a cryptographically secure random number generator for production.

---

Contributions

Contributions, issues, and feature requests are welcome! Feel free to fork this repository and submit pull requests.

---

References

• Shamir's Secret Sharing
• Feldman's Verifiable Secret Sharing