Shamir's Secret Sharing with Verifiable Secret Sharing (VSS)

Overview

shamir_vss is a Rust-based implementation of Shamir's Secret Sharing (SSS) algorithm with Verifiable Secret Sharing (VSS). The primary goal of this project is to securely split a secret into multiple shares, ensuring that only a predefined threshold of shares can reconstruct the original secret while providing cryptographic proof of share validity.

Key Features

• Shamir's Secret Sharing (SSS): Securely splits a secret into multiple shares.
• Threshold-Based Reconstruction: Requires a minimum k shares out of n to recover the secret.
• Verifiable Secret Sharing (VSS): Uses cryptographic commitments to ensure the integrity of shares.
• Multi-Base Support: Handles values in various numeral bases (binary, octal, decimal, hexadecimal, etc.).
• Modular Arithmetic & GCD Optimization: Efficient rational number arithmetic and greatest common divisor calculations.
• Commitment Generation with Modular Exponentiation: Uses a base generator G and prime modulus P to validate shares.
• Error Handling: Detects and prevents invalid or malicious shares from being used in reconstruction.

How It Works

• Share Parsing & Base Conversion: Converts values from different bases into decimal for computation.
• Secret Sharing: The secret is divided into n shares, requiring k shares for reconstruction.
• Commitment Generation: Uses modular exponentiation G^coeff mod P to validate shares.
• Secret Recovery: Given at least k valid shares, the original secret is reconstructed using Lagrange interpolation.
• Modular Arithmetic Operations: Efficient rational number multiplication, addition, and reduction to simplify computations.

Future Enhancements

• Implement elliptic curve-based secret sharing for enhanced security.