Struct ShamirSecretShare 

pub struct ShamirSecretShare {
    pub p: u64,
    pub k: usize,
    pub n: usize,
}

Shamir’s Secret Sharing over a finite field Z_p.

Splits a secret s into n shares such that any k shares can reconstruct s via Lagrange interpolation, but any k-1 shares reveal nothing about s.

WARNING

Educational implementation. The polynomial coefficients are NOT generated with cryptographically secure randomness. Do NOT use for real secrets.

Fields

p: u64

Prime modulus p (field F_p)

k: usize

Threshold k: minimum shares needed for reconstruction

n: usize

Total shares n

Implementations

impl ShamirSecretShare

pub fn new(p: u64, k: usize, n: usize) -> Self

Create a new Shamir secret sharing instance.

pub fn share(&self, secret: u64, seed: u64) -> Vec<(u64, u64)>

Split a secret s into n shares using a deterministic polynomial with coefficients derived from seed (for reproducibility in tests).

Returns a vector of (x, y) pairs where x = 1..=n and y = f(x).

WARNING

The seed-based coefficient generation is NOT secure. Real Shamir’s scheme requires cryptographically random coefficients.

pub fn reconstruct(&self, shares: &[(u64, u64)]) -> Option<u64>

Reconstruct the secret from any k shares using Lagrange interpolation over F_p.

Each share is an (x, y) pair. Computes f(0) = Σ y_i * L_i(0) mod p.