VerifiableSecretSharing/src/vss.rs

use curve25519_dalek::edwards::EdwardsPoint;
use curve25519_dalek::traits::Identity;
use curve25519_dalek::scalar::Scalar;
use curve25519_dalek::constants::ED25519_BASEPOINT_POINT;
use rand::rngs::ThreadRng;

pub type Secret = Scalar;

#[derive(Copy, Clone)]
pub struct Share {
    index: u32,
    value: Scalar,
}

pub struct Commitment {
    coms: Vec<EdwardsPoint>,
}

/// Create secret shares for a given secret.
pub fn generate_shares(secret: Secret, numshares: u32, threshold: u32) -> Result<(Commitment, Vec<Share>), &'static str> {
    if threshold < 1 { return Err("Threshold cannot be 0") }
    if numshares < 1 { return Err("Number of shares cannot be 0") }
    if threshold > numshares { return Err("Threshold cannot exceed numshares") }

    let numcoeffs = (threshold-1) as usize;

    let mut coeffs: Vec<Scalar> = Vec::with_capacity(numcoeffs);

    let mut rng: ThreadRng = rand::thread_rng();

    let mut shares: Vec<Share> = Vec::with_capacity(numshares as usize);

    let mut comm: Commitment = Commitment { coms: Vec::with_capacity(threshold as usize) };

    for _ in 0..numcoeffs {
        coeffs.push(Scalar::random(&mut rng));
    }

    for share_index in 1..numshares+1 {
        // Evaluate the polynomial with `secret` as the constant term
        // and `coeffs` as the other coefficients at the point x=share_index
        // using Horner's method
        let scalar_index = Scalar::from(share_index);
        let mut value = Scalar::zero();
        for i in (0..numcoeffs).rev() {
            value += coeffs[i];
            value *= scalar_index;
        }
        value += secret;
        shares.push(Share{ index: share_index, value: value });
    }

    comm.coms.push(ED25519_BASEPOINT_POINT * secret);
    for c in coeffs {
        comm.coms.push(ED25519_BASEPOINT_POINT * c);
    }

    Ok((comm, shares))
}

/// Verify that a share is consistent with a commitment.
pub fn verify_share(share: Share, commitment: &Commitment) -> Result<bool, &'static str> {
    let f_result = ED25519_BASEPOINT_POINT * share.value;

    let x = Scalar::from(share.index);

    let (_, result) = commitment.coms.iter().fold(
        (Scalar::one(), EdwardsPoint::identity()),
            |(x_to_the_i, sum_so_far), comm_i|
            (x_to_the_i * x, sum_so_far + x_to_the_i * comm_i));

    let is_valid = f_result == result;
    Ok(is_valid)
}

/// Reconstruct the secret from enough (at least the threshold) already-verified shares.
pub fn reconstruct_secret(shares: &Vec<Share>) -> Result<Secret, &'static str> {
    let numshares = shares.len();

    if numshares < 1 { return Err("No shares provided"); }

    let mut lagrange_coeffs: Vec<Scalar> = Vec::with_capacity(numshares);

    for i in 0..numshares {
        let mut num = Scalar::one();
        let mut den = Scalar::one();
        for j in 0..numshares {
            if j==i { continue; }
            num *= Scalar::from(shares[j].index);
            den *= Scalar::from(shares[j].index) - Scalar::from(shares[i].index);
        }
        if den == Scalar::zero() {
            return Err("Duplicate shares provided");
        }
        lagrange_coeffs.push(num * den.invert());
    }

    let mut secret = Scalar::zero();

    for i in 0..numshares {
        secret += lagrange_coeffs[i] * shares[i].value;
    }

    return Ok(secret)
}

/// Create and apply a proactive update to a master commitment.
pub fn update_shares(old_commitment: &Commitment, old_shares: &Vec<Share>) -> Result<(Commitment, Vec<Share>), &'static str> {
    let num_shares = old_shares.len() as u32;
    let threshold = old_commitment.coms.len() as u32;
    let res = generate_shares(Scalar::zero(), num_shares, threshold);

    if !res.is_ok() {
        return res;
    }

    let (update_commitments, update_shares) = res.unwrap();

    let mut new_shares: Vec<Share> = Vec::with_capacity(num_shares as usize);
    for old_share in old_shares {
        let update_share = update_shares[(old_share.index-1) as usize];
        let new_share = Share{
            index: old_share.index,
            value: old_share.value + update_share.value,
        };
        new_shares.push(new_share);
    }

    let mut new_commitments: Commitment = Commitment { coms: Vec::with_capacity(threshold as usize) };
    for i in 0..old_commitment.coms.len() {
        let new_commitment = old_commitment.coms[i] + update_commitments.coms[i];
        new_commitments.coms.push(new_commitment);
    }

    Ok((new_commitments, new_shares))
}

#[cfg(test)]
mod tests {
    use crate::vss::*;

    #[test]
    fn share_simple() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (com, shares) = res.unwrap();
        assert!(shares.len() == 5);
        assert!(com.coms.len() == 2);

        let mut recshares: Vec<Share> = Vec::new();
        recshares.push(shares[1]);
        recshares.push(shares[3]);
        let recres = reconstruct_secret(&recshares);
        assert!(recres.is_ok());
        assert_eq!(recres.unwrap(), s);
    }

    #[test]
    fn share_not_enough() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (_, shares) = res.unwrap();

        let mut recshares: Vec<Share> = Vec::new();
        recshares.push(shares[1]);
        let recres = reconstruct_secret(&recshares);
        assert!(recres.is_ok());
        assert_ne!(recres.unwrap(), s);
    }

    #[test]
    fn share_dup() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (_, shares) = res.unwrap();

        let mut recshares: Vec<Share> = Vec::new();
        recshares.push(shares[1]);
        recshares.push(shares[1]);
        let recres = reconstruct_secret(&recshares);
        assert!(recres.is_err());
        assert_eq!(recres.err(), Some("Duplicate shares provided"));
    }

    #[test]
    fn share_badparams() {
        let s = Secret::from(42u32);

        {
            let res = generate_shares(s, 5, 0);
            assert!(res.is_err());
            assert_eq!(res.err(), Some("Threshold cannot be 0"));
        }
        {
            let res = generate_shares(s, 0, 3);
            assert!(res.is_err());
            assert_eq!(res.err(), Some("Number of shares cannot be 0"));
        }
        {
            let res = generate_shares(s, 1, 3);
            assert!(res.is_err());
            assert_eq!(res.err(), Some("Threshold cannot exceed numshares"));
        }
    }

    #[test]
    fn share_commitment_valid() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 8, 3);
        assert!(res.is_ok());
        let (com, shares) = res.unwrap();

        for share in shares {
            let is_valid = verify_share(share, &com);
            assert!(is_valid.is_ok());
            assert!(is_valid.unwrap());
        }
    }

    #[test]
    fn share_commitment_invalid() {
        let s1 = Secret::from(42u32);
        let s2 = Secret::from(42u32);

        let res1 = generate_shares(s1, 8, 3);
        assert!(res1.is_ok());
        let (_, shares1) = res1.unwrap();

        let res2 = generate_shares(s2, 8, 3);
        assert!(res2.is_ok());
        let (com2, _) = res2.unwrap();

        for share in shares1 {
            // test that commitments to a different set of shares fails
            let is_valid = verify_share(share, &com2);
            assert!(is_valid.is_ok());
            assert_ne!(is_valid.unwrap(), true);
        }
    }

    #[test]
    fn share_update_valid() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (com, shares) = res.unwrap();

        let update_res = update_shares(&com, &shares);
        assert!(update_res.is_ok());
        let (update_com, update_shares) = update_res.unwrap();

        for share in update_shares {
            let is_valid = verify_share(share, &update_com);
            assert!(is_valid.is_ok());
            assert!(is_valid.unwrap());
        }
    }

    #[test]
    fn share_update_invalid() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (com, shares) = res.unwrap();

        let update_res = update_shares(&com, &shares);
        assert!(update_res.is_ok());
        let (update_com, update_shares) = update_res.unwrap();

        // test that the old shares are not valid with the updated commitment
        for share in shares {
            let is_valid = verify_share(share, &update_com);
            assert!(is_valid.is_ok());
            assert!(!is_valid.unwrap());
        }

        // assert that we can recover the original secret using the updated shares
        let recres = reconstruct_secret(&update_shares);
        assert!(recres.is_ok());
        assert_eq!(recres.unwrap(), s);
    }

    #[test]
    fn share_update_valid_multiple_updates() {
        let s = Secret::from(42u32);

        let res = generate_shares(s, 5, 2);
        assert!(res.is_ok());
        let (com, shares) = res.unwrap();

        for _ in 0..5 {
            let update_res = update_shares(&com, &shares);
            assert!(update_res.is_ok());
            let (update_com, update_shares) = update_res.unwrap();

            for share in update_shares {
                let is_valid = verify_share(share, &update_com);
                assert!(is_valid.is_ok());
                assert!(is_valid.unwrap());
            }
        }
    }
}