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/target
**/*.rs.bk
Cargo.lock
.vscode

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[package]
name = "sharks"
version = "0.1.0"
authors = ["Aitor Ruano <codearm@pm.me>"]
description = "Fast, secure and minimal Shamir's Secret Sharing library crate"
homepage = "https://github.com/c0dearm/sharks"
repository = "https://github.com/c0dearm/sharks"
readme = "README.md"
keywords = ["shamir", "secret", "sharing", "share", "crypto"]
categories = ["algorithms", "cryptography", "mathematics"]
license = "MIT/Apache-2.0"
edition = "2018"
[badges]
is-it-maintained-issue-resolution = { repository = "https://github.com/c0dearm/sharks" }
is-it-maintained-open-issues = { repository = "https://github.com/c0dearm/sharks" }
maintenance = { status = "actively-developed" }
# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
[dependencies]
rand = "0.7"
num-bigint = "0.2"
num-traits = "0.2"
[dev-dependencies]
criterion = "0.3"
[[bench]]
name = "benchmarks"
harness = false

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MIT License
Copyright (c) 2020 Aitor Ruano Miralles
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use std::collections::HashMap;
use criterion::{black_box, criterion_group, criterion_main, Criterion};
use sharks::SecretShares;
fn secret_shares_generation(c: &mut Criterion) {
let shamir = SecretShares::new(1000, 128).unwrap();
let mut iter = shamir.iter_shares(12345).unwrap();
c.bench_function("obtain_shares_iterator", |b| b.iter(|| shamir.iter_shares(black_box(12345))));
c.bench_function("step_shares_iterator", |b| b.iter(|| iter.next()));
}
fn secret_from_shares(c: &mut Criterion) {
let shamir = SecretShares::new(10, 128).unwrap();
let shares: HashMap<u128,u128> = shamir.iter_shares(12345).unwrap().take(100).collect();
c.bench_function("recover_secret", |b| b.iter(|| shamir.secret_from(black_box(&shares))));
}
criterion_group!(benches, secret_shares_generation, secret_from_shares);
criterion_main!(benches);

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use std::collections::HashMap;
mod mersenne;
mod math;
/// Generate new [Shamir's secret shares](https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing) or recover secrets from them.
pub struct SecretShares {
min_shares: usize,
prime: u128,
}
impl SecretShares {
/// Returns a result containing a`SecretShares` instance if parameters are reasonable.
///
/// `security_level` is the index of the [Mersenne prime](https://en.wikipedia.org/wiki/Mersenne_prime) to use as the finite field prime modulo (the higher the more secure, but slower).
/// Currently, only up to 12 is supported (`p=127, Mp = 2^127 - 1`).
///
/// If `min_shares` is larger or equal to the Mersenne prime an error is returned, as this configuration would generate insecure shares.
///
/// Example, create an instance with minimum 3 shares to recover a secret and 128 bits of security:
/// ```
/// let shamir = sharks::SecretShares::new(3, 12);
/// assert!(shamir.is_ok());
/// ```
pub fn new(min_shares: usize, security_level: usize) -> Result<Self, &'static str> {
let security_level = std::cmp::min(security_level - 1, mersenne::EXPONENTS.len() - 1);
let prime = u128::pow(2, mersenne::EXPONENTS[security_level]) - 1;
if (min_shares as u128) < prime {
Ok(SecretShares { min_shares, prime })
} else {
Err("Minimum shares for recovery is too large for current security level")
}
}
/// Given a `secret` returns a result with an iterator which generates shares `(x, f(x))` for x from [1, p).
///
/// If `secret` is larger or equal than the Mersenne prime an error is returned, as it would be irrecoverable.
///
/// Example, generate 10 shares for secret `12345`:
/// ```
/// # use std::collections::HashMap;
/// let shamir = sharks::SecretShares::new(3, 12).unwrap();
/// let shares: HashMap<u128, u128> = shamir.iter_shares(12345).unwrap().take(10).collect();
/// ```
pub fn iter_shares(&self, secret: u128) -> Result<impl Iterator<Item = (u128, u128)>, &str> {
if secret < self.prime {
let (p, coeffs) = math::compute_coeffs(secret, self.min_shares, self.prime);
Ok(math::get_evaluator(coeffs, p))
} else {
Err("Secret is too large for current security level")
}
}
/// Given a set of distinct `shares`, returns a result with the recovered secret.
///
/// If the number of `shares` is less than the number of minimum shares an error is returned as the secret is irrecoverable.
///
/// Example, recover the `12345` secret:
/// ```
/// let shamir = sharks::SecretShares::new(3, 12).unwrap();
/// let shares = shamir.iter_shares(12345).unwrap().take(3).collect();
/// let secret = shamir.secret_from(&shares).unwrap();
/// assert_eq!(secret, 12345);
/// ```
pub fn secret_from(&self, shares: &HashMap<u128, u128>) -> Result<u128, &str> {
if shares.len() < self.min_shares {
Err("Not enough shares to recover secret")
} else {
Ok(math::lagrange_root(shares, self.prime))
}
}
}
#[cfg(test)]
mod tests {
use super::SecretShares;
#[test]
fn test_security_level_range() {
let shamir = SecretShares::new(10, 1000).unwrap();
assert_eq!(shamir.prime, u128::pow(2, 127) - 1);
let shamir = SecretShares::new(2, 1).unwrap();
assert_eq!(shamir.prime, 3);
}
#[test]
fn test_min_shares_too_large() {
let shamir = SecretShares::new(3, 1);
assert!(shamir.is_err());
}
#[test]
fn test_secret_too_large() {
let shamir = SecretShares::new(2, 1).unwrap();
let shares = shamir.iter_shares(3);
assert!(shares.is_err());
}
#[test]
fn test_insufficient_shares() {
let shamir = SecretShares::new(2, 1).unwrap();
let shares = shamir.iter_shares(2).unwrap().take(1).collect();
let secret = shamir.secret_from(&shares);
assert!(secret.is_err());
}
#[test]
fn test_integration() {
let shamir = SecretShares::new(10, 128).unwrap();
let shares = shamir.iter_shares(12345).unwrap().take(100).collect();
let secret = shamir.secret_from(&shares).unwrap();
assert_eq!(secret, 12345);
}
}

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use std::collections::HashMap;
use num_bigint::{BigInt, BigUint};
use num_traits::Zero;
use num_traits::cast::ToPrimitive;
use rand::distributions::{Distribution, Uniform};
/// A module that contains necessary algorithms to compute Shamir's shares and recover secrets
/// Computes `num/(num - b) mod p`, a necessary step to compute the [root of the Lagrange polynomial](https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing#Computationally_efficient_approach).
/// To find the modulo multiplicative inverse of `num - b` the [Extended Euclidean Algorithm](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse#Computation) is used.
fn div_diff_mod(num: &u128, b: &u128, p: u128) -> u128 {
let (mut m, mut x, mut inv, mut den) = (p, 0i128, 1i128, if num < b { p - (b - num) } else { num - b });
while den > 1 {
inv -= ((den/m) as i128)*x;
den %= m;
std::mem::swap(&mut den, &mut m);
std::mem::swap(&mut x, &mut inv);
}
let mut res = BigInt::from(inv);
if inv < 0 { res += p }
(num*res % p).to_u128().unwrap()
}
/// Finds the [root of the Lagrange polynomial](https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing#Computationally_efficient_approach).
pub fn lagrange_root(points: &HashMap<u128, u128>, p: u128) -> u128 {
(points.iter().enumerate()
.map(|(j, (xj, yj))|
points.iter().enumerate().filter(|(m, _)| *m != j)
.map(|(_, (xm, _))|
div_diff_mod(xm, xj, p)
)
.product::<BigUint>()*yj % p
)
.sum::<BigUint>() % p)
.to_u128().unwrap()
}
/// Generates `k` polynomial coefficients, being the last one `s` and the others randomly generated between `[1, p)`.
/// Coefficient degrees go from higher to lower in the returned vector order.
pub fn compute_coeffs(s: u128, k: usize, p: u128) -> (u128, Vec<u128>) {
let mut coeffs = Vec::with_capacity(k);
let between = Uniform::new(1, p);
let mut rng = rand::thread_rng();
for _ in 1..k {
coeffs.push(between.sample(&mut rng));
}
coeffs.push(s);
(p, coeffs)
}
/// Given a set of polynomial coefficients `coeffs` and a modulus `p`, returns an iterator that computes a `(x, f(x) mod p)` point
/// on each iteration. The iterator starts for `x = 1` and ends at `x = p-1`.
pub fn get_evaluator(coeffs: Vec<u128>, p: u128) -> impl Iterator<Item = (u128, u128)> {
(1..p).map(move |x| (x, coeffs.iter().fold(BigUint::zero(), |acc, c| (acc*x + c) % p).to_u128().unwrap()))
}
#[cfg(test)]
mod tests {
use super::{div_diff_mod, lagrange_root, compute_coeffs, get_evaluator};
#[test]
fn div_diff_mod_works() {
let res = div_diff_mod(&2, &1, 7);
assert_eq!(res, 2);
let res = div_diff_mod(&1, &2, 7);
assert_eq!(res, 6);
}
#[test]
fn lagrange_root_works() {
let iter = get_evaluator(vec![3,2,1], 7);
let values = iter.take(3).collect();
let root = lagrange_root(&values, 7);
assert_eq!(root, 1);
let iter = get_evaluator(vec![3,2,5], 7);
let values = iter.take(3).collect();
let root = lagrange_root(&values, 7);
assert_eq!(root, 5);
}
#[test]
fn compute_coeffs_works() {
let coeffs = compute_coeffs(1, 4, 7);
assert_eq!(coeffs.0, 7);
assert_eq!(coeffs.1.len(), 4);
assert_eq!(coeffs.1[3], 1);
}
#[test]
fn evaluator_works() {
let iter = get_evaluator(vec![3,2,5], 7);
let values: Vec<_> = iter.take(2).collect();
assert_eq!(values, vec![(1,3), (2,0)]);
}
}

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/// A table containing the exponents of found [Mersenne primes](https://en.wikipedia.org/wiki/Mersenne_prime)
/// To be used as finite field modulo for shares and secret recovery computation
pub const EXPONENTS: [u32; 12] = [
2,
3,
5,
7,
13,
17,
19,
31,
61,
89,
107,
127
];