commit 90c7382c1721e5a020178cb6ac55385ec857ddd9 Author: Aitor Ruano Date: Fri Jan 10 17:08:30 2020 +0100 initial commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..f03942d --- /dev/null +++ b/.gitignore @@ -0,0 +1,5 @@ +/target +**/*.rs.bk +Cargo.lock + +.vscode diff --git a/Cargo.toml b/Cargo.toml new file mode 100644 index 0000000..9a0f735 --- /dev/null +++ b/Cargo.toml @@ -0,0 +1,31 @@ +[package] +name = "sharks" +version = "0.1.0" +authors = ["Aitor Ruano "] +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 diff --git a/LICENSE-APACHE b/LICENSE-APACHE new file mode 100644 index 0000000..af1551d --- /dev/null +++ b/LICENSE-APACHE @@ -0,0 +1,201 @@ +Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..e69de29 diff --git a/benches/benchmarks.rs b/benches/benchmarks.rs new file mode 100644 index 0000000..203557c --- /dev/null +++ b/benches/benchmarks.rs @@ -0,0 +1,23 @@ + +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 = 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); diff --git a/src/lib.rs b/src/lib.rs new file mode 100644 index 0000000..c6fc799 --- /dev/null +++ b/src/lib.rs @@ -0,0 +1,118 @@ +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 { + 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 = shamir.iter_shares(12345).unwrap().take(10).collect(); + /// ``` + pub fn iter_shares(&self, secret: u128) -> Result, &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) -> Result { + 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); + } +} diff --git a/src/math.rs b/src/math.rs new file mode 100644 index 0000000..2c0a0ba --- /dev/null +++ b/src/math.rs @@ -0,0 +1,103 @@ +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, 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::()*yj % p + ) + .sum::() % 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) { + 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, p: u128) -> impl Iterator { + (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)]); + } +} diff --git a/src/mersenne.rs b/src/mersenne.rs new file mode 100644 index 0000000..97ea3cd --- /dev/null +++ b/src/mersenne.rs @@ -0,0 +1,16 @@ +/// 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 +];