openethereum/secret_store/src/key_server_cluster/math.rs
Toralf Wittner 2b05eb43a9 Add util/mem to zero out memory on drop. (#8356)
* Add `util/mem` to zero out memory on drop.

* Remove nonsense.

* Remove `Into` impls for `Memzero`.

* Update ethereum-types and remove H256Mut.
2018-04-11 13:57:12 +02:00

1080 lines
42 KiB
Rust

// Copyright 2015-2017 Parity Technologies (UK) Ltd.
// This file is part of Parity.
// Parity is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// Parity is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with Parity. If not, see <http://www.gnu.org/licenses/>.
use ethkey::{Public, Secret, Signature, Random, Generator, math};
use ethereum_types::{H256, U256};
use hash::keccak;
use key_server_cluster::Error;
/// Encryption result.
#[derive(Debug)]
pub struct EncryptedSecret {
/// Common encryption point.
pub common_point: Public,
/// Ecnrypted point.
pub encrypted_point: Public,
}
/// Create zero scalar.
pub fn zero_scalar() -> Secret {
Secret::zero()
}
/// Convert hash to EC scalar (modulo curve order).
pub fn to_scalar(hash: H256) -> Result<Secret, Error> {
let scalar: U256 = hash.into();
let scalar: H256 = (scalar % math::curve_order()).into();
let scalar = Secret::from(scalar.0);
scalar.check_validity()?;
Ok(scalar)
}
/// Generate random scalar.
pub fn generate_random_scalar() -> Result<Secret, Error> {
Ok(Random.generate()?.secret().clone())
}
/// Generate random point.
pub fn generate_random_point() -> Result<Public, Error> {
Ok(Random.generate()?.public().clone())
}
/// Get X coordinate of point.
fn public_x(public: &Public) -> H256 {
public[0..32].into()
}
/// Get Y coordinate of point.
fn public_y(public: &Public) -> H256 {
public[32..64].into()
}
/// Compute publics sum.
pub fn compute_public_sum<'a, I>(mut publics: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
let mut sum = publics.next().expect("compute_public_sum is called when there's at least one public; qed").clone();
while let Some(public) = publics.next() {
math::public_add(&mut sum, &public)?;
}
Ok(sum)
}
/// Compute secrets sum.
pub fn compute_secret_sum<'a, I>(mut secrets: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
let mut sum = secrets.next().expect("compute_secret_sum is called when there's at least one secret; qed").clone();
while let Some(secret) = secrets.next() {
sum.add(secret)?;
}
Ok(sum)
}
/// Compute secrets multiplication.
pub fn compute_secret_mul(secret1: &Secret, secret2: &Secret) -> Result<Secret, Error> {
let mut secret_mul = secret1.clone();
secret_mul.mul(secret2)?;
Ok(secret_mul)
}
/// Compute secrets 'shadow' multiplication: coeff * multiplication(s[j] / (s[i] - s[j])) for every i != j
pub fn compute_shadow_mul<'a, I>(coeff: &Secret, self_secret: &Secret, mut other_secrets: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
// when there are no other secrets, only coeff is left
let other_secret = match other_secrets.next() {
Some(other_secret) => other_secret,
None => return Ok(coeff.clone()),
};
let mut shadow_mul = self_secret.clone();
shadow_mul.sub(other_secret)?;
shadow_mul.inv()?;
shadow_mul.mul(other_secret)?;
while let Some(other_secret) = other_secrets.next() {
let mut shadow_mul_element = self_secret.clone();
shadow_mul_element.sub(other_secret)?;
shadow_mul_element.inv()?;
shadow_mul_element.mul(other_secret)?;
shadow_mul.mul(&shadow_mul_element)?;
}
shadow_mul.mul(coeff)?;
Ok(shadow_mul)
}
/// Update point by multiplying to random scalar
pub fn update_random_point(point: &mut Public) -> Result<(), Error> {
Ok(math::public_mul_secret(point, &generate_random_scalar()?)?)
}
/// Generate random polynom of threshold degree
pub fn generate_random_polynom(threshold: usize) -> Result<Vec<Secret>, Error> {
(0..threshold + 1)
.map(|_| generate_random_scalar())
.collect()
}
/// Compute value of polynom, using `node_number` as argument
pub fn compute_polynom(polynom: &[Secret], node_number: &Secret) -> Result<Secret, Error> {
debug_assert!(!polynom.is_empty());
let mut result = polynom[0].clone();
for i in 1..polynom.len() {
// calculate pow(node_number, i)
let mut appendum = node_number.clone();
appendum.pow(i)?;
// calculate coeff * pow(point, i)
appendum.mul(&polynom[i])?;
// calculate result + coeff * pow(point, i)
result.add(&appendum)?;
}
Ok(result)
}
/// Generate public keys for other participants.
pub fn public_values_generation(threshold: usize, derived_point: &Public, polynom1: &[Secret], polynom2: &[Secret]) -> Result<Vec<Public>, Error> {
debug_assert_eq!(polynom1.len(), threshold + 1);
debug_assert_eq!(polynom2.len(), threshold + 1);
// compute t+1 public values
let mut publics = Vec::with_capacity(threshold + 1);
for i in 0..threshold + 1 {
let coeff1 = &polynom1[i];
let mut multiplication1 = math::generation_point();
math::public_mul_secret(&mut multiplication1, &coeff1)?;
let coeff2 = &polynom2[i];
let mut multiplication2 = derived_point.clone();
math::public_mul_secret(&mut multiplication2, &coeff2)?;
math::public_add(&mut multiplication1, &multiplication2)?;
publics.push(multiplication1);
}
debug_assert_eq!(publics.len(), threshold + 1);
Ok(publics)
}
/// Check keys passed by other participants.
pub fn keys_verification(threshold: usize, derived_point: &Public, number_id: &Secret, secret1: &Secret, secret2: &Secret, publics: &[Public]) -> Result<bool, Error> {
// calculate left part
let mut multiplication1 = math::generation_point();
math::public_mul_secret(&mut multiplication1, secret1)?;
let mut multiplication2 = derived_point.clone();
math::public_mul_secret(&mut multiplication2, secret2)?;
math::public_add(&mut multiplication1, &multiplication2)?;
let left = multiplication1;
// calculate right part
let mut right = publics[0].clone();
for i in 1..threshold + 1 {
let mut secret_pow = number_id.clone();
secret_pow.pow(i)?;
let mut public_k = publics[i].clone();
math::public_mul_secret(&mut public_k, &secret_pow)?;
math::public_add(&mut right, &public_k)?;
}
Ok(left == right)
}
/// Compute secret subshare from passed secret value.
pub fn compute_secret_subshare<'a, I>(threshold: usize, secret_value: &Secret, sender_id_number: &Secret, other_id_numbers: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
let mut subshare = compute_shadow_mul(secret_value, sender_id_number, other_id_numbers)?;
if threshold % 2 != 0 {
subshare.neg()?;
}
Ok(subshare)
}
/// Compute secret share.
pub fn compute_secret_share<'a, I>(secret_values: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
compute_secret_sum(secret_values)
}
/// Compute public key share.
pub fn compute_public_share(self_secret_value: &Secret) -> Result<Public, Error> {
let mut public_share = math::generation_point();
math::public_mul_secret(&mut public_share, self_secret_value)?;
Ok(public_share)
}
/// Compute joint public key.
pub fn compute_joint_public<'a, I>(public_shares: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
compute_public_sum(public_shares)
}
/// Compute joint secret key from N secret coefficients.
#[cfg(test)]
pub fn compute_joint_secret<'a, I>(secret_coeffs: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
compute_secret_sum(secret_coeffs)
}
/// Compute joint secret key from t+1 secret shares.
pub fn compute_joint_secret_from_shares<'a>(t: usize, secret_shares: &[&'a Secret], id_numbers: &[&'a Secret]) -> Result<Secret, Error> {
let secret_share_0 = secret_shares[0];
let id_number_0 = id_numbers[0];
let other_nodes_numbers = id_numbers.iter().skip(1).cloned();
let mut result = compute_node_shadow(secret_share_0, id_number_0, other_nodes_numbers)?;
for i in 1..secret_shares.len() {
let secret_share_i = secret_shares[i];
let id_number_i = id_numbers[i];
let other_nodes_numbers = id_numbers.iter().enumerate().filter(|&(j, _)| j != i).map(|(_, n)| n).cloned();
let addendum = compute_node_shadow(secret_share_i, id_number_i, other_nodes_numbers)?;
result.add(&addendum)?;
}
if t % 2 != 0 {
result.neg()?;
}
Ok(result)
}
/// Encrypt secret with joint public key.
pub fn encrypt_secret(secret: &Public, joint_public: &Public) -> Result<EncryptedSecret, Error> {
// this is performed by KS-cluster client (or KS master)
let key_pair = Random.generate()?;
// k * T
let mut common_point = math::generation_point();
math::public_mul_secret(&mut common_point, key_pair.secret())?;
// M + k * y
let mut encrypted_point = joint_public.clone();
math::public_mul_secret(&mut encrypted_point, key_pair.secret())?;
math::public_add(&mut encrypted_point, secret)?;
Ok(EncryptedSecret {
common_point: common_point,
encrypted_point: encrypted_point,
})
}
/// Compute shadow for the node.
pub fn compute_node_shadow<'a, I>(node_secret_share: &Secret, node_number: &Secret, other_nodes_numbers: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
compute_shadow_mul(node_secret_share, node_number, other_nodes_numbers)
}
/// Compute shadow point for the node.
pub fn compute_node_shadow_point(access_key: &Secret, common_point: &Public, node_shadow: &Secret, decrypt_shadow: Option<Secret>) -> Result<(Public, Option<Secret>), Error> {
let mut shadow_key = node_shadow.clone();
let decrypt_shadow = match decrypt_shadow {
None => None,
Some(mut decrypt_shadow) => {
// update shadow key
shadow_key.mul(&decrypt_shadow)?;
// now udate decrypt shadow itself
decrypt_shadow.dec()?;
decrypt_shadow.mul(node_shadow)?;
Some(decrypt_shadow)
}
};
shadow_key.mul(access_key)?;
let mut node_shadow_point = common_point.clone();
math::public_mul_secret(&mut node_shadow_point, &shadow_key)?;
Ok((node_shadow_point, decrypt_shadow))
}
/// Compute joint shadow point.
pub fn compute_joint_shadow_point<'a, I>(nodes_shadow_points: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
compute_public_sum(nodes_shadow_points)
}
/// Compute joint shadow point (version for tests).
#[cfg(test)]
pub fn compute_joint_shadow_point_test<'a, I>(access_key: &Secret, common_point: &Public, nodes_shadows: I) -> Result<Public, Error> where I: Iterator<Item=&'a Secret> {
let mut joint_shadow = compute_secret_sum(nodes_shadows)?;
joint_shadow.mul(access_key)?;
let mut joint_shadow_point = common_point.clone();
math::public_mul_secret(&mut joint_shadow_point, &joint_shadow)?;
Ok(joint_shadow_point)
}
/// Decrypt data using joint shadow point.
pub fn decrypt_with_joint_shadow(threshold: usize, access_key: &Secret, encrypted_point: &Public, joint_shadow_point: &Public) -> Result<Public, Error> {
let mut inv_access_key = access_key.clone();
inv_access_key.inv()?;
let mut mul = joint_shadow_point.clone();
math::public_mul_secret(&mut mul, &inv_access_key)?;
let mut decrypted_point = encrypted_point.clone();
if threshold % 2 != 0 {
math::public_add(&mut decrypted_point, &mul)?;
} else {
math::public_sub(&mut decrypted_point, &mul)?;
}
Ok(decrypted_point)
}
/// Prepare common point for shadow decryption.
pub fn make_common_shadow_point(threshold: usize, mut common_point: Public) -> Result<Public, Error> {
if threshold % 2 != 1 {
Ok(common_point)
} else {
math::public_negate(&mut common_point)?;
Ok(common_point)
}
}
/// Decrypt shadow-encrypted secret.
#[cfg(test)]
pub fn decrypt_with_shadow_coefficients(mut decrypted_shadow: Public, mut common_shadow_point: Public, shadow_coefficients: Vec<Secret>) -> Result<Public, Error> {
let shadow_coefficients_sum = compute_secret_sum(shadow_coefficients.iter())?;
math::public_mul_secret(&mut common_shadow_point, &shadow_coefficients_sum)?;
math::public_add(&mut decrypted_shadow, &common_shadow_point)?;
Ok(decrypted_shadow)
}
/// Decrypt data using joint secret (version for tests).
#[cfg(test)]
pub fn decrypt_with_joint_secret(encrypted_point: &Public, common_point: &Public, joint_secret: &Secret) -> Result<Public, Error> {
let mut common_point_mul = common_point.clone();
math::public_mul_secret(&mut common_point_mul, joint_secret)?;
let mut decrypted_point = encrypted_point.clone();
math::public_sub(&mut decrypted_point, &common_point_mul)?;
Ok(decrypted_point)
}
/// Combine message hash with public key X coordinate.
pub fn combine_message_hash_with_public(message_hash: &H256, public: &Public) -> Result<Secret, Error> {
// buffer is just [message_hash | public.x]
let mut buffer = [0; 64];
buffer[0..32].copy_from_slice(&message_hash[0..32]);
buffer[32..64].copy_from_slice(&public[0..32]);
// calculate hash of buffer
let hash = keccak(&buffer[..]);
// map hash to EC finite field value
to_scalar(hash)
}
/// Compute Schnorr signature share.
pub fn compute_schnorr_signature_share<'a, I>(threshold: usize, combined_hash: &Secret, one_time_secret_coeff: &Secret, node_secret_share: &Secret, node_number: &Secret, other_nodes_numbers: I)
-> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
let mut sum = one_time_secret_coeff.clone();
let mut subtrahend = compute_shadow_mul(combined_hash, node_number, other_nodes_numbers)?;
subtrahend.mul(node_secret_share)?;
if threshold % 2 == 0 {
sum.sub(&subtrahend)?;
} else {
sum.add(&subtrahend)?;
}
Ok(sum)
}
/// Check Schnorr signature share.
pub fn _check_schnorr_signature_share<'a, I>(_combined_hash: &Secret, _signature_share: &Secret, _public_share: &Public, _one_time_public_share: &Public, _node_numbers: I)
-> Result<bool, Error> where I: Iterator<Item=&'a Secret> {
// TODO [Trust]: in paper partial signature is checked using comparison:
// sig[i] * T = r[i] - c * lagrange_coeff(i) * y[i]
// => (k[i] - c * lagrange_coeff(i) * s[i]) * T = r[i] - c * lagrange_coeff(i) * y[i]
// => k[i] * T - c * lagrange_coeff(i) * s[i] * T = k[i] * T - c * lagrange_coeff(i) * y[i]
// => this means that y[i] = s[i] * T
// but when verifying signature (for t = 1), nonce public (r) is restored using following expression:
// r = (sig[0] + sig[1]) * T - c * y
// r = (k[0] - c * lagrange_coeff(0) * s[0] + k[1] - c * lagrange_coeff(1) * s[1]) * T - c * y
// r = (k[0] + k[1]) * T - c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T - c * y
// r = r - c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T - c * y
// => -c * y = c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T
// => -y = (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T
// => y[i] != s[i] * T
// => some other way is required
Ok(true)
}
/// Compute Schnorr signature.
pub fn compute_schnorr_signature<'a, I>(signature_shares: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
compute_secret_sum(signature_shares)
}
/// Locally compute Schnorr signature as described in https://en.wikipedia.org/wiki/Schnorr_signature#Signing.
#[cfg(test)]
pub fn local_compute_schnorr_signature(nonce: &Secret, secret: &Secret, message_hash: &Secret) -> Result<(Secret, Secret), Error> {
let mut nonce_public = math::generation_point();
math::public_mul_secret(&mut nonce_public, &nonce).unwrap();
let combined_hash = combine_message_hash_with_public(message_hash, &nonce_public)?;
let mut sig_subtrahend = combined_hash.clone();
sig_subtrahend.mul(secret)?;
let mut sig = nonce.clone();
sig.sub(&sig_subtrahend)?;
Ok((combined_hash, sig))
}
/// Verify Schnorr signature as described in https://en.wikipedia.org/wiki/Schnorr_signature#Verifying.
#[cfg(test)]
pub fn verify_schnorr_signature(public: &Public, signature: &(Secret, Secret), message_hash: &H256) -> Result<bool, Error> {
let mut addendum = math::generation_point();
math::public_mul_secret(&mut addendum, &signature.1)?;
let mut nonce_public = public.clone();
math::public_mul_secret(&mut nonce_public, &signature.0)?;
math::public_add(&mut nonce_public, &addendum)?;
let combined_hash = combine_message_hash_with_public(message_hash, &nonce_public)?;
Ok(combined_hash == signature.0)
}
/// Compute R part of ECDSA signature.
pub fn compute_ecdsa_r(nonce_public: &Public) -> Result<Secret, Error> {
to_scalar(public_x(nonce_public))
}
/// Compute share of S part of ECDSA signature.
pub fn compute_ecdsa_s_share(inv_nonce_share: &Secret, inv_nonce_mul_secret: &Secret, signature_r: &Secret, message_hash: &Secret) -> Result<Secret, Error> {
let mut nonce_inv_share_mul_message_hash = inv_nonce_share.clone();
nonce_inv_share_mul_message_hash.mul(&message_hash.clone().into())?;
let mut nonce_inv_share_mul_secret_share_mul_r = inv_nonce_mul_secret.clone();
nonce_inv_share_mul_secret_share_mul_r.mul(signature_r)?;
let mut signature_s_share = nonce_inv_share_mul_message_hash;
signature_s_share.add(&nonce_inv_share_mul_secret_share_mul_r)?;
Ok(signature_s_share)
}
/// Compute S part of ECDSA signature from shares.
pub fn compute_ecdsa_s(t: usize, signature_s_shares: &[Secret], id_numbers: &[Secret]) -> Result<Secret, Error> {
let double_t = t * 2;
debug_assert!(id_numbers.len() >= double_t + 1);
debug_assert_eq!(signature_s_shares.len(), id_numbers.len());
compute_joint_secret_from_shares(double_t,
&signature_s_shares.iter().take(double_t + 1).collect::<Vec<_>>(),
&id_numbers.iter().take(double_t + 1).collect::<Vec<_>>())
}
/// Serialize ECDSA signature to [r][s]v form.
pub fn serialize_ecdsa_signature(nonce_public: &Public, signature_r: Secret, mut signature_s: Secret) -> Signature {
// compute recovery param
let mut signature_v = {
let nonce_public_x = public_x(nonce_public);
let nonce_public_y: U256 = public_y(nonce_public).into();
let nonce_public_y_is_odd = !(nonce_public_y % 2.into()).is_zero();
let bit0 = if nonce_public_y_is_odd { 1u8 } else { 0u8 };
let bit1 = if nonce_public_x != *signature_r { 2u8 } else { 0u8 };
bit0 | bit1
};
// fix high S
let curve_order = math::curve_order();
let curve_order_half = curve_order / 2.into();
let s_numeric: U256 = (*signature_s).into();
if s_numeric > curve_order_half {
let signature_s_hash: H256 = (curve_order - s_numeric).into();
signature_s = signature_s_hash.into();
signature_v ^= 1;
}
// serialize as [r][s]v
let mut signature = [0u8; 65];
signature[..32].copy_from_slice(&**signature_r);
signature[32..64].copy_from_slice(&**signature_s);
signature[64] = signature_v;
signature.into()
}
/// Compute share of ECDSA reversed-nonce coefficient. Result of this_coeff * secret_share gives us a share of inv(nonce).
pub fn compute_ecdsa_inversed_secret_coeff_share(secret_share: &Secret, nonce_share: &Secret, zero_share: &Secret) -> Result<Secret, Error> {
let mut coeff = secret_share.clone();
coeff.mul(nonce_share).unwrap();
coeff.add(zero_share).unwrap();
Ok(coeff)
}
/// Compute ECDSA reversed-nonce coefficient from its shares. Result of this_coeff * secret_share gives us a share of inv(nonce).
pub fn compute_ecdsa_inversed_secret_coeff_from_shares(t: usize, id_numbers: &[Secret], shares: &[Secret]) -> Result<Secret, Error> {
debug_assert_eq!(shares.len(), 2 * t + 1);
debug_assert_eq!(shares.len(), id_numbers.len());
let u_shares = (0..2*t+1).map(|i| compute_shadow_mul(&shares[i], &id_numbers[i], id_numbers.iter().enumerate()
.filter(|&(j, _)| i != j)
.map(|(_, id)| id)
.take(2 * t))).collect::<Result<Vec<_>, _>>()?;
// compute u
let u = compute_secret_sum(u_shares.iter())?;
// compute inv(u)
let mut u_inv = u;
u_inv.inv()?;
Ok(u_inv)
}
#[cfg(test)]
pub mod tests {
use std::iter::once;
use ethkey::{KeyPair, recover, verify_public};
use super::*;
#[derive(Clone)]
struct KeyGenerationArtifacts {
id_numbers: Vec<Secret>,
polynoms1: Vec<Vec<Secret>>,
secrets1: Vec<Vec<Secret>>,
public_shares: Vec<Public>,
secret_shares: Vec<Secret>,
joint_public: Public,
}
struct ZeroGenerationArtifacts {
polynoms1: Vec<Vec<Secret>>,
secret_shares: Vec<Secret>,
}
fn prepare_polynoms1(t: usize, n: usize, secret_required: Option<Secret>) -> Vec<Vec<Secret>> {
let mut polynoms1: Vec<_> = (0..n).map(|_| generate_random_polynom(t).unwrap()).collect();
// if we need specific secret to be shared, update polynoms so that sum of their free terms = required secret
if let Some(mut secret_required) = secret_required {
for polynom1 in polynoms1.iter_mut().take(n - 1) {
let secret_coeff1 = generate_random_scalar().unwrap();
secret_required.sub(&secret_coeff1).unwrap();
polynom1[0] = secret_coeff1;
}
polynoms1[n - 1][0] = secret_required;
}
polynoms1
}
fn run_key_generation(t: usize, n: usize, id_numbers: Option<Vec<Secret>>, secret_required: Option<Secret>) -> KeyGenerationArtifacts {
// === PART1: DKG ===
// data, gathered during initialization
let derived_point = Random.generate().unwrap().public().clone();
let id_numbers: Vec<_> = match id_numbers {
Some(id_numbers) => id_numbers,
None => (0..n).map(|_| generate_random_scalar().unwrap()).collect(),
};
// data, generated during keys dissemination
let polynoms1 = prepare_polynoms1(t, n, secret_required);
let secrets1: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&polynoms1[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
// following data is used only on verification step
let polynoms2: Vec<_> = (0..n).map(|_| generate_random_polynom(t).unwrap()).collect();
let secrets2: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&polynoms2[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
let publics: Vec<_> = (0..n).map(|i| public_values_generation(t, &derived_point, &polynoms1[i], &polynoms2[i]).unwrap()).collect();
// keys verification
(0..n).map(|i| (0..n).map(|j| if i != j {
assert!(keys_verification(t, &derived_point, &id_numbers[i], &secrets1[j][i], &secrets2[j][i], &publics[j]).unwrap());
}).collect::<Vec<_>>()).collect::<Vec<_>>();
// data, generated during keys generation
let public_shares: Vec<_> = (0..n).map(|i| compute_public_share(&polynoms1[i][0]).unwrap()).collect();
let secret_shares: Vec<_> = (0..n).map(|i| compute_secret_share(secrets1.iter().map(|s| &s[i])).unwrap()).collect();
// joint public key, as a result of DKG
let joint_public = compute_joint_public(public_shares.iter()).unwrap();
KeyGenerationArtifacts {
id_numbers: id_numbers,
polynoms1: polynoms1,
secrets1: secrets1,
public_shares: public_shares,
secret_shares: secret_shares,
joint_public: joint_public,
}
}
fn run_zero_key_generation(t: usize, n: usize, id_numbers: &[Secret]) -> ZeroGenerationArtifacts {
// data, generated during keys dissemination
let polynoms1 = prepare_polynoms1(t, n, Some(zero_scalar()));
let secrets1: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&polynoms1[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
// data, generated during keys generation
let secret_shares: Vec<_> = (0..n).map(|i| compute_secret_share(secrets1.iter().map(|s| &s[i])).unwrap()).collect();
ZeroGenerationArtifacts {
polynoms1: polynoms1,
secret_shares: secret_shares,
}
}
fn run_key_share_refreshing(old_t: usize, new_t: usize, new_n: usize, old_artifacts: &KeyGenerationArtifacts) -> KeyGenerationArtifacts {
// === share refreshing protocol from
// === based on "Verifiable Secret Redistribution for Threshold Sharing Schemes"
// === http://www.cs.cmu.edu/~wing/publications/CMU-CS-02-114.pdf
// generate new id_numbers for new nodes
let new_nodes = new_n.saturating_sub(old_artifacts.id_numbers.len());
let id_numbers: Vec<_> = old_artifacts.id_numbers.iter().take(new_n).cloned()
.chain((0..new_nodes).map(|_| generate_random_scalar().unwrap()))
.collect();
// on every authorized node: generate random polynomial ai(j) = si + ... + ai[new_t - 1] * j^(new_t - 1)
let mut subshare_polynoms = Vec::new();
for i in 0..old_t+1 {
let mut subshare_polynom = generate_random_polynom(new_t).unwrap();
subshare_polynom[0] = old_artifacts.secret_shares[i].clone();
subshare_polynoms.push(subshare_polynom);
}
// on every authorized node: calculate subshare for every new node
let mut subshares = Vec::new();
for j in 0..new_n {
let mut subshares_to_j = Vec::new();
for i in 0..old_t+1 {
let subshare_from_i_to_j = compute_polynom(&subshare_polynoms[i], &id_numbers[j]).unwrap();
subshares_to_j.push(subshare_from_i_to_j);
}
subshares.push(subshares_to_j);
}
// on every new node: generate new share using Lagrange interpolation
// on every node: generate new share using Lagrange interpolation
let mut new_secret_shares = Vec::new();
for j in 0..new_n {
let mut subshares_to_j = Vec::new();
for i in 0..old_t+1 {
let subshare_from_i = &subshares[j][i];
let id_number_i = &id_numbers[i];
let other_id_numbers = (0usize..old_t+1).filter(|j| *j != i).map(|j| &id_numbers[j]);
let mut subshare_from_i = compute_shadow_mul(subshare_from_i, id_number_i, other_id_numbers).unwrap();
if old_t % 2 != 0 {
subshare_from_i.neg().unwrap();
}
subshares_to_j.push(subshare_from_i);
}
new_secret_shares.push(compute_secret_sum(subshares_to_j.iter()).unwrap());
}
let mut result = old_artifacts.clone();
result.id_numbers = id_numbers;
result.secret_shares = new_secret_shares;
result
}
fn run_multiplication_protocol(t: usize, secret_shares1: &[Secret], secret_shares2: &[Secret]) -> Vec<Secret> {
let n = secret_shares1.len();
assert!(t * 2 + 1 <= n);
// shares of secrets multiplication = multiplication of secrets shares
let mul_shares: Vec<_> = (0..n).map(|i| {
let share1 = secret_shares1[i].clone();
let share2 = secret_shares2[i].clone();
let mut mul_share = share1;
mul_share.mul(&share2).unwrap();
mul_share
}).collect();
mul_shares
}
fn run_reciprocal_protocol(t: usize, artifacts: &KeyGenerationArtifacts) -> Vec<Secret> {
// === Given a secret x mod r which is shared among n players, it is
// === required to generate shares of inv(x) mod r with out revealing
// === any information about x or inv(x).
// === https://www.researchgate.net/publication/280531698_Robust_Threshold_Elliptic_Curve_Digital_Signature
// generate shared random secret e for given t
let n = artifacts.id_numbers.len();
assert!(t * 2 + 1 <= n);
let e_artifacts = run_key_generation(t, n, Some(artifacts.id_numbers.clone()), None);
// generate shares of zero for 2 * t threshold
let z_artifacts = run_zero_key_generation(2 * t, n, &artifacts.id_numbers);
// each player computes && broadcast u[i] = x[i] * e[i] + z[i]
let ui: Vec<_> = (0..n).map(|i| compute_ecdsa_inversed_secret_coeff_share(&artifacts.secret_shares[i],
&e_artifacts.secret_shares[i],
&z_artifacts.secret_shares[i]).unwrap()).collect();
// players can interpolate the polynomial of degree 2t and compute u && inv(u):
let u_inv = compute_ecdsa_inversed_secret_coeff_from_shares(t,
&artifacts.id_numbers.iter().take(2*t + 1).cloned().collect::<Vec<_>>(),
&ui.iter().take(2*t + 1).cloned().collect::<Vec<_>>()).unwrap();
// each player Pi computes his share of inv(x) as e[i] * inv(u)
let x_inv_shares: Vec<_> = (0..n).map(|i| {
let mut x_inv_share = e_artifacts.secret_shares[i].clone();
x_inv_share.mul(&u_inv).unwrap();
x_inv_share
}).collect();
x_inv_shares
}
pub fn do_encryption_and_decryption(t: usize, joint_public: &Public, id_numbers: &[Secret], secret_shares: &[Secret], joint_secret: Option<&Secret>, document_secret_plain: Public) -> (Public, Public) {
// === PART2: encryption using joint public key ===
// the next line is executed on KeyServer-client
let encrypted_secret = encrypt_secret(&document_secret_plain, &joint_public).unwrap();
// === PART3: decryption ===
// next line is executed on KeyServer client
let access_key = generate_random_scalar().unwrap();
// use t + 1 nodes to compute joint shadow point
let nodes_shadows: Vec<_> = (0..t + 1).map(|i|
compute_node_shadow(&secret_shares[i], &id_numbers[i], id_numbers.iter()
.enumerate()
.filter(|&(j, _)| j != i)
.take(t)
.map(|(_, id_number)| id_number)).unwrap()).collect();
let nodes_shadow_points: Vec<_> = nodes_shadows.iter()
.map(|s| compute_node_shadow_point(&access_key, &encrypted_secret.common_point, s, None).unwrap())
.map(|sp| sp.0)
.collect();
assert_eq!(nodes_shadows.len(), t + 1);
assert_eq!(nodes_shadow_points.len(), t + 1);
let joint_shadow_point = compute_joint_shadow_point(nodes_shadow_points.iter()).unwrap();
let joint_shadow_point_test = compute_joint_shadow_point_test(&access_key, &encrypted_secret.common_point, nodes_shadows.iter()).unwrap();
assert_eq!(joint_shadow_point, joint_shadow_point_test);
// decrypt encrypted secret using joint shadow point
let document_secret_decrypted = decrypt_with_joint_shadow(t, &access_key, &encrypted_secret.encrypted_point, &joint_shadow_point).unwrap();
// decrypt encrypted secret using joint secret [just for test]
let document_secret_decrypted_test = match joint_secret {
Some(joint_secret) => decrypt_with_joint_secret(&encrypted_secret.encrypted_point, &encrypted_secret.common_point, joint_secret).unwrap(),
None => document_secret_decrypted.clone(),
};
(document_secret_decrypted, document_secret_decrypted_test)
}
#[test]
fn full_encryption_math_session() {
let test_cases = [(0, 2), (1, 2), (1, 3), (2, 3), (1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5), (4, 5),
(1, 10), (2, 10), (3, 10), (4, 10), (5, 10), (6, 10), (7, 10), (8, 10), (9, 10)];
for &(t, n) in &test_cases {
let artifacts = run_key_generation(t, n, None, None);
// compute joint private key [just for test]
let joint_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
let joint_key_pair = KeyPair::from_secret(joint_secret.clone()).unwrap();
assert_eq!(&artifacts.joint_public, joint_key_pair.public());
// check secret shares computation [just for test]
let secret_shares_polynom: Vec<_> = (0..t + 1).map(|k| compute_secret_share(artifacts.polynoms1.iter().map(|p| &p[k])).unwrap()).collect();
let secret_shares_calculated_from_polynom: Vec<_> = artifacts.id_numbers.iter().map(|id_number| compute_polynom(&*secret_shares_polynom, id_number).unwrap()).collect();
assert_eq!(artifacts.secret_shares, secret_shares_calculated_from_polynom);
// now encrypt and decrypt data
let document_secret_plain = generate_random_point().unwrap();
let (document_secret_decrypted, document_secret_decrypted_test) =
do_encryption_and_decryption(t, &artifacts.joint_public, &artifacts.id_numbers, &artifacts.secret_shares, Some(&joint_secret), document_secret_plain.clone());
assert_eq!(document_secret_plain, document_secret_decrypted_test);
assert_eq!(document_secret_plain, document_secret_decrypted);
}
}
#[test]
fn local_signature_works() {
let key_pair = Random.generate().unwrap();
let message_hash = "0000000000000000000000000000000000000000000000000000000000000042".parse().unwrap();
let nonce = generate_random_scalar().unwrap();
let signature = local_compute_schnorr_signature(&nonce, key_pair.secret(), &message_hash).unwrap();
assert_eq!(verify_schnorr_signature(key_pair.public(), &signature, &message_hash), Ok(true));
}
#[test]
fn full_schnorr_signature_math_session() {
let test_cases = [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (1, 4), (2, 4), (3, 4), (1, 5), (2, 5), (3, 5), (4, 5),
(1, 10), (2, 10), (3, 10), (4, 10), (5, 10), (6, 10), (7, 10), (8, 10), (9, 10)];
for &(t, n) in &test_cases {
// hash of the message to be signed
let message_hash: Secret = "0000000000000000000000000000000000000000000000000000000000000042".parse().unwrap();
// === MiDS-S algorithm ===
// setup: all nodes share master secret key && every node knows master public key
let artifacts = run_key_generation(t, n, None, None);
// in this gap (not related to math):
// master node should ask every other node if it is able to do a signing
// if there are < than t+1 nodes, able to sign => error
// select t+1 nodes for signing session
// all steps below are for this subset of nodes
let n = t + 1;
// step 1: run DKG to generate one-time secret key (nonce)
let id_numbers = artifacts.id_numbers.iter().cloned().take(n).collect();
let one_time_artifacts = run_key_generation(t, n, Some(id_numbers), None);
// step 2: message hash && x coordinate of one-time public value are combined
let combined_hash = combine_message_hash_with_public(&message_hash, &one_time_artifacts.joint_public).unwrap();
// step 3: compute signature shares
let partial_signatures: Vec<_> = (0..n)
.map(|i| compute_schnorr_signature_share(
t,
&combined_hash,
&one_time_artifacts.polynoms1[i][0],
&artifacts.secret_shares[i],
&artifacts.id_numbers[i],
artifacts.id_numbers.iter()
.enumerate()
.filter(|&(j, _)| i != j)
.map(|(_, n)| n)
.take(t)
).unwrap())
.collect();
// step 4: receive and verify signatures shares from other nodes
let received_signatures: Vec<Vec<_>> = (0..n)
.map(|i| (0..n)
.filter(|j| i != *j)
.map(|j| {
let signature_share = partial_signatures[j].clone();
assert!(_check_schnorr_signature_share(&combined_hash,
&signature_share,
&artifacts.public_shares[j],
&one_time_artifacts.public_shares[j],
artifacts.id_numbers.iter().take(t)).unwrap_or(false));
signature_share
})
.collect())
.collect();
// step 5: compute signature
let signatures: Vec<_> = (0..n)
.map(|i| (combined_hash.clone(), compute_schnorr_signature(received_signatures[i].iter().chain(once(&partial_signatures[i]))).unwrap()))
.collect();
// === verify signature ===
let master_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
let nonce = compute_joint_secret(one_time_artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
let local_signature = local_compute_schnorr_signature(&nonce, &master_secret, &message_hash).unwrap();
for signature in &signatures {
assert_eq!(signature, &local_signature);
assert_eq!(verify_schnorr_signature(&artifacts.joint_public, signature, &message_hash), Ok(true));
}
}
}
#[test]
fn full_ecdsa_signature_math_session() {
let test_cases = [(2, 5), (2, 6), (3, 11), (4, 11)];
for &(t, n) in &test_cases {
// values that can be hardcoded
let joint_secret: Secret = Random.generate().unwrap().secret().clone();
let joint_nonce: Secret = Random.generate().unwrap().secret().clone();
let message_hash: H256 = H256::random();
// convert message hash to EC scalar
let message_hash_scalar = to_scalar(message_hash.clone()).unwrap();
// generate secret key shares
let artifacts = run_key_generation(t, n, None, Some(joint_secret));
// generate nonce shares
let nonce_artifacts = run_key_generation(t, n, Some(artifacts.id_numbers.clone()), Some(joint_nonce));
// compute nonce public
// x coordinate (mapped to EC field) of this public is the r-portion of signature
let nonce_public_shares: Vec<_> = (0..n).map(|i| compute_public_share(&nonce_artifacts.polynoms1[i][0]).unwrap()).collect();
let nonce_public = compute_joint_public(nonce_public_shares.iter()).unwrap();
let signature_r = compute_ecdsa_r(&nonce_public).unwrap();
// compute shares of inv(nonce) so that both nonce && inv(nonce) are still unknown to all nodes
let nonce_inv_shares = run_reciprocal_protocol(t, &nonce_artifacts);
// compute multiplication of secret-shares * inv-nonce-shares
let mul_shares = run_multiplication_protocol(t, &artifacts.secret_shares, &nonce_inv_shares);
// compute shares for s portion of signature: nonce_inv * (message_hash + secret * signature_r)
// every node broadcasts this share
let double_t = 2 * t;
let signature_s_shares: Vec<_> = (0..double_t+1).map(|i| compute_ecdsa_s_share(
&nonce_inv_shares[i],
&mul_shares[i],
&signature_r,
&message_hash_scalar
).unwrap()).collect();
// compute signature_s from received shares
let signature_s = compute_ecdsa_s(t,
&signature_s_shares,
&artifacts.id_numbers.iter().take(double_t + 1).cloned().collect::<Vec<_>>()
).unwrap();
// check signature
let signature_actual = serialize_ecdsa_signature(&nonce_public, signature_r, signature_s);
let joint_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
let joint_secret_pair = KeyPair::from_secret(joint_secret).unwrap();
assert_eq!(recover(&signature_actual, &message_hash).unwrap(), *joint_secret_pair.public());
assert!(verify_public(joint_secret_pair.public(), &signature_actual, &message_hash).unwrap());
}
}
#[test]
fn full_generation_math_session_with_refreshing_shares() {
let test_cases = vec![(1, 4), (6, 10)];
for (t, n) in test_cases {
// generate key using t-of-n session
let artifacts1 = run_key_generation(t, n, None, None);
let joint_secret1 = compute_joint_secret(artifacts1.polynoms1.iter().map(|p1| &p1[0])).unwrap();
// let's say we want to refresh existing secret shares
// by doing this every T seconds, and assuming that in each T-second period adversary KS is not able to collect t+1 secret shares
// we can be sure that the scheme is secure
let artifacts2 = run_key_share_refreshing(t, t, n, &artifacts1);
let joint_secret2 = compute_joint_secret_from_shares(t, &artifacts2.secret_shares.iter().take(t + 1).collect::<Vec<_>>(),
&artifacts2.id_numbers.iter().take(t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret2);
// refresh again
let artifacts3 = run_key_share_refreshing(t, t, n, &artifacts2);
let joint_secret3 = compute_joint_secret_from_shares(t, &artifacts3.secret_shares.iter().take(t + 1).collect::<Vec<_>>(),
&artifacts3.id_numbers.iter().take(t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret3);
}
}
#[test]
fn full_generation_math_session_with_adding_new_nodes() {
let test_cases = vec![(1, 3), (1, 4), (6, 10)];
for (t, n) in test_cases {
// generate key using t-of-n session
let artifacts1 = run_key_generation(t, n, None, None);
let joint_secret1 = compute_joint_secret(artifacts1.polynoms1.iter().map(|p1| &p1[0])).unwrap();
// let's say we want to include additional couple of servers to the set
// so that scheme becames t-of-n+2
let artifacts2 = run_key_share_refreshing(t, t, n + 2, &artifacts1);
let joint_secret2 = compute_joint_secret_from_shares(t, &artifacts2.secret_shares.iter().take(t + 1).collect::<Vec<_>>(),
&artifacts2.id_numbers.iter().take(t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret2);
// include another server (t-of-n+3)
let artifacts3 = run_key_share_refreshing(t, t, n + 3, &artifacts2);
let joint_secret3 = compute_joint_secret_from_shares(t, &artifacts3.secret_shares.iter().take(t + 1).collect::<Vec<_>>(),
&artifacts3.id_numbers.iter().take(t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret3);
}
}
#[test]
fn full_generation_math_session_with_decreasing_threshold() {
let (t, n) = (3, 5);
// generate key using t-of-n session
let artifacts1 = run_key_generation(t, n, None, None);
let joint_secret1 = compute_joint_secret(artifacts1.polynoms1.iter().map(|p1| &p1[0])).unwrap();
// let's say we want to decrease threshold so that it becames (t-1)-of-n
let new_t = t - 1;
let artifacts2 = run_key_share_refreshing(t, new_t, n, &artifacts1);
let joint_secret2 = compute_joint_secret_from_shares(new_t, &artifacts2.secret_shares.iter().take(new_t + 1).collect::<Vec<_>>(),
&artifacts2.id_numbers.iter().take(new_t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret2);
// let's say we want to decrease threshold once again so that it becames (t-2)-of-n
let t = t - 1;
let new_t = t - 2;
let artifacts3 = run_key_share_refreshing(t, new_t, n, &artifacts2);
let joint_secret3 = compute_joint_secret_from_shares(new_t, &artifacts3.secret_shares.iter().take(new_t + 1).collect::<Vec<_>>(),
&artifacts3.id_numbers.iter().take(new_t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(joint_secret1, joint_secret3);
}
#[test]
fn full_zero_secret_generation_math_session() {
let test_cases = vec![(1, 4), (2, 4)];
for (t, n) in test_cases {
// run joint zero generation session
let id_numbers: Vec<_> = (0..n).map(|_| generate_random_scalar().unwrap()).collect();
let artifacts = run_zero_key_generation(t, n, &id_numbers);
// check that zero secret is generated
// we can't compute secrets sum here, because result will be zero (invalid secret, unsupported by SECP256k1)
// so just use complement trick: x + (-x) = 0
// TODO [Refac]: switch to SECP256K1-free scalar EC arithmetic
let partial_joint_secret = compute_secret_sum(artifacts.polynoms1.iter().take(n - 1).map(|p| &p[0])).unwrap();
let mut partial_joint_secret_complement = artifacts.polynoms1[n - 1][0].clone();
partial_joint_secret_complement.neg().unwrap();
assert_eq!(partial_joint_secret, partial_joint_secret_complement);
}
}
#[test]
fn full_generation_with_multiplication() {
let test_cases = vec![(1, 3), (2, 5), (2, 7), (3, 8)];
for (t, n) in test_cases {
// generate two shared secrets
let artifacts1 = run_key_generation(t, n, None, None);
let artifacts2 = run_key_generation(t, n, Some(artifacts1.id_numbers.clone()), None);
// multiplicate original secrets
let joint_secret1 = compute_joint_secret(artifacts1.polynoms1.iter().map(|p| &p[0])).unwrap();
let joint_secret2 = compute_joint_secret(artifacts2.polynoms1.iter().map(|p| &p[0])).unwrap();
let mut expected_joint_secret_mul = joint_secret1;
expected_joint_secret_mul.mul(&joint_secret2).unwrap();
// run multiplication protocol
let joint_secret_mul_shares = run_multiplication_protocol(t, &artifacts1.secret_shares, &artifacts2.secret_shares);
// calculate actual secrets multiplication
let double_t = t * 2;
let actual_joint_secret_mul = compute_joint_secret_from_shares(double_t,
&joint_secret_mul_shares.iter().take(double_t + 1).collect::<Vec<_>>(),
&artifacts1.id_numbers.iter().take(double_t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(actual_joint_secret_mul, expected_joint_secret_mul);
}
}
#[test]
fn full_generation_with_reciprocal() {
let test_cases = vec![(1, 3), (2, 5), (2, 7), (2, 7), (3, 8)];
for (t, n) in test_cases {
// generate shared secret
let artifacts = run_key_generation(t, n, None, None);
// calculate inversion of original shared secret
let joint_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
let mut expected_joint_secret_inv = joint_secret.clone();
expected_joint_secret_inv.inv().unwrap();
// run inversion protocol
let reciprocal_shares = run_reciprocal_protocol(t, &artifacts);
// calculate actual secret inversion
let double_t = t * 2;
let actual_joint_secret_inv = compute_joint_secret_from_shares(double_t,
&reciprocal_shares.iter().take(double_t + 1).collect::<Vec<_>>(),
&artifacts.id_numbers.iter().take(double_t + 1).collect::<Vec<_>>()).unwrap();
assert_eq!(actual_joint_secret_inv, expected_joint_secret_inv);
}
}
}