766 lines
30 KiB
Rust
766 lines
30 KiB
Rust
// Copyright 2015-2017 Parity Technologies (UK) Ltd.
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// This file is part of Parity.
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// Parity is free software: you can redistribute it and/or modify
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// it under the terms of the GNU General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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// Parity is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License
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// along with Parity. If not, see <http://www.gnu.org/licenses/>.
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use ethkey::{Public, Secret, Random, Generator, math};
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use bigint::prelude::U256;
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use bigint::hash::H256;
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use hash::keccak;
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use key_server_cluster::Error;
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/// Encryption result.
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#[derive(Debug)]
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pub struct EncryptedSecret {
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/// Common encryption point.
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pub common_point: Public,
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/// Ecnrypted point.
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pub encrypted_point: Public,
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}
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/// Generate random scalar
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pub fn generate_random_scalar() -> Result<Secret, Error> {
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Ok(Random.generate()?.secret().clone())
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}
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/// Generate random point
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pub fn generate_random_point() -> Result<Public, Error> {
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Ok(Random.generate()?.public().clone())
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}
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/// Compute publics sum.
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pub fn compute_public_sum<'a, I>(mut publics: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
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let mut sum = publics.next().expect("compute_public_sum is called when there's at least one public; qed").clone();
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while let Some(public) = publics.next() {
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math::public_add(&mut sum, &public)?;
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}
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Ok(sum)
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}
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/// Compute secrets sum.
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pub fn compute_secret_sum<'a, I>(mut secrets: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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let mut sum = secrets.next().expect("compute_secret_sum is called when there's at least one secret; qed").clone();
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while let Some(secret) = secrets.next() {
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sum.add(secret)?;
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}
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Ok(sum)
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}
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/// Compute secrets 'shadow' multiplication: coeff * multiplication(s[j] / (s[i] - s[j])) for every i != j
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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> {
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// when there are no other secrets, only coeff is left
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let other_secret = match other_secrets.next() {
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Some(other_secret) => other_secret,
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None => return Ok(coeff.clone()),
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};
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let mut shadow_mul = self_secret.clone();
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shadow_mul.sub(other_secret)?;
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shadow_mul.inv()?;
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shadow_mul.mul(other_secret)?;
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while let Some(other_secret) = other_secrets.next() {
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let mut shadow_mul_element = self_secret.clone();
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shadow_mul_element.sub(other_secret)?;
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shadow_mul_element.inv()?;
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shadow_mul_element.mul(other_secret)?;
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shadow_mul.mul(&shadow_mul_element)?;
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}
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shadow_mul.mul(coeff)?;
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Ok(shadow_mul)
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}
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/// Update point by multiplying to random scalar
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pub fn update_random_point(point: &mut Public) -> Result<(), Error> {
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Ok(math::public_mul_secret(point, &generate_random_scalar()?)?)
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}
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/// Generate random polynom of threshold degree
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pub fn generate_random_polynom(threshold: usize) -> Result<Vec<Secret>, Error> {
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(0..threshold + 1)
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.map(|_| generate_random_scalar())
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.collect()
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}
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/// Compute absolute term of additional polynom1 when new node is added to the existing generation node set
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#[cfg(test)]
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pub fn compute_additional_polynom1_absolute_term<'a, I>(secret_values: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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let mut absolute_term = compute_secret_sum(secret_values)?;
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absolute_term.neg()?;
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Ok(absolute_term)
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}
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/// Add two polynoms together (coeff = coeff1 + coeff2).
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#[cfg(test)]
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pub fn add_polynoms(polynom1: &[Secret], polynom2: &[Secret], is_absolute_term2_zero: bool) -> Result<Vec<Secret>, Error> {
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polynom1.iter().zip(polynom2.iter())
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.enumerate()
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.map(|(i, (c1, c2))| {
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let mut sum_coeff = c1.clone();
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if !is_absolute_term2_zero || i != 0 {
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sum_coeff.add(c2)?;
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}
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Ok(sum_coeff)
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})
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.collect()
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}
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/// Compute value of polynom, using `node_number` as argument
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pub fn compute_polynom(polynom: &[Secret], node_number: &Secret) -> Result<Secret, Error> {
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debug_assert!(!polynom.is_empty());
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let mut result = polynom[0].clone();
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for i in 1..polynom.len() {
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// calculate pow(node_number, i)
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let mut appendum = node_number.clone();
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appendum.pow(i)?;
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// calculate coeff * pow(point, i)
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appendum.mul(&polynom[i])?;
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// calculate result + coeff * pow(point, i)
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result.add(&appendum)?;
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}
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Ok(result)
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}
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/// Generate public keys for other participants.
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pub fn public_values_generation(threshold: usize, derived_point: &Public, polynom1: &[Secret], polynom2: &[Secret]) -> Result<Vec<Public>, Error> {
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debug_assert_eq!(polynom1.len(), threshold + 1);
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debug_assert_eq!(polynom2.len(), threshold + 1);
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// compute t+1 public values
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let mut publics = Vec::with_capacity(threshold + 1);
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for i in 0..threshold + 1 {
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let coeff1 = &polynom1[i];
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let mut multiplication1 = math::generation_point();
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math::public_mul_secret(&mut multiplication1, &coeff1)?;
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let coeff2 = &polynom2[i];
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let mut multiplication2 = derived_point.clone();
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math::public_mul_secret(&mut multiplication2, &coeff2)?;
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math::public_add(&mut multiplication1, &multiplication2)?;
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publics.push(multiplication1);
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}
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debug_assert_eq!(publics.len(), threshold + 1);
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Ok(publics)
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}
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/// Check keys passed by other participants.
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pub fn keys_verification(threshold: usize, derived_point: &Public, number_id: &Secret, secret1: &Secret, secret2: &Secret, publics: &[Public]) -> Result<bool, Error> {
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// calculate left part
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let mut multiplication1 = math::generation_point();
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math::public_mul_secret(&mut multiplication1, secret1)?;
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let mut multiplication2 = derived_point.clone();
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math::public_mul_secret(&mut multiplication2, secret2)?;
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math::public_add(&mut multiplication1, &multiplication2)?;
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let left = multiplication1;
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// calculate right part
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let mut right = publics[0].clone();
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for i in 1..threshold + 1 {
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let mut secret_pow = number_id.clone();
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secret_pow.pow(i)?;
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let mut public_k = publics[i].clone();
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math::public_mul_secret(&mut public_k, &secret_pow)?;
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math::public_add(&mut right, &public_k)?;
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}
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Ok(left == right)
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}
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/// Check refreshed keys passed by other participants.
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#[cfg(test)]
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pub fn refreshed_keys_verification(threshold: usize, number_id: &Secret, secret1: &Secret, publics: &[Public]) -> Result<bool, Error> {
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// calculate left part
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let mut left = math::generation_point();
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math::public_mul_secret(&mut left, secret1)?;
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// calculate right part
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let mut right = publics[0].clone();
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for i in 1..threshold + 1 {
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let mut secret_pow = number_id.clone();
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secret_pow.pow(i)?;
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let mut public_k = publics[i].clone();
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math::public_mul_secret(&mut public_k, &secret_pow)?;
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math::public_add(&mut right, &public_k)?;
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}
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Ok(left == right)
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}
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/// Compute secret share.
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pub fn compute_secret_share<'a, I>(secret_values: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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compute_secret_sum(secret_values)
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}
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/// Compute public key share.
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pub fn compute_public_share(self_secret_value: &Secret) -> Result<Public, Error> {
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let mut public_share = math::generation_point();
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math::public_mul_secret(&mut public_share, self_secret_value)?;
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Ok(public_share)
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}
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/// Compute joint public key.
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pub fn compute_joint_public<'a, I>(public_shares: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
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compute_public_sum(public_shares)
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}
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/// Compute joint secret key.
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#[cfg(test)]
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pub fn compute_joint_secret<'a, I>(secret_coeffs: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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compute_secret_sum(secret_coeffs)
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}
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/// Encrypt secret with joint public key.
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pub fn encrypt_secret(secret: &Public, joint_public: &Public) -> Result<EncryptedSecret, Error> {
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// this is performed by KS-cluster client (or KS master)
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let key_pair = Random.generate()?;
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// k * T
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let mut common_point = math::generation_point();
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math::public_mul_secret(&mut common_point, key_pair.secret())?;
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// M + k * y
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let mut encrypted_point = joint_public.clone();
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math::public_mul_secret(&mut encrypted_point, key_pair.secret())?;
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math::public_add(&mut encrypted_point, secret)?;
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Ok(EncryptedSecret {
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common_point: common_point,
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encrypted_point: encrypted_point,
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})
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}
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/// Compute shadow for the node.
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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> {
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compute_shadow_mul(node_secret_share, node_number, other_nodes_numbers)
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}
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/// Compute shadow point for the node.
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pub fn compute_node_shadow_point(access_key: &Secret, common_point: &Public, node_shadow: &Secret, decrypt_shadow: Option<Secret>) -> Result<(Public, Option<Secret>), Error> {
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let mut shadow_key = node_shadow.clone();
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let decrypt_shadow = match decrypt_shadow {
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None => None,
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Some(mut decrypt_shadow) => {
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// update shadow key
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shadow_key.mul(&decrypt_shadow)?;
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// now udate decrypt shadow itself
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decrypt_shadow.dec()?;
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decrypt_shadow.mul(node_shadow)?;
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Some(decrypt_shadow)
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}
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};
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shadow_key.mul(access_key)?;
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let mut node_shadow_point = common_point.clone();
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math::public_mul_secret(&mut node_shadow_point, &shadow_key)?;
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Ok((node_shadow_point, decrypt_shadow))
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}
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/// Compute joint shadow point.
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pub fn compute_joint_shadow_point<'a, I>(nodes_shadow_points: I) -> Result<Public, Error> where I: Iterator<Item=&'a Public> {
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compute_public_sum(nodes_shadow_points)
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}
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/// Compute joint shadow point (version for tests).
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#[cfg(test)]
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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> {
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let mut joint_shadow = compute_secret_sum(nodes_shadows)?;
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joint_shadow.mul(access_key)?;
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let mut joint_shadow_point = common_point.clone();
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math::public_mul_secret(&mut joint_shadow_point, &joint_shadow)?;
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Ok(joint_shadow_point)
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}
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/// Decrypt data using joint shadow point.
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pub fn decrypt_with_joint_shadow(threshold: usize, access_key: &Secret, encrypted_point: &Public, joint_shadow_point: &Public) -> Result<Public, Error> {
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let mut inv_access_key = access_key.clone();
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inv_access_key.inv()?;
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let mut mul = joint_shadow_point.clone();
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math::public_mul_secret(&mut mul, &inv_access_key)?;
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let mut decrypted_point = encrypted_point.clone();
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if threshold % 2 != 0 {
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math::public_add(&mut decrypted_point, &mul)?;
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} else {
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math::public_sub(&mut decrypted_point, &mul)?;
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}
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Ok(decrypted_point)
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}
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/// Prepare common point for shadow decryption.
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pub fn make_common_shadow_point(threshold: usize, mut common_point: Public) -> Result<Public, Error> {
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if threshold % 2 != 1 {
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Ok(common_point)
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} else {
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math::public_negate(&mut common_point)?;
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Ok(common_point)
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}
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}
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/// Decrypt shadow-encrypted secret.
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#[cfg(test)]
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pub fn decrypt_with_shadow_coefficients(mut decrypted_shadow: Public, mut common_shadow_point: Public, shadow_coefficients: Vec<Secret>) -> Result<Public, Error> {
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let shadow_coefficients_sum = compute_secret_sum(shadow_coefficients.iter())?;
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math::public_mul_secret(&mut common_shadow_point, &shadow_coefficients_sum)?;
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math::public_add(&mut decrypted_shadow, &common_shadow_point)?;
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Ok(decrypted_shadow)
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}
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/// Decrypt data using joint secret (version for tests).
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#[cfg(test)]
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pub fn decrypt_with_joint_secret(encrypted_point: &Public, common_point: &Public, joint_secret: &Secret) -> Result<Public, Error> {
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let mut common_point_mul = common_point.clone();
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math::public_mul_secret(&mut common_point_mul, joint_secret)?;
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let mut decrypted_point = encrypted_point.clone();
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math::public_sub(&mut decrypted_point, &common_point_mul)?;
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Ok(decrypted_point)
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}
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/// Combine message hash with public key X coordinate.
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pub fn combine_message_hash_with_public(message_hash: &H256, public: &Public) -> Result<Secret, Error> {
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// buffer is just [message_hash | public.x]
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let mut buffer = [0; 64];
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buffer[0..32].copy_from_slice(&message_hash[0..32]);
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buffer[32..64].copy_from_slice(&public[0..32]);
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// calculate hash of buffer
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let hash = keccak(&buffer[..]);
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// map hash to EC finite field value
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let hash: U256 = hash.into();
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let hash: H256 = (hash % math::curve_order()).into();
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let hash = Secret::from_slice(&*hash);
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hash.check_validity()?;
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Ok(hash)
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}
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/// Compute signature share.
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pub fn compute_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)
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-> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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let mut sum = one_time_secret_coeff.clone();
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let mut subtrahend = compute_shadow_mul(combined_hash, node_number, other_nodes_numbers)?;
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subtrahend.mul(node_secret_share)?;
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if threshold % 2 == 0 {
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sum.sub(&subtrahend)?;
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} else {
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sum.add(&subtrahend)?;
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}
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Ok(sum)
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}
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/// Check signature share.
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pub fn _check_signature_share<'a, I>(_combined_hash: &Secret, _signature_share: &Secret, _public_share: &Public, _one_time_public_share: &Public, _node_numbers: I)
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-> Result<bool, Error> where I: Iterator<Item=&'a Secret> {
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// TODO: in paper partial signature is checked using comparison:
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// sig[i] * T = r[i] - c * lagrange_coeff(i) * y[i]
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// => (k[i] - c * lagrange_coeff(i) * s[i]) * T = r[i] - c * lagrange_coeff(i) * y[i]
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// => k[i] * T - c * lagrange_coeff(i) * s[i] * T = k[i] * T - c * lagrange_coeff(i) * y[i]
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// => this means that y[i] = s[i] * T
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// but when verifying signature (for t = 1), nonce public (r) is restored using following expression:
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// r = (sig[0] + sig[1]) * T - c * y
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// r = (k[0] - c * lagrange_coeff(0) * s[0] + k[1] - c * lagrange_coeff(1) * s[1]) * T - c * y
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// r = (k[0] + k[1]) * T - c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T - c * y
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// r = r - c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T - c * y
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// => -c * y = c * (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T
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// => -y = (lagrange_coeff(0) * s[0] + lagrange_coeff(1) * s[1]) * T
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// => y[i] != s[i] * T
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// => some other way is required
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Ok(true)
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}
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/// Compute signature.
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pub fn compute_signature<'a, I>(signature_shares: I) -> Result<Secret, Error> where I: Iterator<Item=&'a Secret> {
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compute_secret_sum(signature_shares)
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}
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/// Locally compute Schnorr signature as described in https://en.wikipedia.org/wiki/Schnorr_signature#Signing.
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#[cfg(test)]
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pub fn local_compute_signature(nonce: &Secret, secret: &Secret, message_hash: &Secret) -> Result<(Secret, Secret), Error> {
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let mut nonce_public = math::generation_point();
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math::public_mul_secret(&mut nonce_public, &nonce).unwrap();
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let combined_hash = combine_message_hash_with_public(message_hash, &nonce_public)?;
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let mut sig_subtrahend = combined_hash.clone();
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sig_subtrahend.mul(secret)?;
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let mut sig = nonce.clone();
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sig.sub(&sig_subtrahend)?;
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Ok((combined_hash, sig))
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}
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/// Verify signature as described in https://en.wikipedia.org/wiki/Schnorr_signature#Verifying.
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#[cfg(test)]
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pub fn verify_signature(public: &Public, signature: &(Secret, Secret), message_hash: &H256) -> Result<bool, Error> {
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let mut addendum = math::generation_point();
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math::public_mul_secret(&mut addendum, &signature.1)?;
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let mut nonce_public = public.clone();
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math::public_mul_secret(&mut nonce_public, &signature.0)?;
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math::public_add(&mut nonce_public, &addendum)?;
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let combined_hash = combine_message_hash_with_public(message_hash, &nonce_public)?;
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Ok(combined_hash == signature.0)
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}
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#[cfg(test)]
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pub mod tests {
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use std::iter::once;
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use ethkey::KeyPair;
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use super::*;
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#[derive(Clone)]
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struct KeyGenerationArtifacts {
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id_numbers: Vec<Secret>,
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polynoms1: Vec<Vec<Secret>>,
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secrets1: Vec<Vec<Secret>>,
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public_shares: Vec<Public>,
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secret_shares: Vec<Secret>,
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joint_public: Public,
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}
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fn run_key_generation(t: usize, n: usize, id_numbers: Option<Vec<Secret>>) -> KeyGenerationArtifacts {
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// === PART1: DKG ===
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// data, gathered during initialization
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let derived_point = Random.generate().unwrap().public().clone();
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let id_numbers: Vec<_> = match id_numbers {
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Some(id_numbers) => id_numbers,
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None => (0..n).map(|_| generate_random_scalar().unwrap()).collect(),
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};
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// data, generated during keys dissemination
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let polynoms1: Vec<_> = (0..n).map(|_| generate_random_polynom(t).unwrap()).collect();
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let secrets1: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&polynoms1[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
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// following data is used only on verification step
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let polynoms2: Vec<_> = (0..n).map(|_| generate_random_polynom(t).unwrap()).collect();
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let secrets2: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&polynoms2[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
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let publics: Vec<_> = (0..n).map(|i| public_values_generation(t, &derived_point, &polynoms1[i], &polynoms2[i]).unwrap()).collect();
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// keys verification
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(0..n).map(|i| (0..n).map(|j| if i != j {
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assert!(keys_verification(t, &derived_point, &id_numbers[i], &secrets1[j][i], &secrets2[j][i], &publics[j]).unwrap());
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}).collect::<Vec<_>>()).collect::<Vec<_>>();
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// data, generated during keys generation
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let public_shares: Vec<_> = (0..n).map(|i| compute_public_share(&polynoms1[i][0]).unwrap()).collect();
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let secret_shares: Vec<_> = (0..n).map(|i| compute_secret_share(secrets1.iter().map(|s| &s[i])).unwrap()).collect();
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// joint public key, as a result of DKG
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let joint_public = compute_joint_public(public_shares.iter()).unwrap();
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KeyGenerationArtifacts {
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id_numbers: id_numbers,
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polynoms1: polynoms1,
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secrets1: secrets1,
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public_shares: public_shares,
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secret_shares: secret_shares,
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joint_public: joint_public,
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}
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}
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fn run_key_share_refreshing(t: usize, n: usize, artifacts: &KeyGenerationArtifacts) -> KeyGenerationArtifacts {
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// === share refreshing protocol from http://www.wu.ece.ufl.edu/mypapers/msig.pdf
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// key refreshing distribution algorithm (KRD)
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let refreshed_polynoms1: Vec<_> = (0..n).map(|_| generate_random_polynom(t).unwrap()).collect();
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let refreshed_polynoms1_sum: Vec<_> = (0..n).map(|i| add_polynoms(&artifacts.polynoms1[i], &refreshed_polynoms1[i], true).unwrap()).collect();
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let refreshed_secrets1: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&refreshed_polynoms1_sum[i], &artifacts.id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
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let refreshed_publics: Vec<_> = (0..n).map(|i| {
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(0..t+1).map(|j| compute_public_share(&refreshed_polynoms1_sum[i][j]).unwrap()).collect::<Vec<_>>()
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}).collect();
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// key refreshing verification algorithm (KRV)
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(0..n).map(|i| (0..n).map(|j| if i != j {
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assert!(refreshed_keys_verification(t, &artifacts.id_numbers[i], &refreshed_secrets1[j][i], &refreshed_publics[j]).unwrap())
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}).collect::<Vec<_>>()).collect::<Vec<_>>();
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// data, generated during keys generation
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let public_shares: Vec<_> = (0..n).map(|i| compute_public_share(&refreshed_polynoms1_sum[i][0]).unwrap()).collect();
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let secret_shares: Vec<_> = (0..n).map(|i| compute_secret_share(refreshed_secrets1.iter().map(|s| &s[i])).unwrap()).collect();
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// joint public key, as a result of DKG
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let joint_public = compute_joint_public(public_shares.iter()).unwrap();
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KeyGenerationArtifacts {
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id_numbers: artifacts.id_numbers.clone(),
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polynoms1: refreshed_polynoms1_sum,
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secrets1: refreshed_secrets1,
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public_shares: public_shares,
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secret_shares: secret_shares,
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joint_public: joint_public,
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}
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}
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fn run_key_share_refreshing_and_add_new_nodes(t: usize, n: usize, new_nodes: usize, artifacts: &KeyGenerationArtifacts) -> KeyGenerationArtifacts {
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// === share refreshing protocol (with new node addition) from http://www.wu.ece.ufl.edu/mypapers/msig.pdf
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let mut id_numbers: Vec<_> = artifacts.id_numbers.iter().cloned().collect();
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// key refreshing distribution algorithm (KRD)
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// for each new node: generate random polynom
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let refreshed_polynoms1: Vec<_> = (0..n).map(|_| (0..new_nodes).map(|_| generate_random_polynom(t).unwrap()).collect::<Vec<_>>()).collect();
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let mut refreshed_polynoms1_sum: Vec<_> = (0..n).map(|i| {
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let mut refreshed_polynom1_sum = artifacts.polynoms1[i].clone();
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for refreshed_polynom1 in &refreshed_polynoms1[i] {
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refreshed_polynom1_sum = add_polynoms(&refreshed_polynom1_sum, refreshed_polynom1, false).unwrap();
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}
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refreshed_polynom1_sum
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}).collect();
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// new nodes receiving private information and generates its own polynom
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let mut new_nodes_polynom1 = Vec::with_capacity(new_nodes);
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for i in 0..new_nodes {
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let mut new_polynom1 = generate_random_polynom(t).unwrap();
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let new_polynom_absolute_term = compute_additional_polynom1_absolute_term(refreshed_polynoms1.iter().map(|polynom1| &polynom1[i][0])).unwrap();
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new_polynom1[0] = new_polynom_absolute_term;
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new_nodes_polynom1.push(new_polynom1);
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}
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// new nodes sends its own information to all other nodes
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let n = n + new_nodes;
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id_numbers.extend((0..new_nodes).map(|_| Random.generate().unwrap().secret().clone()));
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refreshed_polynoms1_sum.extend(new_nodes_polynom1);
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// the rest of protocol is the same as without new node
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let refreshed_secrets1: Vec<_> = (0..n).map(|i| (0..n).map(|j| compute_polynom(&refreshed_polynoms1_sum[i], &id_numbers[j]).unwrap()).collect::<Vec<_>>()).collect();
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let refreshed_publics: Vec<_> = (0..n).map(|i| {
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(0..t+1).map(|j| compute_public_share(&refreshed_polynoms1_sum[i][j]).unwrap()).collect::<Vec<_>>()
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}).collect();
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// key refreshing verification algorithm (KRV)
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(0..n).map(|i| (0..n).map(|j| if i != j {
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assert!(refreshed_keys_verification(t, &id_numbers[i], &refreshed_secrets1[j][i], &refreshed_publics[j]).unwrap())
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}).collect::<Vec<_>>()).collect::<Vec<_>>();
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// data, generated during keys generation
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let public_shares: Vec<_> = (0..n).map(|i| compute_public_share(&refreshed_polynoms1_sum[i][0]).unwrap()).collect();
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let secret_shares: Vec<_> = (0..n).map(|i| compute_secret_share(refreshed_secrets1.iter().map(|s| &s[i])).unwrap()).collect();
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// joint public key, as a result of DKG
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let joint_public = compute_joint_public(public_shares.iter()).unwrap();
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KeyGenerationArtifacts {
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id_numbers: id_numbers,
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polynoms1: refreshed_polynoms1_sum,
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secrets1: refreshed_secrets1,
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public_shares: public_shares,
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secret_shares: secret_shares,
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joint_public: joint_public,
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}
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}
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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) {
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// === PART2: encryption using joint public key ===
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// the next line is executed on KeyServer-client
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let encrypted_secret = encrypt_secret(&document_secret_plain, &joint_public).unwrap();
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// === PART3: decryption ===
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// next line is executed on KeyServer client
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let access_key = generate_random_scalar().unwrap();
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// use t + 1 nodes to compute joint shadow point
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let nodes_shadows: Vec<_> = (0..t + 1).map(|i|
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compute_node_shadow(&secret_shares[i], &id_numbers[i], id_numbers.iter()
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.enumerate()
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.filter(|&(j, _)| j != i)
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.take(t)
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.map(|(_, id_number)| id_number)).unwrap()).collect();
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let nodes_shadow_points: Vec<_> = nodes_shadows.iter()
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.map(|s| compute_node_shadow_point(&access_key, &encrypted_secret.common_point, s, None).unwrap())
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.map(|sp| sp.0)
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.collect();
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assert_eq!(nodes_shadows.len(), t + 1);
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assert_eq!(nodes_shadow_points.len(), t + 1);
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let joint_shadow_point = compute_joint_shadow_point(nodes_shadow_points.iter()).unwrap();
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let joint_shadow_point_test = compute_joint_shadow_point_test(&access_key, &encrypted_secret.common_point, nodes_shadows.iter()).unwrap();
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assert_eq!(joint_shadow_point, joint_shadow_point_test);
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// decrypt encrypted secret using joint shadow point
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let document_secret_decrypted = decrypt_with_joint_shadow(t, &access_key, &encrypted_secret.encrypted_point, &joint_shadow_point).unwrap();
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// decrypt encrypted secret using joint secret [just for test]
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let document_secret_decrypted_test = match joint_secret {
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Some(joint_secret) => decrypt_with_joint_secret(&encrypted_secret.encrypted_point, &encrypted_secret.common_point, joint_secret).unwrap(),
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None => document_secret_decrypted.clone(),
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};
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(document_secret_decrypted, document_secret_decrypted_test)
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}
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#[test]
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fn full_encryption_math_session() {
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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),
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(1, 10), (2, 10), (3, 10), (4, 10), (5, 10), (6, 10), (7, 10), (8, 10), (9, 10)];
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for &(t, n) in &test_cases {
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let artifacts = run_key_generation(t, n, None);
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// compute joint private key [just for test]
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let joint_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
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let joint_key_pair = KeyPair::from_secret(joint_secret.clone()).unwrap();
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assert_eq!(&artifacts.joint_public, joint_key_pair.public());
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// check secret shares computation [just for test]
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let secret_shares_polynom: Vec<_> = (0..t + 1).map(|k| compute_secret_share(artifacts.polynoms1.iter().map(|p| &p[k])).unwrap()).collect();
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let secret_shares_calculated_from_polynom: Vec<_> = artifacts.id_numbers.iter().map(|id_number| compute_polynom(&*secret_shares_polynom, id_number).unwrap()).collect();
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assert_eq!(artifacts.secret_shares, secret_shares_calculated_from_polynom);
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// now encrypt and decrypt data
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let document_secret_plain = generate_random_point().unwrap();
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let (document_secret_decrypted, document_secret_decrypted_test) =
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do_encryption_and_decryption(t, &artifacts.joint_public, &artifacts.id_numbers, &artifacts.secret_shares, Some(&joint_secret), document_secret_plain.clone());
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assert_eq!(document_secret_plain, document_secret_decrypted_test);
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assert_eq!(document_secret_plain, document_secret_decrypted);
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}
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}
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#[test]
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fn local_signature_works() {
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let key_pair = Random.generate().unwrap();
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let message_hash = "0000000000000000000000000000000000000000000000000000000000000042".parse().unwrap();
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let nonce = generate_random_scalar().unwrap();
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let signature = local_compute_signature(&nonce, key_pair.secret(), &message_hash).unwrap();
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assert_eq!(verify_signature(key_pair.public(), &signature, &message_hash), Ok(true));
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}
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#[test]
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fn full_signature_math_session() {
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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),
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(1, 10), (2, 10), (3, 10), (4, 10), (5, 10), (6, 10), (7, 10), (8, 10), (9, 10)];
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for &(t, n) in &test_cases {
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// hash of the message to be signed
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let message_hash: Secret = "0000000000000000000000000000000000000000000000000000000000000042".parse().unwrap();
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// === MiDS-S algorithm ===
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// setup: all nodes share master secret key && every node knows master public key
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let artifacts = run_key_generation(t, n, None);
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// in this gap (not related to math):
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// master node should ask every other node if it is able to do a signing
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// if there are < than t+1 nodes, able to sign => error
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// select t+1 nodes for signing session
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// all steps below are for this subset of nodes
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let n = t + 1;
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// step 1: run DKG to generate one-time secret key (nonce)
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let id_numbers = artifacts.id_numbers.iter().cloned().take(n).collect();
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let one_time_artifacts = run_key_generation(t, n, Some(id_numbers));
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// step 2: message hash && x coordinate of one-time public value are combined
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let combined_hash = combine_message_hash_with_public(&message_hash, &one_time_artifacts.joint_public).unwrap();
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// step 3: compute signature shares
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let partial_signatures: Vec<_> = (0..n)
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.map(|i| compute_signature_share(
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t,
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&combined_hash,
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&one_time_artifacts.polynoms1[i][0],
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&artifacts.secret_shares[i],
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&artifacts.id_numbers[i],
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artifacts.id_numbers.iter()
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.enumerate()
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.filter(|&(j, _)| i != j)
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.map(|(_, n)| n)
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.take(t)
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).unwrap())
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.collect();
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// step 4: receive and verify signatures shares from other nodes
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let received_signatures: Vec<Vec<_>> = (0..n)
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.map(|i| (0..n)
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.filter(|j| i != *j)
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.map(|j| {
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let signature_share = partial_signatures[j].clone();
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assert!(_check_signature_share(&combined_hash,
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&signature_share,
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&artifacts.public_shares[j],
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&one_time_artifacts.public_shares[j],
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artifacts.id_numbers.iter().take(t)).unwrap_or(false));
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signature_share
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})
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.collect())
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.collect();
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// step 5: compute signature
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let signatures: Vec<_> = (0..n)
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.map(|i| (combined_hash.clone(), compute_signature(received_signatures[i].iter().chain(once(&partial_signatures[i]))).unwrap()))
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.collect();
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// === verify signature ===
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let master_secret = compute_joint_secret(artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
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let nonce = compute_joint_secret(one_time_artifacts.polynoms1.iter().map(|p| &p[0])).unwrap();
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let local_signature = local_compute_signature(&nonce, &master_secret, &message_hash).unwrap();
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for signature in &signatures {
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assert_eq!(signature, &local_signature);
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assert_eq!(verify_signature(&artifacts.joint_public, signature, &message_hash), Ok(true));
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}
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}
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}
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#[test]
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fn full_generation_math_session_with_refreshing_shares() {
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// generate key using 6-of-10 session
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let (t, n) = (5, 10);
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let artifacts1 = run_key_generation(t, n, None);
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// let's say we want to refresh existing secret shares
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// 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
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// we can be sure that the scheme is secure
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let artifacts2 = run_key_share_refreshing(t, n, &artifacts1);
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assert_eq!(artifacts1.joint_public, artifacts2.joint_public);
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// refresh again
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let artifacts3 = run_key_share_refreshing(t, n, &artifacts2);
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assert_eq!(artifacts1.joint_public, artifacts3.joint_public);
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}
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#[test]
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fn full_generation_math_session_with_adding_new_nodes() {
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// generate key using 6-of-10 session
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let (t, n) = (5, 10);
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let artifacts1 = run_key_generation(t, n, None);
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// let's say we want to include additional server to the set
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// so that scheme becames 6-of-11
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let artifacts2 = run_key_share_refreshing_and_add_new_nodes(t, n, 1, &artifacts1);
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assert_eq!(artifacts1.joint_public, artifacts2.joint_public);
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// include another couple of servers (6-of-13)
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let artifacts3 = run_key_share_refreshing_and_add_new_nodes(t, n + 1, 2, &artifacts2);
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assert_eq!(artifacts1.joint_public, artifacts3.joint_public);
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}
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}
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