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Implement polynomials for distributed key generation.

This commit is contained in:
Andreas Fackler 2018-06-07 21:48:48 +02:00
parent d1362ed500
commit 6cc2302e61
5 changed files with 775 additions and 119 deletions
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2
Cargo.toml
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@ -13,7 +13,7 @@ init_with = "1.1.0"
itertools = "0.7"
log = "0.4.1"
merkle = { git = "https://github.com/afck/merkle.rs", branch = "public-proof" }
pairing = "0.14.2"
pairing = { version = "0.14.2", features = ["u128-support"] }
protobuf = { version = "2.0.0", optional = true }
rand = "0.4.2"
reed-solomon-erasure = "3.1.0"

613
src/crypto/keygen.rs Normal file
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@ -0,0 +1,613 @@
//! Utilities for distributed key generation.
//!
//! A `BivarPoly` can be used for Verifiable Secret Sharing (VSS) and for key generation by a
//! trusted dealer. In a perfectly synchronous setting, e.g. on a blockchain or other agreed
//! transaction log, it works like this:
//!
//! The dealer generates a `BivarPoly` of degree `t` and publishes the `BivariateCommitment`,
//! with which the polynomial's values can be publicly verified. They then send _row_ `m > 0` to
//! node number `m`. Node `m`, in turn, sends _value_ `s` to node number `s`. Then if `2 * t + 1`
//! nodes confirm that they received a valid row, and there are at most `t` faulty nodes, then at
//! least `t + 1` honest nodes sent on an entry of every other node's column to that node. So we
//! know that every node can now reconstruct its column and the value at `0` of its column. These
//! values all lie on a univariate polynomial of degree `t`, so they can be used as secret keys.
//!
//! For Distributed Key Generation (DKG), every node proposes a polynomial via VSS. After a fixed
//! number (at least `N - 2 * t` if there are `N` nodes and up to `t` faulty ones) of them have
//! successfully been distributed, every node adds up the resulting secrets. Since the sum of
//! polynomials of degree `t` is itself a polynomial of degree `t`, these sums are still valid
//! secret keys, but now nobody knows the master key (number `0`).
// TODO: Expand this explanation and add examples, once the API is complete and stable.
use std::borrow::Borrow;
use std::{cmp, iter, ops};
use pairing::{CurveAffine, CurveProjective, Engine, Field, PrimeField};
use rand::Rng;
/// A univariate polynomial in the prime field.
#[derive(Clone, Debug)]
pub struct Poly<E: Engine> {
/// The coefficients of a polynomial.
coeff: Vec<E::Fr>,
}
impl<E: Engine> PartialEq for Poly<E> {
fn eq(&self, other: &Self) -> bool {
self.coeff == other.coeff
}
}
impl<B: Borrow<Poly<E>>, E: Engine> ops::AddAssign<B> for Poly<E> {
fn add_assign(&mut self, rhs: B) {
let len = cmp::max(self.coeff.len(), rhs.borrow().coeff.len());
self.coeff.resize(len, E::Fr::zero());
for (self_c, rhs_c) in self.coeff.iter_mut().zip(&rhs.borrow().coeff) {
self_c.add_assign(rhs_c);
}
self.remove_zeros();
}
}
impl<'a, B: Borrow<Poly<E>>, E: Engine> ops::Add<B> for &'a Poly<E> {
type Output = Poly<E>;
fn add(self, rhs: B) -> Poly<E> {
(*self).clone() + rhs
}
}
impl<B: Borrow<Poly<E>>, E: Engine> ops::Add<B> for Poly<E> {
type Output = Poly<E>;
fn add(mut self, rhs: B) -> Poly<E> {
self += rhs;
self
}
}
impl<B: Borrow<Poly<E>>, E: Engine> ops::SubAssign<B> for Poly<E> {
fn sub_assign(&mut self, rhs: B) {
let len = cmp::max(self.coeff.len(), rhs.borrow().coeff.len());
self.coeff.resize(len, E::Fr::zero());
for (self_c, rhs_c) in self.coeff.iter_mut().zip(&rhs.borrow().coeff) {
self_c.sub_assign(rhs_c);
}
self.remove_zeros();
}
}
impl<'a, B: Borrow<Poly<E>>, E: Engine> ops::Sub<B> for &'a Poly<E> {
type Output = Poly<E>;
fn sub(self, rhs: B) -> Poly<E> {
(*self).clone() - rhs
}
}
impl<B: Borrow<Poly<E>>, E: Engine> ops::Sub<B> for Poly<E> {
type Output = Poly<E>;
fn sub(mut self, rhs: B) -> Poly<E> {
self -= rhs;
self
}
}
// Clippy thinks using any `+` and `-` in a `Mul` implementation is suspicious.
#[cfg_attr(feature = "cargo-clippy", allow(suspicious_arithmetic_impl))]
impl<'a, B: Borrow<Poly<E>>, E: Engine> ops::Mul<B> for &'a Poly<E> {
type Output = Poly<E>;
fn mul(self, rhs: B) -> Self::Output {
let coeff = (0..(self.coeff.len() + rhs.borrow().coeff.len() - 1))
.map(|i| {
let mut c = E::Fr::zero();
for j in i.saturating_sub(rhs.borrow().degree())..(1 + cmp::min(i, self.degree())) {
let mut s = self.coeff[j];
s.mul_assign(&rhs.borrow().coeff[i - j]);
c.add_assign(&s);
}
c
})
.collect();
Poly { coeff }
}
}
impl<B: Borrow<Poly<E>>, E: Engine> ops::Mul<B> for Poly<E> {
type Output = Poly<E>;
fn mul(self, rhs: B) -> Self::Output {
&self * rhs
}
}
impl<B: Borrow<Self>, E: Engine> ops::MulAssign<B> for Poly<E> {
fn mul_assign(&mut self, rhs: B) {
*self = &*self * rhs;
}
}
impl<E: Engine> Poly<E> {
/// Creates a random polynomial.
pub fn random<R: Rng>(degree: usize, rng: &mut R) -> Self {
Poly {
coeff: (0..(degree + 1)).map(|_| rng.gen()).collect(),
}
}
/// Returns the polynomial with constant value `0`.
pub fn zero() -> Self {
Poly { coeff: Vec::new() }
}
/// Returns the polynomial with constant value `1`.
pub fn one() -> Self {
Self::monomial(0)
}
/// Returns the polynomial with constant value `c`.
pub fn constant(c: E::Fr) -> Self {
Poly { coeff: vec![c] }
}
/// Returns the identity function, i.e. the polynomial "`x`".
pub fn identity() -> Self {
Self::monomial(1)
}
/// Returns the (monic) monomial "`x.pow(degree)`".
pub fn monomial(degree: usize) -> Self {
Poly {
coeff: iter::repeat(E::Fr::zero())
.take(degree)
.chain(iter::once(E::Fr::one()))
.collect(),
}
}
/// Returns the unique polynomial `f` of degree `samples.len() - 1` with the given values
/// `(x, f(x))`.
pub fn interpolate<'a, T, I>(samples_repr: I) -> Self
where
I: IntoIterator<Item = (&'a T, &'a E::Fr)>,
T: Into<<E::Fr as PrimeField>::Repr> + Clone + 'a,
{
let convert = |(x_repr, y): (&T, &E::Fr)| {
let x = E::Fr::from_repr(x_repr.clone().into()).expect("invalid index");
(x, *y)
};
let samples: Vec<(E::Fr, E::Fr)> = samples_repr.into_iter().map(convert).collect();
Self::compute_interpolation(&samples)
}
/// Returns the degree.
pub fn degree(&self) -> usize {
self.coeff.len() - 1
}
/// Returns the value at the point `i`.
pub fn evaluate<T: Into<<E::Fr as PrimeField>::Repr>>(&self, i: T) -> E::Fr {
let mut result = match self.coeff.last() {
None => return E::Fr::zero(),
Some(c) => *c,
};
let x = E::Fr::from_repr(i.into()).expect("invalid index");
for c in self.coeff.iter().rev().skip(1) {
result.mul_assign(&x);
result.add_assign(c);
}
result
}
/// Returns the corresponding commitment.
pub fn commitment(&self) -> Commitment<E> {
let to_g1 = |c: &E::Fr| E::G1Affine::one().mul(*c);
Commitment {
coeff: self.coeff.iter().map(to_g1).collect(),
}
}
/// Removes all trailing zero coefficients.
fn remove_zeros(&mut self) {
let zeros = self.coeff.iter().rev().take_while(|c| c.is_zero()).count();
let len = self.coeff.len() - zeros;
self.coeff.truncate(len)
}
/// Returns the unique polynomial `f` of degree `samples.len() - 1` with the given values
/// `(x, f(x))`.
fn compute_interpolation(samples: &[(E::Fr, E::Fr)]) -> Self {
if samples.is_empty() {
return Poly::zero();
} else if samples.len() == 1 {
return Poly::constant(samples[0].1);
}
// The degree is at least 1 now.
let degree = samples.len() - 1;
// Interpolate all but the last sample.
let prev = Self::compute_interpolation(&samples[..degree]);
let (x, mut y) = samples[degree]; // The last sample.
y.sub_assign(&prev.evaluate(x));
let step = Self::lagrange(x, &samples[..degree]);
prev + step * Self::constant(y)
}
/// Returns the Lagrange base polynomial that is `1` in `p` and `0` in every `samples[i].0`.
fn lagrange(p: E::Fr, samples: &[(E::Fr, E::Fr)]) -> Self {
let mut result = Self::one();
for &(sx, _) in samples {
let mut denom = p;
denom.sub_assign(&sx);
denom = denom.inverse().expect("sample points must be distinct");
result *= (Self::identity() - Self::constant(sx)) * Self::constant(denom);
}
result
}
}
/// A commitment to a univariate polynomial.
#[derive(Debug, Clone)]
#[cfg_attr(feature = "serialization-serde", derive(Serialize, Deserialize))]
pub struct Commitment<E: Engine> {
/// The coefficients of the polynomial.
#[cfg_attr(feature = "serialization-serde", serde(with = "super::serde_impl::projective_vec"))]
coeff: Vec<E::G1>,
}
impl<E: Engine> PartialEq for Commitment<E> {
fn eq(&self, other: &Self) -> bool {
self.coeff == other.coeff
}
}
impl<B: Borrow<Commitment<E>>, E: Engine> ops::AddAssign<B> for Commitment<E> {
fn add_assign(&mut self, rhs: B) {
let len = cmp::max(self.coeff.len(), rhs.borrow().coeff.len());
self.coeff.resize(len, E::G1::zero());
for (self_c, rhs_c) in self.coeff.iter_mut().zip(&rhs.borrow().coeff) {
self_c.add_assign(rhs_c);
}
self.remove_zeros();
}
}
impl<'a, B: Borrow<Commitment<E>>, E: Engine> ops::Add<B> for &'a Commitment<E> {
type Output = Commitment<E>;
fn add(self, rhs: B) -> Commitment<E> {
(*self).clone() + rhs
}
}
impl<B: Borrow<Commitment<E>>, E: Engine> ops::Add<B> for Commitment<E> {
type Output = Commitment<E>;
fn add(mut self, rhs: B) -> Commitment<E> {
self += rhs;
self
}
}
impl<E: Engine> Commitment<E> {
/// Returns the polynomial's degree.
pub fn degree(&self) -> usize {
self.coeff.len() - 1
}
/// Returns the `i`-th public key share.
pub fn evaluate<T: Into<<E::Fr as PrimeField>::Repr>>(&self, i: T) -> E::G1 {
let mut result = match self.coeff.last() {
None => return E::G1::zero(),
Some(c) => *c,
};
let x = E::Fr::from_repr(i.into()).expect("invalid index");
for c in self.coeff.iter().rev().skip(1) {
result.mul_assign(x);
result.add_assign(c);
}
result
}
/// Removes all trailing zero coefficients.
fn remove_zeros(&mut self) {
let zeros = self.coeff.iter().rev().take_while(|c| c.is_zero()).count();
let len = self.coeff.len() - zeros;
self.coeff.truncate(len)
}
}
/// A symmetric bivariate polynomial in the prime field.
///
/// This can be used for Verifiable Secret Sharing and Distributed Key Generation. See the module
/// documentation for details.
#[derive(Debug, Clone)]
pub struct BivarPoly<E: Engine> {
/// The polynomial's degree in each of the two variables.
degree: usize,
/// The coefficients of the polynomial. Coefficient `(i, j)` for `i <= j` is in position
/// `j * (j + 1) / 2 + i`.
coeff: Vec<E::Fr>,
}
impl<E: Engine> BivarPoly<E> {
/// Creates a random polynomial.
pub fn random<R: Rng>(degree: usize, rng: &mut R) -> Self {
BivarPoly {
degree,
coeff: (0..coeff_pos(degree + 1, 0)).map(|_| rng.gen()).collect(),
}
}
/// Returns the polynomial's degree: It is the same in both variables.
pub fn degree(&self) -> usize {
self.degree
}
/// Returns the polynomial's value at the point `(x, y)`.
pub fn evaluate<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x: T, y: T) -> E::Fr {
let x_pow = self.powers(x);
let y_pow = self.powers(y);
// TODO: Can we save a few multiplication steps here due to the symmetry?
let mut result = E::Fr::zero();
for (i, x_pow_i) in x_pow.into_iter().enumerate() {
for (j, y_pow_j) in y_pow.iter().enumerate() {
let mut summand = self.coeff[coeff_pos(i, j)];
summand.mul_assign(&x_pow_i);
summand.mul_assign(y_pow_j);
result.add_assign(&summand);
}
}
result
}
/// Returns the `x`-th row, as a univariate polynomial.
pub fn row<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x: T) -> Poly<E> {
let x_pow = self.powers(x);
let coeff: Vec<E::Fr> = (0..=self.degree)
.map(|i| {
let mut result = E::Fr::zero();
for (j, x_pow_j) in x_pow.iter().enumerate() {
let mut summand = self.coeff[coeff_pos(i, j)];
summand.mul_assign(x_pow_j);
result.add_assign(&summand);
}
result
})
.collect();
Poly { coeff }
}
/// Returns the corresponding commitment. That information can be shared publicly.
pub fn commitment(&self) -> BivarCommitment<E> {
let to_pub = |c: &E::Fr| E::G1Affine::one().mul(*c);
BivarCommitment {
degree: self.degree,
coeff: self.coeff.iter().map(to_pub).collect(),
}
}
/// Returns the `0`-th to `degree`-th power of `x`.
fn powers<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x_repr: T) -> Vec<E::Fr> {
powers(x_repr, self.degree)
}
}
/// A commitment to a bivariate polynomial.
#[derive(Debug, Clone)]
#[cfg_attr(feature = "serialization-serde", derive(Serialize, Deserialize))]
pub struct BivarCommitment<E: Engine> {
/// The polynomial's degree in each of the two variables.
degree: usize,
/// The commitments to the coefficients.
#[cfg_attr(feature = "serialization-serde", serde(with = "super::serde_impl::projective_vec"))]
coeff: Vec<E::G1>,
}
impl<E: Engine> BivarCommitment<E> {
/// Returns the polynomial's degree: It is the same in both variables.
pub fn degree(&self) -> usize {
self.degree
}
/// Returns the commitment's value at the point `(x, y)`.
pub fn evaluate<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x: T, y: T) -> E::G1 {
let x_pow = self.powers(x);
let y_pow = self.powers(y);
// TODO: Can we save a few multiplication steps here due to the symmetry?
let mut result = E::G1::zero();
for (i, x_pow_i) in x_pow.into_iter().enumerate() {
for (j, y_pow_j) in y_pow.iter().enumerate() {
let mut summand = self.coeff[coeff_pos(i, j)];
summand.mul_assign(x_pow_i);
summand.mul_assign(*y_pow_j);
result.add_assign(&summand);
}
}
result
}
/// Returns the `x`-th row, as a commitment to a univariate polynomial.
pub fn row<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x: T) -> Commitment<E> {
let x_pow = self.powers(x);
let coeff: Vec<E::G1> = (0..=self.degree)
.map(|i| {
let mut result = E::G1::zero();
for (j, x_pow_j) in x_pow.iter().enumerate() {
let mut summand = self.coeff[coeff_pos(i, j)];
summand.mul_assign(*x_pow_j);
result.add_assign(&summand);
}
result
})
.collect();
Commitment { coeff }
}
/// Returns the `0`-th to `degree`-th power of `x`.
fn powers<T: Into<<E::Fr as PrimeField>::Repr>>(&self, x_repr: T) -> Vec<E::Fr> {
powers(x_repr, self.degree)
}
}
/// Returns the `0`-th to `degree`-th power of `x`.
fn powers<P: PrimeField, T: Into<P::Repr>>(x_repr: T, degree: usize) -> Vec<P> {
let x = &P::from_repr(x_repr.into()).expect("invalid index");
let mut x_pow_i = P::one();
iter::once(x_pow_i)
.chain((0..degree).map(|_| {
x_pow_i.mul_assign(x);
x_pow_i
}))
.collect()
}
/// Returns the position of coefficient `(i, j)` in the vector describing a symmetric bivariate
/// polynomial.
fn coeff_pos(i: usize, j: usize) -> usize {
// Since the polynomial is symmetric, we can order such that `j >= i`.
if j >= i {
j * (j + 1) / 2 + i
} else {
i * (i + 1) / 2 + j
}
}
#[cfg(test)]
mod tests {
use std::collections::BTreeMap;
use super::{coeff_pos, BivarPoly, Poly};
use pairing::bls12_381::Bls12;
use pairing::{CurveAffine, Engine, Field, PrimeField};
use rand;
type Fr = <Bls12 as Engine>::Fr;
fn fr(x: i64) -> Fr {
let mut result = Fr::from_repr((x.abs() as u64).into()).unwrap();
if x < 0 {
result.negate();
}
result
}
#[test]
fn test_coeff_pos() {
let mut i = 0;
let mut j = 0;
for n in 0..100 {
assert_eq!(n, coeff_pos(i, j));
if i >= j {
j += 1;
i = 0;
} else {
i += 1;
}
}
}
#[test]
fn poly() {
// The polynomial "`5 * x.pow(3) + x.pow(1) - 2`".
let poly: Poly<Bls12> =
Poly::monomial(3) * Poly::constant(fr(5)) + Poly::monomial(1) - Poly::constant(fr(2));
let coeff = vec![fr(-2), fr(1), fr(0), fr(5)];
assert_eq!(Poly { coeff }, poly);
let samples = vec![
(fr(-1), fr(-8)),
(fr(2), fr(40)),
(fr(3), fr(136)),
(fr(5), fr(628)),
];
for &(x, y) in &samples {
assert_eq!(y, poly.evaluate(x));
}
let sample_iter = samples.iter().map(|&(ref x, ref y)| (x, y));
assert_eq!(Poly::interpolate(sample_iter), poly);
}
#[test]
fn distributed_key_generation() {
let mut rng = rand::thread_rng();
let dealer_num = 3;
let node_num = 5;
let faulty_num = 2;
// For distributed key generation, a number of dealers, only one of who needs to be honest,
// generates random bivariate polynomials and publicly commits to them. In partice, the
// dealers can e.g. be any `faulty_num + 1` nodes.
let bi_polys: Vec<BivarPoly<Bls12>> = (0..dealer_num)
.map(|_| BivarPoly::random(faulty_num, &mut rng))
.collect();
let pub_bi_commits: Vec<_> = bi_polys.iter().map(BivarPoly::commitment).collect();
let mut sec_keys = vec![fr(0); node_num];
// Each dealer sends row `m` to node `m`, where the index starts at `1`. Don't send row `0`
// to anyone! The nodes verify their rows, and send _value_ `s` on to node `s`. They again
// verify the values they received, and collect them.
for (bi_poly, bi_commit) in bi_polys.iter().zip(&pub_bi_commits) {
for m in 1..=node_num {
// Node `m` receives its row and verifies it.
let row_poly = bi_poly.row(m as u64);
let row_commit = bi_commit.row(m as u64);
assert_eq!(row_poly.commitment(), row_commit);
// Node `s` receives the `s`-th value and verifies it.
for s in 1..=node_num {
let val = row_poly.evaluate(s as u64);
let val_g1 = <Bls12 as Engine>::G1Affine::one().mul(val);
assert_eq!(bi_commit.evaluate(m as u64, s as u64), val_g1);
// The node can't verify this directly, but it should have the correct value:
assert_eq!(bi_poly.evaluate(m as u64, s as u64), val);
}
// A cheating dealer who modified the polynomial would be detected.
let wrong_poly = row_poly.clone() + Poly::monomial(2) * Poly::constant(fr(5));
assert_ne!(wrong_poly.commitment(), row_commit);
// If `2 * faulty_num + 1` nodes confirm that they received a valid row, then at
// least `faulty_num + 1` honest ones did, and sent the correct values on to node
// `s`. So every node received at least `faulty_num + 1` correct entries of their
// column/row (remember that the bivariate polynomial is symmetric). They can
// reconstruct the full row and in particular value `0` (which no other node knows,
// only the dealer). E.g. let's say nodes `1`, `2` and `4` are honest. Then node
// `m` received three correct entries from that row:
let received: BTreeMap<_, _> = [1, 2, 4]
.iter()
.map(|&i| (i, bi_poly.evaluate(m as u64, i as u64)))
.collect();
let my_row = Poly::interpolate(&received);
assert_eq!(bi_poly.evaluate(m as u64, 0), my_row.evaluate(0));
assert_eq!(row_poly, my_row);
// The node sums up all values number `0` it received from the different dealer. No
// dealer and no other node knows the sum in the end.
sec_keys[m - 1].add_assign(&my_row.evaluate(0));
}
}
// Each node now adds up all the first values of the rows it received from the different
// dealers (excluding the dealers where fewer than `2 * faulty_num + 1` nodes confirmed).
// The whole first column never gets added up in practice, because nobody has all the
// information. We do it anyway here; entry `0` is the secret key that is not known to
// anyone, neither a dealer, nor a node:
let mut sec_key_set = Poly::zero();
for bi_poly in &bi_polys {
sec_key_set += bi_poly.row(0);
}
for m in 1..=node_num {
assert_eq!(sec_key_set.evaluate(m as u64), sec_keys[m - 1]);
}
// The sum of the first rows of the public commitments is the commitment to the secret key
// set.
let mut sum_commit = Poly::zero().commitment();
for bi_commit in &pub_bi_commits {
sum_commit += bi_commit.row(0);
}
assert_eq!(sum_commit, sec_key_set.commitment());
}
}

158
src/crypto/mod.rs
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@ -1,5 +1,9 @@
mod error;
pub mod keygen;
#[cfg(feature = "serialization-serde")]
mod serde_impl;
use self::keygen::{Commitment, Poly};
use byteorder::{BigEndian, ByteOrder};
use init_with::InitWith;
use pairing::{CurveAffine, CurveProjective, Engine, Field, PrimeField};
@ -149,34 +153,30 @@ impl<E: Engine> PartialEq for DecryptionShare<E> {
pub struct PublicKeySet<E: Engine> {
/// The coefficients of a polynomial whose value at `0` is the "master key", and value at
/// `i + 1` is key share number `i`.
coeff: Vec<PublicKey<E>>,
commit: Commitment<E>,
}
impl<E: Engine> From<Commitment<E>> for PublicKeySet<E> {
fn from(commit: Commitment<E>) -> PublicKeySet<E> {
PublicKeySet { commit }
}
}
impl<E: Engine> PublicKeySet<E> {
/// Returns the threshold `t`: any set of `t + 1` signature shares can be combined into a full
/// signature.
pub fn threshold(&self) -> usize {
self.coeff.len() - 1
self.commit.degree()
}
/// Returns the public key.
pub fn public_key(&self) -> &PublicKey<E> {
&self.coeff[0]
pub fn public_key(&self) -> PublicKey<E> {
PublicKey(self.commit.evaluate(0))
}
/// Returns the `i`-th public key share.
pub fn public_key_share<T>(&self, i: T) -> PublicKey<E>
where
T: Into<<E::Fr as PrimeField>::Repr>,
{
let mut x = E::Fr::one();
x.add_assign(&E::Fr::from_repr(i.into()).expect("invalid index"));
let mut pk = self.coeff.last().expect("at least one coefficient").0;
for c in self.coeff.iter().rev().skip(1) {
pk.mul_assign(x);
pk.add_assign(&c.0);
}
PublicKey(pk)
pub fn public_key_share<T: Into<<E::Fr as PrimeField>::Repr>>(&self, i: T) -> PublicKey<E> {
PublicKey(self.commit.evaluate(from_repr_plus_1::<E::Fr>(i.into())))
}
/// Combines the shares into a signature that can be verified with the main public key.
@ -186,7 +186,7 @@ impl<E: Engine> PublicKeySet<E> {
IND: Into<<E::Fr as PrimeField>::Repr> + Clone + 'a,
{
let samples = shares.into_iter().map(|(i, share)| (i, &share.0));
Ok(Signature(interpolate(self.coeff.len(), samples)?))
Ok(Signature(interpolate(self.commit.degree() + 1, samples)?))
}
/// Combines the shares to decrypt the ciphertext.
@ -196,7 +196,7 @@ impl<E: Engine> PublicKeySet<E> {
IND: Into<<E::Fr as PrimeField>::Repr> + Clone + 'a,
{
let samples = shares.into_iter().map(|(i, share)| (i, &share.0));
let g = interpolate(self.coeff.len(), samples)?;
let g = interpolate(self.commit.degree() + 1, samples)?;
Ok(xor_vec(&hash_bytes::<E>(g, ct.1.len()), &ct.1))
}
}
@ -205,45 +205,41 @@ impl<E: Engine> PublicKeySet<E> {
pub struct SecretKeySet<E: Engine> {
/// The coefficients of a polynomial whose value at `0` is the "master key", and value at
/// `i + 1` is key share number `i`.
coeff: Vec<E::Fr>,
poly: Poly<E>,
}
impl<E: Engine> SecretKeySet<E> {
/// Creates a set of secret key shares, where any `threshold + 1` of them can collaboratively
/// sign and decrypt.
pub fn new<R: Rng>(threshold: usize, rng: &mut R) -> Self {
pub fn random<R: Rng>(threshold: usize, rng: &mut R) -> Self {
SecretKeySet {
coeff: (0..(threshold + 1)).map(|_| rng.gen()).collect(),
poly: Poly::random(threshold, rng),
}
}
/// Returns the threshold `t`: any set of `t + 1` signature shares can be combined into a full
/// signature.
pub fn threshold(&self) -> usize {
self.coeff.len() - 1
self.poly.degree()
}
/// Returns the `i`-th secret key share.
pub fn secret_key_share<T>(&self, i: T) -> SecretKey<E>
where
T: Into<<E::Fr as PrimeField>::Repr>,
{
let x = from_repr_plus_1(i.into());
let mut pk = *self.coeff.last().expect("at least one coefficient");
for c in self.coeff.iter().rev().skip(1) {
pk.mul_assign(&x);
pk.add_assign(c);
}
SecretKey(pk)
pub fn secret_key_share<T: Into<<E::Fr as PrimeField>::Repr>>(&self, i: T) -> SecretKey<E> {
SecretKey(self.poly.evaluate(from_repr_plus_1::<E::Fr>(i.into())))
}
/// Returns the corresponding public key set. That information can be shared publicly.
pub fn public_keys(&self) -> PublicKeySet<E> {
let to_pub = |c: &E::Fr| PublicKey(E::G1Affine::one().mul(*c));
PublicKeySet {
coeff: self.coeff.iter().map(to_pub).collect(),
commit: self.poly.commitment(),
}
}
/// Returns the secret master key.
#[cfg(test)]
fn secret_key(&self) -> SecretKey<E> {
SecretKey(self.poly.evaluate(0))
}
}
/// Returns a hash of the given message in `G2`.
@ -287,7 +283,7 @@ fn xor_vec(x: &[u8], y: &[u8]) -> Vec<u8> {
/// Given a list of `t` samples `(i - 1, f(i) * g)` for a polynomial `f` of degree `t - 1`, and a
/// group generator `g`, returns `f(0) * g`.
pub fn interpolate<'a, C, ITR, IND>(t: usize, items: ITR) -> Result<C>
fn interpolate<'a, C, ITR, IND>(t: usize, items: ITR) -> Result<C>
where
C: CurveProjective,
ITR: IntoIterator<Item = (&'a IND, &'a C)>,
@ -352,19 +348,18 @@ mod tests {
#[test]
fn test_threshold_sig() {
let mut rng = rand::thread_rng();
let sk_set = SecretKeySet::<Bls12>::new(3, &mut rng);
let sk_set = SecretKeySet::<Bls12>::random(3, &mut rng);
let pk_set = sk_set.public_keys();
// Make sure the keys are different, and the first coefficient is the main key.
assert_eq!(*pk_set.public_key(), pk_set.coeff[0]);
assert_ne!(*pk_set.public_key(), pk_set.public_key_share(0));
assert_ne!(*pk_set.public_key(), pk_set.public_key_share(1));
assert_ne!(*pk_set.public_key(), pk_set.public_key_share(2));
assert_ne!(pk_set.public_key(), pk_set.public_key_share(0));
assert_ne!(pk_set.public_key(), pk_set.public_key_share(1));
assert_ne!(pk_set.public_key(), pk_set.public_key_share(2));
// Make sure we don't hand out the main secret key to anyone.
assert_ne!(SecretKey(sk_set.coeff[0]), sk_set.secret_key_share(0));
assert_ne!(SecretKey(sk_set.coeff[0]), sk_set.secret_key_share(1));
assert_ne!(SecretKey(sk_set.coeff[0]), sk_set.secret_key_share(2));
assert_ne!(sk_set.secret_key(), sk_set.secret_key_share(0));
assert_ne!(sk_set.secret_key(), sk_set.secret_key_share(1));
assert_ne!(sk_set.secret_key(), sk_set.secret_key_share(2));
let msg = "Totally real news";
@ -420,7 +415,7 @@ mod tests {
#[test]
fn test_threshold_enc() {
let mut rng = rand::thread_rng();
let sk_set = SecretKeySet::<Bls12>::new(3, &mut rng);
let sk_set = SecretKeySet::<Bls12>::random(3, &mut rng);
let pk_set = sk_set.public_keys();
let msg = b"Totally real news";
let ciphertext = pk_set.public_key().encrypt(&msg[..]);
@ -511,76 +506,3 @@ mod tests {
assert_eq!(sig, deser_sig);
}
}
#[cfg(feature = "serialization-serde")]
mod serde {
use pairing::{CurveAffine, CurveProjective, EncodedPoint, Engine};
use super::{DecryptionShare, PublicKey, Signature};
use serde::de::Error as DeserializeError;
use serde::{Deserialize, Deserializer, Serialize, Serializer};
const ERR_LEN: &str = "wrong length of deserialized group element";
const ERR_CODE: &str = "deserialized bytes don't encode a group element";
impl<E: Engine> Serialize for PublicKey<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for PublicKey<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(PublicKey(deserialize_projective(d)?))
}
}
impl<E: Engine> Serialize for Signature<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for Signature<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(Signature(deserialize_projective(d)?))
}
}
impl<E: Engine> Serialize for DecryptionShare<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for DecryptionShare<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(DecryptionShare(deserialize_projective(d)?))
}
}
/// Serializes the compressed representation of a group element.
fn serialize_projective<S, C>(c: &C, s: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
C: CurveProjective,
{
c.into_affine().into_compressed().as_ref().serialize(s)
}
/// Deserializes the compressed representation of a group element.
fn deserialize_projective<'de, D, C>(d: D) -> Result<C, D::Error>
where
D: Deserializer<'de>,
C: CurveProjective,
{
let bytes = <Vec<u8>>::deserialize(d)?;
if bytes.len() != <C::Affine as CurveAffine>::Compressed::size() {
return Err(D::Error::custom(ERR_LEN));
}
let mut compressed = <C::Affine as CurveAffine>::Compressed::empty();
compressed.as_mut().copy_from_slice(&bytes);
let to_err = |_| D::Error::custom(ERR_CODE);
Ok(compressed.into_affine().map_err(to_err)?.into_projective())
}
}

119
src/crypto/serde_impl.rs Normal file
View File

@ -0,0 +1,119 @@
use std::borrow::Borrow;
use std::marker::PhantomData;
use pairing::{CurveAffine, CurveProjective, EncodedPoint, Engine};
use super::{DecryptionShare, PublicKey, Signature};
use serde::de::Error as DeserializeError;
use serde::{Deserialize, Deserializer, Serialize, Serializer};
const ERR_LEN: &str = "wrong length of deserialized group element";
const ERR_CODE: &str = "deserialized bytes don't encode a group element";
/// A wrapper type to facilitate serialization and deserialization of group elements.
struct CurveWrap<C, B>(B, PhantomData<C>);
impl<C, B> CurveWrap<C, B> {
fn new(c: B) -> Self {
CurveWrap(c, PhantomData)
}
}
impl<C: CurveProjective, B: Borrow<C>> Serialize for CurveWrap<C, B> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(self.0.borrow(), s)
}
}
impl<'de, C: CurveProjective> Deserialize<'de> for CurveWrap<C, C> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(CurveWrap::new(deserialize_projective(d)?))
}
}
impl<E: Engine> Serialize for PublicKey<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for PublicKey<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(PublicKey(deserialize_projective(d)?))
}
}
impl<E: Engine> Serialize for Signature<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for Signature<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(Signature(deserialize_projective(d)?))
}
}
impl<E: Engine> Serialize for DecryptionShare<E> {
fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
serialize_projective(&self.0, s)
}
}
impl<'de, E: Engine> Deserialize<'de> for DecryptionShare<E> {
fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
Ok(DecryptionShare(deserialize_projective(d)?))
}
}
/// Serializes the compressed representation of a group element.
fn serialize_projective<S, C>(c: &C, s: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
C: CurveProjective,
{
c.into_affine().into_compressed().as_ref().serialize(s)
}
/// Deserializes the compressed representation of a group element.
fn deserialize_projective<'de, D, C>(d: D) -> Result<C, D::Error>
where
D: Deserializer<'de>,
C: CurveProjective,
{
let bytes = <Vec<u8>>::deserialize(d)?;
if bytes.len() != <C::Affine as CurveAffine>::Compressed::size() {
return Err(D::Error::custom(ERR_LEN));
}
let mut compressed = <C::Affine as CurveAffine>::Compressed::empty();
compressed.as_mut().copy_from_slice(&bytes);
let to_err = |_| D::Error::custom(ERR_CODE);
Ok(compressed.into_affine().map_err(to_err)?.into_projective())
}
/// Serialization and deserialization of vectors of projective curve elements.
pub mod projective_vec {
use super::CurveWrap;
use pairing::CurveProjective;
use serde::{Deserialize, Deserializer, Serialize, Serializer};
pub fn serialize<S, C>(vec: &[C], s: S) -> Result<S::Ok, S::Error>
where
S: Serializer,
C: CurveProjective,
{
let wrap_vec: Vec<CurveWrap<C, &C>> = vec.iter().map(CurveWrap::new).collect();
wrap_vec.serialize(s)
}
pub fn deserialize<'de, D, C>(d: D) -> Result<Vec<C>, D::Error>
where
D: Deserializer<'de>,
C: CurveProjective,
{
let wrap_vec = <Vec<CurveWrap<C, C>>>::deserialize(d)?;
Ok(wrap_vec.into_iter().map(|CurveWrap(c, _)| c).collect())
}
}

2
src/lib.rs
View File

@ -4,6 +4,8 @@
//! honey badger of BFT protocols" after a paper with the same title.
#![feature(optin_builtin_traits)]
// TODO: Remove this once https://github.com/rust-lang-nursery/error-chain/issues/245 is resolved.
#![allow(renamed_and_removed_lints)]
extern crate bincode;
extern crate byteorder;