608 lines
20 KiB
Rust
608 lines
20 KiB
Rust
//! FROST keys, keygen, key shares
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#![allow(clippy::type_complexity)]
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use std::{
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collections::HashMap,
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convert::TryFrom,
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default::Default,
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fmt::{self, Debug},
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iter,
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};
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#[cfg(any(test, feature = "test-impl"))]
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use hex::FromHex;
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use rand_core::{CryptoRng, RngCore};
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use zeroize::{DefaultIsZeroes, Zeroize};
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use crate::{
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frost::Identifier, random_nonzero, Ciphersuite, Element, Error, Field, Group, Scalar,
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VerifyingKey,
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};
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pub mod dkg;
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/// Return a vector of randomly generated polynomial coefficients ([`Scalar`]s).
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pub(crate) fn generate_coefficients<C: Ciphersuite, R: RngCore + CryptoRng>(
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size: usize,
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rng: &mut R,
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) -> Vec<Scalar<C>> {
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iter::repeat_with(|| <<C::Group as Group>::Field>::random(rng))
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.take(size)
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.collect()
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}
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/// A group secret to be split between participants.
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///
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/// This is similar to a [`crate::SigningKey`], but this secret is not intended to be used
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/// on its own for signing, but split into shares that a threshold number of signers will use to
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/// sign.
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#[derive(Clone, Copy, PartialEq, Eq)]
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pub struct SharedSecret<C: Ciphersuite>(pub(crate) Scalar<C>);
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impl<C> SharedSecret<C>
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where
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C: Ciphersuite,
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{
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/// Deserialize from bytes
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pub fn from_bytes(
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bytes: <<C::Group as Group>::Field as Field>::Serialization,
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) -> Result<Self, Error<C>> {
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<<C::Group as Group>::Field>::deserialize(&bytes)
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.map(|scalar| Self(scalar))
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.map_err(|e| e.into())
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}
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/// Serialize to bytes
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pub fn to_bytes(&self) -> <<C::Group as Group>::Field as Field>::Serialization {
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<<C::Group as Group>::Field>::serialize(&self.0)
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}
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/// Generates a new uniformly random secret value using the provided RNG.
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// TODO: should this only be behind test?
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pub fn random<R>(rng: &mut R) -> Self
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where
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R: CryptoRng + RngCore,
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{
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Self(random_nonzero::<C, R>(rng))
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}
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}
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impl<C> Debug for SharedSecret<C>
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where
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C: Ciphersuite,
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{
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> std::fmt::Result {
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f.debug_tuple("SharedSecret")
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.field(&hex::encode(self.to_bytes()))
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.finish()
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}
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}
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impl<C> Default for SharedSecret<C>
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where
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C: Ciphersuite,
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{
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fn default() -> Self {
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Self(<<C::Group as Group>::Field>::zero())
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}
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}
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// Implements [`Zeroize`] by overwriting a value with the [`Default::default()`] value
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impl<C> DefaultIsZeroes for SharedSecret<C> where C: Ciphersuite {}
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impl<C> From<&SharedSecret<C>> for VerifyingKey<C>
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where
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C: Ciphersuite,
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{
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fn from(secret: &SharedSecret<C>) -> Self {
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let element = <C::Group>::generator() * secret.0;
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VerifyingKey { element }
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}
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}
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#[cfg(any(test, feature = "test-impl"))]
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impl<C> FromHex for SharedSecret<C>
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where
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C: Ciphersuite,
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{
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type Error = &'static str;
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fn from_hex<T: AsRef<[u8]>>(hex: T) -> Result<Self, Self::Error> {
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let v: Vec<u8> = FromHex::from_hex(hex).map_err(|_| "invalid hex")?;
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match v.try_into() {
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Ok(bytes) => Self::from_bytes(bytes).map_err(|_| "malformed secret encoding"),
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Err(_) => Err("malformed secret encoding"),
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}
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}
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}
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/// A secret scalar value representing a signer's share of the group secret.
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#[derive(Clone, Copy, PartialEq, Eq)]
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pub struct SigningShare<C: Ciphersuite>(pub(crate) Scalar<C>);
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impl<C> SigningShare<C>
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where
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C: Ciphersuite,
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{
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/// Deserialize from bytes
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pub fn from_bytes(
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bytes: <<C::Group as Group>::Field as Field>::Serialization,
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) -> Result<Self, Error<C>> {
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<<C::Group as Group>::Field>::deserialize(&bytes)
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.map(|scalar| Self(scalar))
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.map_err(|e| e.into())
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}
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/// Serialize to bytes
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pub fn to_bytes(&self) -> <<C::Group as Group>::Field as Field>::Serialization {
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<<C::Group as Group>::Field>::serialize(&self.0)
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}
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}
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impl<C> Debug for SigningShare<C>
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where
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C: Ciphersuite,
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{
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> std::fmt::Result {
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f.debug_tuple("SigningShare")
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.field(&hex::encode(self.to_bytes()))
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.finish()
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}
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}
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impl<C> Default for SigningShare<C>
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where
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C: Ciphersuite,
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{
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fn default() -> Self {
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Self(<<C::Group as Group>::Field>::zero())
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}
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}
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// Implements [`Zeroize`] by overwriting a value with the [`Default::default()`] value
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impl<C> DefaultIsZeroes for SigningShare<C> where C: Ciphersuite {}
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#[cfg(any(test, feature = "test-impl"))]
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impl<C> FromHex for SigningShare<C>
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where
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C: Ciphersuite,
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{
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type Error = &'static str;
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fn from_hex<T: AsRef<[u8]>>(hex: T) -> Result<Self, Self::Error> {
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let v: Vec<u8> = FromHex::from_hex(hex).map_err(|_| "invalid hex")?;
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match v.try_into() {
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Ok(bytes) => Self::from_bytes(bytes).map_err(|_| "malformed secret encoding"),
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Err(_) => Err("malformed secret encoding"),
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}
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}
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}
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/// A public group element that represents a single signer's public verification share.
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#[derive(Copy, Clone, PartialEq, Eq)]
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pub struct VerifyingShare<C>(pub(super) Element<C>)
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where
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C: Ciphersuite;
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impl<C> VerifyingShare<C>
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where
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C: Ciphersuite,
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{
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/// Deserialize from bytes
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pub fn from_bytes(bytes: <C::Group as Group>::Serialization) -> Result<Self, Error<C>> {
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<C::Group as Group>::deserialize(&bytes)
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.map(|element| Self(element))
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.map_err(|e| e.into())
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}
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/// Serialize to bytes
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pub fn to_bytes(&self) -> <C::Group as Group>::Serialization {
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<C::Group as Group>::serialize(&self.0)
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}
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}
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impl<C> Debug for VerifyingShare<C>
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where
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C: Ciphersuite,
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{
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fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
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f.debug_tuple("VerifyingShare")
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.field(&hex::encode(self.to_bytes()))
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.finish()
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}
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}
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impl<C> From<SigningShare<C>> for VerifyingShare<C>
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where
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C: Ciphersuite,
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{
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fn from(secret: SigningShare<C>) -> VerifyingShare<C> {
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VerifyingShare(<C::Group>::generator() * secret.0 as Scalar<C>)
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}
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}
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/// A [`Group::Element`] newtype that is a commitment to one coefficient of our secret polynomial.
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///
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/// This is a (public) commitment to one coefficient of a secret polynomial used for performing
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/// verifiable secret sharing for a Shamir secret share.
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#[derive(Clone, Copy, PartialEq)]
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pub(super) struct CoefficientCommitment<C: Ciphersuite>(pub(super) Element<C>);
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/// Contains the commitments to the coefficients for our secret polynomial _f_,
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/// used to generate participants' key shares.
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///
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/// [`VerifiableSecretSharingCommitment`] contains a set of commitments to the coefficients (which
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/// themselves are scalars) for a secret polynomial f, where f is used to
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/// generate each ith participant's key share f(i). Participants use this set of
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/// commitments to perform verifiable secret sharing.
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///
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/// Note that participants MUST be assured that they have the *same*
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/// [`VerifiableSecretSharingCommitment`], either by performing pairwise comparison, or by using
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/// some agreed-upon public location for publication, where each participant can
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/// ensure that they received the correct (and same) value.
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#[derive(Clone)]
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pub struct VerifiableSecretSharingCommitment<C: Ciphersuite>(
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pub(super) Vec<CoefficientCommitment<C>>,
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);
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/// A secret share generated by performing a (t-out-of-n) secret sharing scheme,
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/// generated by a dealer performing [`keygen_with_dealer`].
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///
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/// `n` is the total number of shares and `t` is the threshold required to reconstruct the secret;
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/// in this case we use Shamir's secret sharing.
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///
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/// As a solution to the secret polynomial _f_ (a 'point'), the `identifier` is the x-coordinate, and the
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/// `value` is the y-coordinate.
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///
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/// To derive a FROST keypair, the receiver of the [`SecretShare`] *must* call
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/// .into(), which under the hood also performs validation.
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#[derive(Clone, Zeroize)]
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pub struct SecretShare<C: Ciphersuite> {
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/// The participant identifier of this [`SecretShare`].
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pub identifier: Identifier<C>,
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/// Secret Key.
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pub value: SigningShare<C>,
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/// The commitments to be distributed among signers.
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pub commitment: VerifiableSecretSharingCommitment<C>,
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}
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impl<C> SecretShare<C>
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where
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C: Ciphersuite,
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{
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/// Gets the inner [`SigningShare`] value.
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pub fn secret(&self) -> &SigningShare<C> {
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&self.value
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}
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/// Verifies that a secret share is consistent with a verifiable secret sharing commitment,
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/// and returns the derived group info for the participant (their public verification share,
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/// and the group public key) if successful.
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///
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/// This ensures that this participant's share has been generated using the same
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/// mechanism as all other signing participants. Note that participants *MUST*
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/// ensure that they have the same view as all other participants of the
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/// commitment!
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///
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/// An implementation of `vss_verify()` from the [spec].
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/// This also implements `derive_group_info()` from the [spec] (which is very similar),
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/// but only for this participant.
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///
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/// [spec]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#appendix-C.2-4
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pub fn verify(&self) -> Result<(VerifyingShare<C>, VerifyingKey<C>), Error<C>> {
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let f_result = <C::Group>::generator() * self.value.0;
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let result = evaluate_vss(&self.commitment, self.identifier);
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if !(f_result == result) {
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return Err(Error::InvalidSecretShare);
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}
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let group_public = VerifyingKey {
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element: self.commitment.0[0].0,
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};
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Ok((VerifyingShare(result), group_public))
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}
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}
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/// Allows all participants' keys to be generated using a central, trusted
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/// dealer.
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///
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/// Under the hood, this performs verifiable secret sharing, which itself uses
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/// Shamir secret sharing, from which each share becomes a participant's secret
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/// key. The output from this function is a set of shares along with one single
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/// commitment that participants use to verify the integrity of the share. The
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/// number of signers is limited to 255.
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///
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/// Implements [`trusted_dealer_keygen`] from the spec.
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///
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/// [`trusted_dealer_keygen`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#appendix-C
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pub fn keygen_with_dealer<C: Ciphersuite, R: RngCore + CryptoRng>(
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max_signers: u16,
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min_signers: u16,
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rng: &mut R,
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) -> Result<(Vec<SecretShare<C>>, PublicKeyPackage<C>), Error<C>> {
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let mut bytes = [0; 64];
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rng.fill_bytes(&mut bytes);
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let secret = SharedSecret::random(rng);
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let group_public = VerifyingKey::from(&secret);
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let coefficients = generate_coefficients::<C, R>(min_signers as usize - 1, rng);
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let secret_shares = generate_secret_shares(&secret, max_signers, min_signers, coefficients)?;
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let mut signer_pubkeys: HashMap<Identifier<C>, VerifyingShare<C>> =
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HashMap::with_capacity(max_signers as usize);
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for secret_share in &secret_shares {
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let signer_public = secret_share.value.into();
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signer_pubkeys.insert(secret_share.identifier, signer_public);
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}
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Ok((
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secret_shares,
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PublicKeyPackage {
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signer_pubkeys,
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group_public,
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},
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))
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}
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/// Evaluate the polynomial with the given coefficients (constant term first)
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/// at the point x=identifier using Horner's method.
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///
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/// Implements [`polynomial_evaluate`] from the spec.
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///
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/// [`polynomial_evaluate`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#name-evaluation-of-a-polynomial
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fn evaluate_polynomial<C: Ciphersuite>(
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identifier: Identifier<C>,
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coefficients: &[Scalar<C>],
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) -> Scalar<C> {
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let mut value = <<C::Group as Group>::Field>::zero();
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let ell_scalar = identifier;
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for coeff in coefficients.iter().skip(1).rev() {
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value = value + *coeff;
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value *= ell_scalar;
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}
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value = value + coefficients[0];
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value
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}
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/// Evaluates the right-hand side of the VSS verification equation, namely
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/// ∏^{t−1}_{k=0} φ^{i^k mod q}_{ℓk} using `identifier` as `i` and the
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/// `commitment` as the commitment vector φ_ℓ
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fn evaluate_vss<C: Ciphersuite>(
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commitment: &VerifiableSecretSharingCommitment<C>,
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identifier: Identifier<C>,
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) -> Element<C> {
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let i = identifier;
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let (_, result) = commitment.0.iter().fold(
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(<<C::Group as Group>::Field>::one(), <C::Group>::identity()),
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|(i_to_the_k, sum_so_far), comm_k| (i * i_to_the_k, sum_so_far + comm_k.0 * i_to_the_k),
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);
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result
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}
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/// A FROST keypair, which can be generated either by a trusted dealer or using
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/// a DKG.
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///
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/// When using a central dealer, [`SecretShare`]s are distributed to
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/// participants, who then perform verification, before deriving
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/// [`KeyPackage`]s, which they store to later use during signing.
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#[derive(Clone)]
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pub struct KeyPackage<C: Ciphersuite> {
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/// Denotes the participant identifier each secret share key package is owned by.
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pub identifier: Identifier<C>,
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/// This participant's secret share.
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pub secret_share: SigningShare<C>,
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/// This participant's public key.
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pub public: VerifyingShare<C>,
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/// The public signing key that represents the entire group.
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pub group_public: VerifyingKey<C>,
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}
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impl<C> KeyPackage<C>
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where
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C: Ciphersuite,
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{
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/// Gets the participant identifier associated with this [`KeyPackage`].
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pub fn identifier(&self) -> &Identifier<C> {
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&self.identifier
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}
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/// Gets the participant's [`SigningShare`] associated with this [`KeyPackage`].
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pub fn secret_share(&self) -> &SigningShare<C> {
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&self.secret_share
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}
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/// Gets the participant's [`VerifyingShare`] associated with the [`SigningShare`] in this [`KeyPackage`].
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pub fn public(&self) -> &VerifyingShare<C> {
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&self.public
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}
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/// Gets the group [`VerifyingKey`] associated with the entire group in this [`KeyPackage`].
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pub fn group_public(&self) -> &VerifyingKey<C> {
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&self.group_public
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}
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}
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impl<C> TryFrom<SecretShare<C>> for KeyPackage<C>
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where
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C: Ciphersuite,
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{
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type Error = Error<C>;
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/// Tries to verify a share and construct a [`KeyPackage`] from it.
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///
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/// When participants receive a [`SecretShare`] from the dealer, they
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/// *MUST* verify the integrity of the share before continuing on to
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/// transform it into a signing/verification keypair. Here, we assume that
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/// every participant has the same view of the commitment issued by the
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/// dealer, but implementations *MUST* make sure that all participants have
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/// a consistent view of this commitment in practice.
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fn try_from(secret_share: SecretShare<C>) -> Result<Self, Error<C>> {
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let (public, group_public) = secret_share.verify()?;
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Ok(KeyPackage {
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identifier: secret_share.identifier,
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secret_share: secret_share.value,
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public,
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group_public,
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})
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}
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}
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/// Public data that contains all the signers' public keys as well as the
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/// group public key.
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///
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/// Used for verification purposes before publishing a signature.
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pub struct PublicKeyPackage<C: Ciphersuite> {
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/// When performing signing, the coordinator must ensure that they have the
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/// correct view of participants' public keys to perform verification before
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/// publishing a signature. `signer_pubkeys` represents all signers for a
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/// signing operation.
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pub signer_pubkeys: HashMap<Identifier<C>, VerifyingShare<C>>,
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/// The joint public key for the entire group.
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pub group_public: VerifyingKey<C>,
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}
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/// Generate a secret polynomial to use in secret sharing, for the given
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/// secret value. Also validates the given parameters.
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///
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/// Returns the full vector of coefficients in little-endian order (including the
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/// given secret, which is the first element) and a [`VerifiableSecretSharingCommitment`]
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/// which contains commitments to those coefficients.
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///
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/// Returns an error if the parameters (max_signers, min_signers) are inconsistent.
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pub(crate) fn generate_secret_polynomial<C: Ciphersuite>(
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secret: &SharedSecret<C>,
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max_signers: u16,
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min_signers: u16,
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mut coefficients: Vec<Scalar<C>>,
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) -> Result<(Vec<Scalar<C>>, VerifiableSecretSharingCommitment<C>), Error<C>> {
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if min_signers < 2 {
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return Err(Error::InvalidMinSigners);
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}
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if max_signers < 2 {
|
||
return Err(Error::InvalidMaxSigners);
|
||
}
|
||
|
||
if min_signers > max_signers {
|
||
return Err(Error::InvalidMinSigners);
|
||
}
|
||
|
||
if coefficients.len() != min_signers as usize - 1 {
|
||
return Err(Error::InvalidCoefficients);
|
||
}
|
||
|
||
// Prepend the secret, which is the 0th coefficient
|
||
coefficients.insert(0, secret.0);
|
||
|
||
// Create the vector of commitments
|
||
let commitment: Vec<_> = coefficients
|
||
.iter()
|
||
.map(|c| CoefficientCommitment(<C::Group as Group>::generator() * *c))
|
||
.collect();
|
||
let commitment: VerifiableSecretSharingCommitment<C> =
|
||
VerifiableSecretSharingCommitment(commitment);
|
||
|
||
Ok((coefficients, commitment))
|
||
}
|
||
|
||
/// Creates secret shares for a given secret using the given coefficients.
|
||
///
|
||
/// This function accepts a secret from which shares are generated,
|
||
/// and a list of threshold-1 coefficients. While in FROST this secret
|
||
/// and coefficients should always be generated randomly, we allow them
|
||
/// to be specified for this internal function for testability.
|
||
///
|
||
/// Internally, [`generate_secret_shares`] performs verifiable secret sharing, which
|
||
/// generates shares via Shamir Secret Sharing, and then generates public
|
||
/// commitments to those shares.
|
||
///
|
||
/// More specifically, [`generate_secret_shares`]:
|
||
/// - Interpret [secret, `coefficients[0]`, ...] as a secret polynomial f
|
||
/// - For each participant i, their secret share is f(i)
|
||
/// - The commitment to the secret polynomial f is [g^secret, `g^coefficients[0]`, ...]
|
||
///
|
||
/// Implements [`secret_share_shard`] from the spec.
|
||
///
|
||
/// [`secret_share_shard`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#appendix-C.1
|
||
pub(crate) fn generate_secret_shares<C: Ciphersuite>(
|
||
secret: &SharedSecret<C>,
|
||
max_signers: u16,
|
||
min_signers: u16,
|
||
coefficients: Vec<Scalar<C>>,
|
||
) -> Result<Vec<SecretShare<C>>, Error<C>> {
|
||
let mut secret_shares: Vec<SecretShare<C>> = Vec::with_capacity(max_signers as usize);
|
||
|
||
let (coefficients, commitment) =
|
||
generate_secret_polynomial(secret, max_signers, min_signers, coefficients)?;
|
||
|
||
for idx in 1..=max_signers {
|
||
let id = Identifier::<C>::try_from(idx)?;
|
||
let value = evaluate_polynomial(id, &coefficients);
|
||
|
||
secret_shares.push(SecretShare {
|
||
identifier: id,
|
||
value: SigningShare(value),
|
||
commitment: commitment.clone(),
|
||
});
|
||
}
|
||
|
||
Ok(secret_shares)
|
||
}
|
||
|
||
/// Recompute the secret from t-of-n secret shares using Lagrange interpolation.
|
||
pub fn reconstruct_secret<C: Ciphersuite>(
|
||
secret_shares: Vec<SecretShare<C>>,
|
||
) -> Result<SharedSecret<C>, &'static str> {
|
||
if secret_shares.is_empty() {
|
||
return Err("No secret_shares provided");
|
||
}
|
||
|
||
let secret_share_map: HashMap<Identifier<C>, SecretShare<C>> = secret_shares
|
||
.into_iter()
|
||
.map(|share| (share.identifier, share))
|
||
.collect();
|
||
|
||
let mut secret = <<C::Group as Group>::Field>::zero();
|
||
|
||
// Compute the Lagrange coefficients
|
||
for (i, secret_share) in secret_share_map.clone() {
|
||
let mut num = <<C::Group as Group>::Field>::one();
|
||
let mut den = <<C::Group as Group>::Field>::one();
|
||
|
||
for j in secret_share_map.clone().into_keys() {
|
||
if j == i {
|
||
continue;
|
||
}
|
||
|
||
// numerator *= j
|
||
num *= j;
|
||
|
||
// denominator *= j - i
|
||
den *= j - i;
|
||
}
|
||
|
||
// If at this step, the denominator is zero in the scalar field, there must be a duplicate
|
||
// secret share.
|
||
if den == <<C::Group as Group>::Field>::zero() {
|
||
return Err("Duplicate shares provided");
|
||
}
|
||
|
||
// Save numerator * 1/denomintor in the scalar field
|
||
let lagrange_coefficient = num * <<C::Group as Group>::Field>::invert(&den).unwrap();
|
||
|
||
// Compute y = f(0) via polynomial interpolation of these t-of-n solutions ('points) of f
|
||
secret = secret + (lagrange_coefficient * secret_share.value.0);
|
||
}
|
||
|
||
Ok(SharedSecret::from_bytes(<<C::Group as Group>::Field>::serialize(&secret)).unwrap())
|
||
}
|