448 lines
16 KiB
Rust
448 lines
16 KiB
Rust
//! An implementation of FROST (Flexible Round-Optimized Schnorr Threshold)
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//! signatures.
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//!
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//! If you are interested in deploying FROST, please do not hesitate to consult the FROST authors.
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//!
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//! This implementation currently only supports key generation using a central
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//! dealer. In the future, we will add support for key generation via a DKG,
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//! as specified in the FROST paper.
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//!
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//! Internally, generate_with_dealer generates keys using Verifiable Secret
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//! Sharing, where shares are generated using Shamir Secret Sharing.
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use std::{
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collections::{BTreeMap, HashMap},
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fmt::{self, Debug},
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ops::Index,
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};
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use derive_getters::Getters;
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#[cfg(any(test, feature = "test-impl"))]
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use hex::FromHex;
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mod identifier;
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pub mod keys;
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pub mod round1;
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pub mod round2;
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use crate::{
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scalar_mul::VartimeMultiscalarMul, Ciphersuite, Element, Error, Field, Group, Scalar, Signature,
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};
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pub use self::identifier::Identifier;
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/// The binding factor, also known as _rho_ (ρ)
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///
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/// Ensures each signature share is strongly bound to a signing set, specific set
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/// of commitments, and a specific message.
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///
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/// <https://github.com/cfrg/draft-irtf-cfrg-frost/blob/master/draft-irtf-cfrg-frost.md>
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#[derive(Clone, PartialEq, Eq)]
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pub struct BindingFactor<C: Ciphersuite>(Scalar<C>);
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impl<C> BindingFactor<C>
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where
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C: Ciphersuite,
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{
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/// Deserializes [`BindingFactor`] from bytes.
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pub fn deserialize(
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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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/// Serializes [`BindingFactor`] to bytes.
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pub fn serialize(&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 BindingFactor<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("BindingFactor")
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.field(&hex::encode(self.serialize()))
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.finish()
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}
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}
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/// A list of binding factors and their associated identifiers.
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#[derive(Clone)]
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pub struct BindingFactorList<C: Ciphersuite>(BTreeMap<Identifier<C>, BindingFactor<C>>);
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impl<C> BindingFactorList<C>
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where
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C: Ciphersuite,
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{
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/// Create a new [`BindingFactorList`] from a vector of binding factors.
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#[cfg(feature = "internals")]
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pub fn new(binding_factors: BTreeMap<Identifier<C>, BindingFactor<C>>) -> Self {
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Self(binding_factors)
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}
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/// Return iterator through all factors.
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pub fn iter(&self) -> impl Iterator<Item = (&Identifier<C>, &BindingFactor<C>)> {
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self.0.iter()
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}
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}
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impl<C> Index<Identifier<C>> for BindingFactorList<C>
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where
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C: Ciphersuite,
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{
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type Output = BindingFactor<C>;
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// Get the binding factor of a participant in the list.
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//
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// [`binding_factor_for_participant`] in the spec
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//
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// [`binding_factor_for_participant`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#section-4.3
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fn index(&self, identifier: Identifier<C>) -> &Self::Output {
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&self.0[&identifier]
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}
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}
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/// [`compute_binding_factors`] in the spec
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///
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/// [`compute_binding_factors`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-10.html#section-4.4
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#[cfg_attr(feature = "internals", visibility::make(pub))]
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pub(crate) fn compute_binding_factor_list<C>(
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signing_package: &SigningPackage<C>,
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additional_prefix: &[u8],
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) -> BindingFactorList<C>
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where
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C: Ciphersuite,
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{
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let preimages = signing_package.binding_factor_preimages(additional_prefix);
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BindingFactorList(
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preimages
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.iter()
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.map(|(identifier, preimage)| {
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let binding_factor = C::H1(preimage);
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(*identifier, BindingFactor(binding_factor))
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})
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.collect(),
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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 BindingFactor<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::deserialize(bytes).map_err(|_| "malformed scalar encoding"),
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Err(_) => Err("malformed scalar encoding"),
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}
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}
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}
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// TODO: pub struct Lagrange<C: Ciphersuite>(Scalar);
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/// Generates the lagrange coefficient for the i'th participant.
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#[cfg_attr(feature = "internals", visibility::make(pub))]
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fn derive_interpolating_value<C: Ciphersuite>(
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signer_id: &Identifier<C>,
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signing_package: &SigningPackage<C>,
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) -> Result<Scalar<C>, Error<C>> {
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let zero = <<C::Group as Group>::Field>::zero();
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let mut num = <<C::Group as Group>::Field>::one();
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let mut den = <<C::Group as Group>::Field>::one();
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// Ala the sorting of B, just always sort by identifier in ascending order
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//
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// https://github.com/cfrg/draft-irtf-cfrg-frost/blob/master/draft-irtf-cfrg-frost.md#encoding-operations-dep-encoding
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for commitment_identifier in signing_package.signing_commitments().keys() {
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if *commitment_identifier == *signer_id {
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continue;
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}
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num *= *commitment_identifier;
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den *= *commitment_identifier - *signer_id;
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}
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if den == zero {
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return Err(Error::DuplicatedShares);
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}
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// TODO(dconnolly): return this error if the inversion result == zero
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let lagrange_coeff = num * <<C::Group as Group>::Field>::invert(&den).unwrap();
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Ok(lagrange_coeff)
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}
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/// Generated by the coordinator of the signing operation and distributed to
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/// each signing party
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#[derive(Clone, Debug, PartialEq, Eq, Getters)]
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#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
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#[cfg_attr(feature = "serde", serde(deny_unknown_fields))]
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pub struct SigningPackage<C: Ciphersuite> {
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/// The set of commitments participants published in the first round of the
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/// protocol.
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signing_commitments: BTreeMap<Identifier<C>, round1::SigningCommitments<C>>,
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/// Message which each participant will sign.
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///
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/// Each signer should perform protocol-specific verification on the
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/// message.
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#[cfg_attr(
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feature = "serde",
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serde(
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serialize_with = "serdect::slice::serialize_hex_lower_or_bin",
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deserialize_with = "serdect::slice::deserialize_hex_or_bin_vec"
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)
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)]
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message: Vec<u8>,
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/// Ciphersuite ID for serialization
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#[cfg_attr(
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feature = "serde",
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serde(serialize_with = "crate::ciphersuite_serialize::<_, C>")
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)]
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#[cfg_attr(
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feature = "serde",
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serde(deserialize_with = "crate::ciphersuite_deserialize::<_, C>")
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)]
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#[getter(skip)]
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ciphersuite: (),
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}
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impl<C> SigningPackage<C>
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where
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C: Ciphersuite,
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{
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/// Create a new `SigningPackage`
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///
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/// The `signing_commitments` are sorted by participant `identifier`.
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pub fn new(
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signing_commitments: BTreeMap<Identifier<C>, round1::SigningCommitments<C>>,
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message: &[u8],
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) -> SigningPackage<C> {
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SigningPackage {
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signing_commitments,
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message: message.to_vec(),
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ciphersuite: (),
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}
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}
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/// Get a signing commitment by its participant identifier.
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pub fn signing_commitment(&self, identifier: &Identifier<C>) -> round1::SigningCommitments<C> {
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self.signing_commitments[identifier]
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}
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/// Compute the preimages to H1 to compute the per-signer binding factors
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// We separate this out into its own method so it can be tested
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#[cfg_attr(feature = "internals", visibility::make(pub))]
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pub fn binding_factor_preimages(
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&self,
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additional_prefix: &[u8],
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) -> Vec<(Identifier<C>, Vec<u8>)> {
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let mut binding_factor_input_prefix = vec![];
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// The message is hashed with H4 to force the variable-length message
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// into a fixed-length byte string, same for hashing the variable-sized
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// (between runs of the protocol) set of group commitments, but with H5.
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binding_factor_input_prefix.extend_from_slice(C::H4(self.message.as_slice()).as_ref());
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binding_factor_input_prefix.extend_from_slice(
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C::H5(&round1::encode_group_commitments(self.signing_commitments())[..]).as_ref(),
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);
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binding_factor_input_prefix.extend_from_slice(additional_prefix);
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self.signing_commitments()
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.keys()
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.map(|identifier| {
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let mut binding_factor_input = vec![];
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binding_factor_input.extend_from_slice(&binding_factor_input_prefix);
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binding_factor_input.extend_from_slice(identifier.serialize().as_ref());
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(*identifier, binding_factor_input)
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})
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.collect()
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}
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}
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/// The product of all signers' individual commitments, published as part of the
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/// final signature.
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#[derive(Clone, PartialEq, Eq)]
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pub struct GroupCommitment<C: Ciphersuite>(pub(super) Element<C>);
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impl<C> GroupCommitment<C>
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where
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C: Ciphersuite,
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{
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/// Return the underlying element.
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#[cfg(feature = "internals")]
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pub fn to_element(self) -> <C::Group as Group>::Element {
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self.0
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}
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}
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/// Generates the group commitment which is published as part of the joint
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/// Schnorr signature.
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///
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/// Implements [`compute_group_commitment`] from the spec.
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///
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/// [`compute_group_commitment`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-10.html#section-4.5
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#[cfg_attr(feature = "internals", visibility::make(pub))]
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fn compute_group_commitment<C>(
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signing_package: &SigningPackage<C>,
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binding_factor_list: &BindingFactorList<C>,
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) -> Result<GroupCommitment<C>, Error<C>>
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where
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C: Ciphersuite,
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{
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let identity = <C::Group as Group>::identity();
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let mut group_commitment = <C::Group as Group>::identity();
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// Number of signing participants we are iterating over.
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let n = signing_package.signing_commitments().len();
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let mut binding_scalars = Vec::with_capacity(n);
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let mut binding_elements = Vec::with_capacity(n);
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// Ala the sorting of B, just always sort by identifier in ascending order
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//
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// https://github.com/cfrg/draft-irtf-cfrg-frost/blob/master/draft-irtf-cfrg-frost.md#encoding-operations-dep-encoding
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for (commitment_identifier, commitment) in signing_package.signing_commitments() {
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// The following check prevents a party from accidentally revealing their share.
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// Note that the '&&' operator would be sufficient.
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if identity == commitment.binding.0 || identity == commitment.hiding.0 {
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return Err(Error::IdentityCommitment);
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}
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let binding_factor = binding_factor_list[*commitment_identifier].clone();
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// Collect the binding commitments and their binding factors for one big
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// multiscalar multiplication at the end.
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binding_elements.push(commitment.binding.0);
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binding_scalars.push(binding_factor.0);
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group_commitment = group_commitment + commitment.hiding.0;
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}
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let accumulated_binding_commitment: Element<C> =
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VartimeMultiscalarMul::<C>::vartime_multiscalar_mul(binding_scalars, binding_elements);
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group_commitment = group_commitment + accumulated_binding_commitment;
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Ok(GroupCommitment(group_commitment))
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}
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////////////////////////////////////////////////////////////////////////////////
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// Aggregation
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////////////////////////////////////////////////////////////////////////////////
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/// Aggregates the signature shares to produce a final signature that
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/// can be verified with the group public key.
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///
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/// `signature_shares` maps the identifier of each participant to the
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/// [`round2::SignatureShare`] they sent. These identifiers must come from whatever mapping
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/// the coordinator has between communication channels and participants, i.e.
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/// they must have assurance that the [`round2::SignatureShare`] came from
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/// the participant with that identifier.
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///
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/// This operation is performed by a coordinator that can communicate with all
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/// the signing participants before publishing the final signature. The
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/// coordinator can be one of the participants or a semi-trusted third party
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/// (who is trusted to not perform denial of service attacks, but does not learn
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/// any secret information). Note that because the coordinator is trusted to
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/// report misbehaving parties in order to avoid publishing an invalid
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/// signature, if the coordinator themselves is a signer and misbehaves, they
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/// can avoid that step. However, at worst, this results in a denial of
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/// service attack due to publishing an invalid signature.
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pub fn aggregate<C>(
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signing_package: &SigningPackage<C>,
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signature_shares: &HashMap<Identifier<C>, round2::SignatureShare<C>>,
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pubkeys: &keys::PublicKeyPackage<C>,
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) -> Result<Signature<C>, Error<C>>
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where
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C: Ciphersuite,
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{
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// Encodes the signing commitment list produced in round one as part of generating [`BindingFactor`], the
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// binding factor.
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let binding_factor_list: BindingFactorList<C> =
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compute_binding_factor_list(signing_package, &[]);
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// Compute the group commitment from signing commitments produced in round one.
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let group_commitment = compute_group_commitment(signing_package, &binding_factor_list)?;
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// The aggregation of the signature shares by summing them up, resulting in
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// a plain Schnorr signature.
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//
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// Implements [`aggregate`] from the spec.
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//
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// [`aggregate`]: https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#section-5.3
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let mut z = <<C::Group as Group>::Field>::zero();
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for signature_share in signature_shares.values() {
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z = z + signature_share.share;
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}
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let signature = Signature {
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R: group_commitment.0,
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z,
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};
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// Verify the aggregate signature
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let verification_result = pubkeys
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.group_public
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.verify(signing_package.message(), &signature);
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// Only if the verification of the aggregate signature failed; verify each share to find the cheater.
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// This approach is more efficient since we don't need to verify all shares
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// if the aggregate signature is valid (which should be the common case).
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if let Err(err) = verification_result {
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// Compute the per-message challenge.
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let challenge = crate::challenge::<C>(
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&group_commitment.0,
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&pubkeys.group_public.element,
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signing_package.message().as_slice(),
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);
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// Verify the signature shares.
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for (signature_share_identifier, signature_share) in signature_shares {
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// Look up the public key for this signer, where `signer_pubkey` = _G.ScalarBaseMult(s[i])_,
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// and where s[i] is a secret share of the constant term of _f_, the secret polynomial.
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let signer_pubkey = pubkeys
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.signer_pubkeys
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.get(signature_share_identifier)
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.unwrap();
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// Compute Lagrange coefficient.
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let lambda_i = derive_interpolating_value(signature_share_identifier, signing_package)?;
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let binding_factor = binding_factor_list[*signature_share_identifier].clone();
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// Compute the commitment share.
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let R_share = signing_package
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.signing_commitment(signature_share_identifier)
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.to_group_commitment_share(&binding_factor);
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// Compute relation values to verify this signature share.
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signature_share.verify(
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*signature_share_identifier,
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&R_share,
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signer_pubkey,
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lambda_i,
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&challenge,
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)?;
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}
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// We should never reach here; but we return the verification error to be safe.
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return Err(err);
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}
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Ok(signature)
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}
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