serai/crypto/dkg/src/frost.rs

use core::{
  marker::PhantomData,
  ops::Deref,
  fmt::{Debug, Formatter},
};
use std::{
  io::{self, Read, Write},
  collections::HashMap,
};

use rand_core::{RngCore, CryptoRng};

use zeroize::{Zeroize, ZeroizeOnDrop, Zeroizing};

use transcript::{Transcript, RecommendedTranscript};

use group::{
  ff::{Field, PrimeField},
  Group, GroupEncoding,
};
use ciphersuite::Ciphersuite;
use multiexp::{multiexp_vartime, BatchVerifier};

use schnorr::SchnorrSignature;

use crate::{
  DkgError, ThresholdParams, ThresholdCore, validate_map,
  encryption::{
    ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption, EncryptionKeyProof,
    DecryptionError,
  },
};

type FrostError<C> = DkgError<EncryptionKeyProof<C>>;

#[allow(non_snake_case)]
fn challenge<C: Ciphersuite>(context: &str, l: u16, R: &[u8], Am: &[u8]) -> C::F {
  let mut transcript = RecommendedTranscript::new(b"DKG FROST v0.2");
  transcript.domain_separate(b"schnorr_proof_of_knowledge");
  transcript.append_message(b"context", context.as_bytes());
  transcript.append_message(b"participant", l.to_le_bytes());
  transcript.append_message(b"nonce", R);
  transcript.append_message(b"commitments", Am);
  C::hash_to_F(b"DKG-FROST-proof_of_knowledge-0", &transcript.challenge(b"schnorr"))
}

/// The commitments message, intended to be broadcast to all other parties.
/// Every participant should only provide one set of commitments to all parties.
/// If any participant sends multiple sets of commitments, they are faulty and should be presumed
/// malicious.
/// As this library does not handle networking, it is also unable to detect if any participant is
/// so faulty. That responsibility lies with the caller.
#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
pub struct Commitments<C: Ciphersuite> {
  commitments: Vec<C::G>,
  cached_msg: Vec<u8>,
  sig: SchnorrSignature<C>,
}

impl<C: Ciphersuite> ReadWrite for Commitments<C> {
  fn read<R: Read>(reader: &mut R, params: ThresholdParams) -> io::Result<Self> {
    let mut commitments = Vec::with_capacity(params.t().into());
    let mut cached_msg = vec![];

    #[allow(non_snake_case)]
    let mut read_G = || -> io::Result<C::G> {
      let mut buf = <C::G as GroupEncoding>::Repr::default();
      reader.read_exact(buf.as_mut())?;
      let point = C::read_G(&mut buf.as_ref())?;
      cached_msg.extend(buf.as_ref());
      Ok(point)
    };

    for _ in 0 .. params.t() {
      commitments.push(read_G()?);
    }

    Ok(Commitments { commitments, cached_msg, sig: SchnorrSignature::read(reader)? })
  }

  fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
    writer.write_all(&self.cached_msg)?;
    self.sig.write(writer)
  }
}

/// State machine to begin the key generation protocol.
pub struct KeyGenMachine<C: Ciphersuite> {
  params: ThresholdParams,
  context: String,
  _curve: PhantomData<C>,
}

impl<C: Ciphersuite> KeyGenMachine<C> {
  /// Creates a new machine to generate a key for the specified curve in the specified multisig.
  // The context string should be unique among multisigs.
  pub fn new(params: ThresholdParams, context: String) -> KeyGenMachine<C> {
    KeyGenMachine { params, context, _curve: PhantomData }
  }

  /// Start generating a key according to the FROST DKG spec.
  /// Returns a commitments message to be sent to all parties over an authenticated channel. If any
  /// party submits multiple sets of commitments, they MUST be treated as malicious.
  pub fn generate_coefficients<R: RngCore + CryptoRng>(
    self,
    rng: &mut R,
  ) -> (SecretShareMachine<C>, EncryptionKeyMessage<C, Commitments<C>>) {
    let t = usize::from(self.params.t);
    let mut coefficients = Vec::with_capacity(t);
    let mut commitments = Vec::with_capacity(t);
    let mut cached_msg = vec![];

    for i in 0 .. t {
      // Step 1: Generate t random values to form a polynomial with
      coefficients.push(Zeroizing::new(C::random_nonzero_F(&mut *rng)));
      // Step 3: Generate public commitments
      commitments.push(C::generator() * coefficients[i].deref());
      cached_msg.extend(commitments[i].to_bytes().as_ref());
    }

    // Step 2: Provide a proof of knowledge
    let r = Zeroizing::new(C::random_nonzero_F(rng));
    let nonce = C::generator() * r.deref();
    let sig = SchnorrSignature::<C>::sign(
      &coefficients[0],
      // This could be deterministic as the PoK is a singleton never opened up to cooperative
      // discussion
      // There's no reason to spend the time and effort to make this deterministic besides a
      // general obsession with canonicity and determinism though
      r,
      challenge::<C>(&self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
    );

    // Additionally create an encryption mechanism to protect the secret shares
    let encryption = Encryption::new(b"FROST", self.params.i, rng);

    // Step 4: Broadcast
    let msg =
      encryption.registration(Commitments { commitments: commitments.clone(), cached_msg, sig });
    (
      SecretShareMachine {
        params: self.params,
        context: self.context,
        coefficients,
        our_commitments: commitments,
        encryption,
      },
      msg,
    )
  }
}

fn polynomial<F: PrimeField + Zeroize>(coefficients: &[Zeroizing<F>], l: u16) -> Zeroizing<F> {
  let l = F::from(u64::from(l));
  let mut share = Zeroizing::new(F::zero());
  for (idx, coefficient) in coefficients.iter().rev().enumerate() {
    *share += coefficient.deref();
    if idx != (coefficients.len() - 1) {
      *share *= l;
    }
  }
  share
}

/// The secret share message, to be sent to the party it's intended for over an authenticated
/// channel.
/// If any participant sends multiple secret shares to another participant, they are faulty.
// This should presumably be written as SecretShare(Zeroizing<F::Repr>).
// It's unfortunately not possible as F::Repr doesn't have Zeroize as a bound.
// The encryption system also explicitly uses Zeroizing<M> so it can ensure anything being
// encrypted is within Zeroizing. Accordingly, internally having Zeroizing would be redundant.
#[derive(Clone, PartialEq, Eq)]
pub struct SecretShare<F: PrimeField>(F::Repr);
impl<F: PrimeField> AsRef<[u8]> for SecretShare<F> {
  fn as_ref(&self) -> &[u8] {
    self.0.as_ref()
  }
}
impl<F: PrimeField> AsMut<[u8]> for SecretShare<F> {
  fn as_mut(&mut self) -> &mut [u8] {
    self.0.as_mut()
  }
}
impl<F: PrimeField> Debug for SecretShare<F> {
  fn fmt(&self, fmt: &mut Formatter<'_>) -> Result<(), core::fmt::Error> {
    fmt.debug_struct("SecretShare").finish_non_exhaustive()
  }
}
impl<F: PrimeField> Zeroize for SecretShare<F> {
  fn zeroize(&mut self) {
    self.0.as_mut().zeroize()
  }
}
// Still manually implement ZeroizeOnDrop to ensure these don't stick around.
// We could replace Zeroizing<M> with a bound M: ZeroizeOnDrop.
// Doing so would potentially fail to highlight thr expected behavior with these and remove a layer
// of depth.
impl<F: PrimeField> Drop for SecretShare<F> {
  fn drop(&mut self) {
    self.zeroize();
  }
}
impl<F: PrimeField> ZeroizeOnDrop for SecretShare<F> {}

impl<F: PrimeField> ReadWrite for SecretShare<F> {
  fn read<R: Read>(reader: &mut R, _: ThresholdParams) -> io::Result<Self> {
    let mut repr = F::Repr::default();
    reader.read_exact(repr.as_mut())?;
    Ok(SecretShare(repr))
  }

  fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
    writer.write_all(self.0.as_ref())
  }
}

/// Advancement of the key generation state machine.
#[derive(Zeroize)]
pub struct SecretShareMachine<C: Ciphersuite> {
  params: ThresholdParams,
  context: String,
  coefficients: Vec<Zeroizing<C::F>>,
  our_commitments: Vec<C::G>,
  encryption: Encryption<C>,
}

impl<C: Ciphersuite> SecretShareMachine<C> {
  /// Verify the data from the previous round (canonicity, PoKs, message authenticity)
  #[allow(clippy::type_complexity)]
  fn verify_r1<R: RngCore + CryptoRng>(
    &mut self,
    rng: &mut R,
    mut commitments: HashMap<u16, EncryptionKeyMessage<C, Commitments<C>>>,
  ) -> Result<HashMap<u16, Vec<C::G>>, FrostError<C>> {
    validate_map(&commitments, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;

    let mut batch = BatchVerifier::<u16, C::G>::new(commitments.len());
    let mut commitments = commitments
      .drain()
      .map(|(l, msg)| {
        let mut msg = self.encryption.register(l, msg);

        // Step 5: Validate each proof of knowledge
        // This is solely the prep step for the latter batch verification
        msg.sig.batch_verify(
          rng,
          &mut batch,
          l,
          msg.commitments[0],
          challenge::<C>(&self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
        );

        (l, msg.commitments.drain(..).collect::<Vec<_>>())
      })
      .collect::<HashMap<_, _>>();

    batch.verify_with_vartime_blame().map_err(FrostError::InvalidProofOfKnowledge)?;

    commitments.insert(self.params.i, self.our_commitments.drain(..).collect());
    Ok(commitments)
  }

  /// Continue generating a key.
  /// Takes in everyone else's commitments. Returns a HashMap of encrypted secret shares to be sent
  /// over authenticated channels to their relevant counterparties.
  /// If any participant sends multiple secret shares to another participant, they are faulty.
  #[allow(clippy::type_complexity)]
  pub fn generate_secret_shares<R: RngCore + CryptoRng>(
    mut self,
    rng: &mut R,
    commitments: HashMap<u16, EncryptionKeyMessage<C, Commitments<C>>>,
  ) -> Result<(KeyMachine<C>, HashMap<u16, EncryptedMessage<C, SecretShare<C::F>>>), FrostError<C>>
  {
    let commitments = self.verify_r1(&mut *rng, commitments)?;

    // Step 1: Generate secret shares for all other parties
    let mut res = HashMap::new();
    for l in 1 ..= self.params.n() {
      // Don't insert our own shares to the byte buffer which is meant to be sent around
      // An app developer could accidentally send it. Best to keep this black boxed
      if l == self.params.i() {
        continue;
      }

      let mut share = polynomial(&self.coefficients, l);
      let share_bytes = Zeroizing::new(SecretShare::<C::F>(share.to_repr()));
      share.zeroize();
      res.insert(l, self.encryption.encrypt(rng, l, share_bytes));
    }

    // Calculate our own share
    let share = polynomial(&self.coefficients, self.params.i());
    self.coefficients.zeroize();

    Ok((
      KeyMachine { params: self.params, secret: share, commitments, encryption: self.encryption },
      res,
    ))
  }
}

/// Advancement of the the secret share state machine protocol.
/// This machine will 'complete' the protocol, by a local perspective, and can be the last
/// interactive component. In order to be secure, the parties must confirm having successfully
/// completed the protocol (an effort out of scope to this library), yet this is modelled by one
/// more state transition.
pub struct KeyMachine<C: Ciphersuite> {
  params: ThresholdParams,
  secret: Zeroizing<C::F>,
  commitments: HashMap<u16, Vec<C::G>>,
  encryption: Encryption<C>,
}

impl<C: Ciphersuite> Zeroize for KeyMachine<C> {
  fn zeroize(&mut self) {
    self.params.zeroize();
    self.secret.zeroize();
    for (_, commitments) in self.commitments.iter_mut() {
      commitments.zeroize();
    }
    self.encryption.zeroize();
  }
}

// Calculate the exponent for a given participant and apply it to a series of commitments
// Initially used with the actual commitments to verify the secret share, later used with
// stripes to generate the verification shares
fn exponential<C: Ciphersuite>(i: u16, values: &[C::G]) -> Vec<(C::F, C::G)> {
  let i = C::F::from(i.into());
  let mut res = Vec::with_capacity(values.len());
  (0 .. values.len()).fold(C::F::one(), |exp, l| {
    res.push((exp, values[l]));
    exp * i
  });
  res
}

fn share_verification_statements<C: Ciphersuite>(
  target: u16,
  commitments: &[C::G],
  mut share: Zeroizing<C::F>,
) -> Vec<(C::F, C::G)> {
  // This can be insecurely linearized from n * t to just n using the below sums for a given
  // stripe. Doing so uses naive addition which is subject to malleability. The only way to
  // ensure that malleability isn't present is to use this n * t algorithm, which runs
  // per sender and not as an aggregate of all senders, which also enables blame
  let mut values = exponential::<C>(target, commitments);

  // Perform the share multiplication outside of the multiexp to minimize stack copying
  // While the multiexp BatchVerifier does zeroize its flattened multiexp, and itself, it still
  // converts whatever we give to an iterator and then builds a Vec internally, welcoming copies
  let neg_share_pub = C::generator() * -*share;
  share.zeroize();
  values.push((C::F::one(), neg_share_pub));

  values
}

#[derive(Clone, Copy, Hash, Debug, Zeroize)]
enum BatchId {
  Decryption(u16),
  Share(u16),
}

impl<C: Ciphersuite> KeyMachine<C> {
  /// Calculate our share given the shares sent to us.
  /// Returns a BlameMachine usable to determine if faults in the protocol occurred.
  /// Will error on, and return a blame proof for, the first-observed case of faulty behavior.
  pub fn calculate_share<R: RngCore + CryptoRng>(
    mut self,
    rng: &mut R,
    mut shares: HashMap<u16, EncryptedMessage<C, SecretShare<C::F>>>,
  ) -> Result<BlameMachine<C>, FrostError<C>> {
    validate_map(&shares, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;

    let mut batch = BatchVerifier::new(shares.len());
    let mut blames = HashMap::new();
    for (l, share_bytes) in shares.drain() {
      let (mut share_bytes, blame) =
        self.encryption.decrypt(rng, &mut batch, BatchId::Decryption(l), l, share_bytes);
      let share =
        Zeroizing::new(Option::<C::F>::from(C::F::from_repr(share_bytes.0)).ok_or_else(|| {
          FrostError::InvalidShare { participant: l, blame: Some(blame.clone()) }
        })?);
      share_bytes.zeroize();
      *self.secret += share.deref();

      blames.insert(l, blame);
      batch.queue(
        rng,
        BatchId::Share(l),
        share_verification_statements::<C>(self.params.i(), &self.commitments[&l], share),
      );
    }
    batch.verify_with_vartime_blame().map_err(|id| {
      let (l, blame) = match id {
        BatchId::Decryption(l) => (l, None),
        BatchId::Share(l) => (l, Some(blames.remove(&l).unwrap())),
      };
      FrostError::InvalidShare { participant: l, blame }
    })?;

    // Stripe commitments per t and sum them in advance. Calculating verification shares relies on
    // these sums so preprocessing them is a massive speedup
    // If these weren't just sums, yet the tables used in multiexp, this would be further optimized
    // As of right now, each multiexp will regenerate them
    let mut stripes = Vec::with_capacity(usize::from(self.params.t()));
    for t in 0 .. usize::from(self.params.t()) {
      stripes.push(self.commitments.values().map(|commitments| commitments[t]).sum());
    }

    // Calculate each user's verification share
    let mut verification_shares = HashMap::new();
    for i in 1 ..= self.params.n() {
      verification_shares.insert(
        i,
        if i == self.params.i() {
          C::generator() * self.secret.deref()
        } else {
          multiexp_vartime(&exponential::<C>(i, &stripes))
        },
      );
    }

    let KeyMachine { commitments, encryption, params, secret } = self;
    Ok(BlameMachine {
      commitments,
      encryption,
      result: ThresholdCore {
        params,
        secret_share: secret,
        group_key: stripes[0],
        verification_shares,
      },
    })
  }
}

pub struct BlameMachine<C: Ciphersuite> {
  commitments: HashMap<u16, Vec<C::G>>,
  encryption: Encryption<C>,
  result: ThresholdCore<C>,
}

impl<C: Ciphersuite> Zeroize for BlameMachine<C> {
  fn zeroize(&mut self) {
    for (_, commitments) in self.commitments.iter_mut() {
      commitments.zeroize();
    }
    self.encryption.zeroize();
    self.result.zeroize();
  }
}

impl<C: Ciphersuite> BlameMachine<C> {
  /// Mark the protocol as having been successfully completed, returning the generated keys.
  /// This should only be called after having confirmed, with all participants, successful
  /// completion.
  ///
  /// Confirming successful completion is not necessarily as simple as everyone reporting their
  /// completion. Everyone must also receive everyone's report of completion, entering into the
  /// territory of consensus protocols. This library does not handle that nor does it provide any
  /// tooling to do so. This function is solely intended to force users to acknowledge they're
  /// completing the protocol, not processing any blame.
  pub fn complete(self) -> ThresholdCore<C> {
    self.result
  }

  fn blame_internal(
    &self,
    sender: u16,
    recipient: u16,
    msg: EncryptedMessage<C, SecretShare<C::F>>,
    proof: Option<EncryptionKeyProof<C>>,
  ) -> u16 {
    let share_bytes = match self.encryption.decrypt_with_proof(sender, recipient, msg, proof) {
      Ok(share_bytes) => share_bytes,
      // If there's an invalid signature, the sender did not send a properly formed message
      Err(DecryptionError::InvalidSignature) => return sender,
      // Decryption will fail if the provided ECDH key wasn't correct for the given message
      Err(DecryptionError::InvalidProof) => return recipient,
    };

    let share = match Option::<C::F>::from(C::F::from_repr(share_bytes.0)) {
      Some(share) => share,
      // If this isn't a valid scalar, the sender is faulty
      None => return sender,
    };

    // If this isn't a valid share, the sender is faulty
    if !bool::from(
      multiexp_vartime(&share_verification_statements::<C>(
        recipient,
        &self.commitments[&sender],
        Zeroizing::new(share),
      ))
      .is_identity(),
    ) {
      return sender;
    }

    // The share was canonical and valid
    recipient
  }

  /// Given an accusation of fault, determine the faulty party (either the sender, who sent an
  /// invalid secret share, or the receiver, who claimed a valid secret share was invalid). No
  /// matter which, prevent completion of the machine, forcing an abort of the protocol.
  ///
  /// The message should be a copy of the encrypted secret share from the accused sender to the
  /// accusing recipient. This message must have been authenticated as actually having come from
  /// the sender in question.
  ///
  /// In order to enable detecting multiple faults, an `AdditionalBlameMachine` is returned, which
  /// can be used to determine further blame. These machines will process the same blame statements
  /// multiple times, always identifying blame. It is the caller's job to ensure they're unique in
  /// order to prevent multiple instances of blame over a single incident.
  pub fn blame(
    self,
    sender: u16,
    recipient: u16,
    msg: EncryptedMessage<C, SecretShare<C::F>>,
    proof: Option<EncryptionKeyProof<C>>,
  ) -> (AdditionalBlameMachine<C>, u16) {
    let faulty = self.blame_internal(sender, recipient, msg, proof);
    (AdditionalBlameMachine(self), faulty)
  }
}

#[derive(Zeroize)]
pub struct AdditionalBlameMachine<C: Ciphersuite>(BlameMachine<C>);
impl<C: Ciphersuite> AdditionalBlameMachine<C> {
  /// Given an accusation of fault, determine the faulty party (either the sender, who sent an
  /// invalid secret share, or the receiver, who claimed a valid secret share was invalid).
  ///
  /// The message should be a copy of the encrypted secret share from the accused sender to the
  /// accusing recipient. This message must have been authenticated as actually having come from
  /// the sender in question.
  ///
  /// This will process the same blame statement multiple times, always identifying blame. It is
  /// the caller's job to ensure they're unique in order to prevent multiple instances of blame
  /// over a single incident.
  pub fn blame(
    self,
    sender: u16,
    recipient: u16,
    msg: EncryptedMessage<C, SecretShare<C::F>>,
    proof: Option<EncryptionKeyProof<C>>,
  ) -> u16 {
    self.0.blame_internal(sender, recipient, msg, proof)
  }
}