Create a dedicated crate for the DKG (#141)

* Add dkg crate

* Remove F_len and G_len

They're generally no longer used.

* Replace hash_to_vec with a provided method around associated type H: Digest

Part of trying to minimize this trait so it can be moved elsewhere. Vec, 
which isn't std, may have been a blocker.

* Encrypt secret shares within the FROST library

Reduces requirements on callers in order to be correct.

* Update usage of Zeroize within FROST

* Inline functions in key_gen

There was no reason to have them separated as they were. sign probably 
has the same statement available, yet that isn't the focus right now.

* Add a ciphersuite package which provides hash_to_F

* Set the Ciphersuite version to something valid

* Have ed448 export Scalar/FieldElement/Point at the top level

* Move FROST over to Ciphersuite

* Correct usage of ff in ciphersuite

* Correct documentation handling

* Move Schnorr signatures to their own crate

* Remove unused feature from schnorr

* Fix Schnorr tests

* Split DKG into a separate crate

* Add serialize to Commitments and SecretShare

Helper for buf = vec![]; .write(buf).unwrap(); buf

* Move FROST over to the new dkg crate

* Update Monero lib to latest FROST

* Correct ethereum's usage of features

* Add serialize to GeneratorProof

* Add serialize helper function to FROST

* Rename AddendumSerialize to WriteAddendum

* Update processor

* Slight fix to processor

crypto/dkg/src/frost.rs

@@ -0,0 +1,458 @@
+use std::{
+  marker::PhantomData,
+  io::{self, Read, Write},
+  collections::HashMap,
+};
+
+use rand_core::{RngCore, CryptoRng};
+
+use zeroize::{Zeroize, ZeroizeOnDrop};
+
+use digest::Digest;
+use hkdf::{Hkdf, hmac::SimpleHmac};
+use chacha20::{
+  cipher::{crypto_common::KeyIvInit, StreamCipher},
+  Key as Cc20Key, Nonce as Cc20Iv, ChaCha20,
+};
+
+use group::{
+  ff::{Field, PrimeField},
+  GroupEncoding,
+};
+
+use ciphersuite::Ciphersuite;
+
+use multiexp::{multiexp_vartime, BatchVerifier};
+
+use schnorr::SchnorrSignature;
+
+use crate::{DkgError, ThresholdParams, ThresholdCore, validate_map};
+
+#[allow(non_snake_case)]
+fn challenge<C: Ciphersuite>(context: &str, l: u16, R: &[u8], Am: &[u8]) -> C::F {
+  const DST: &[u8] = b"FROST Schnorr Proof of Knowledge";
+
+  // Hashes the context to get a fixed size value out of it
+  let mut transcript = C::H::digest(context.as_bytes()).as_ref().to_vec();
+  transcript.extend(l.to_be_bytes());
+  transcript.extend(R);
+  transcript.extend(Am);
+  C::hash_to_F(DST, &transcript)
+}
+
+/// Commitments message to be broadcast to all other parties.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+pub struct Commitments<C: Ciphersuite> {
+  commitments: Vec<C::G>,
+  enc_key: C::G,
+  cached_msg: Vec<u8>,
+  sig: SchnorrSignature<C>,
+}
+impl<C: Ciphersuite> Drop for Commitments<C> {
+  fn drop(&mut self) {
+    self.zeroize();
+  }
+}
+impl<C: Ciphersuite> ZeroizeOnDrop for Commitments<C> {}
+
+impl<C: Ciphersuite> Commitments<C> {
+  pub 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()?);
+    }
+    let enc_key = read_G()?;
+
+    Ok(Commitments { commitments, enc_key, cached_msg, sig: SchnorrSignature::read(reader)? })
+  }
+
+  pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
+    writer.write_all(&self.cached_msg)?;
+    self.sig.write(writer)
+  }
+
+  pub fn serialize(&self) -> Vec<u8> {
+    let mut buf = vec![];
+    self.write(&mut buf).unwrap();
+    buf
+  }
+}
+
+/// 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>, 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(C::random_nonzero_F(&mut *rng));
+      // Step 3: Generate public commitments
+      commitments.push(C::generator() * coefficients[i]);
+      cached_msg.extend(commitments[i].to_bytes().as_ref());
+    }
+
+    // Generate an encryption key for transmitting the secret shares
+    // It would probably be perfectly fine to use one of our polynomial elements, yet doing so
+    // puts the integrity of FROST at risk. While there's almost no way it could, as it's used in
+    // an ECDH with validated group elemnents, better to avoid any questions on it
+    let enc_key = C::random_nonzero_F(&mut *rng);
+    let pub_enc_key = C::generator() * enc_key;
+    cached_msg.extend(pub_enc_key.to_bytes().as_ref());
+
+    // Step 2: Provide a proof of knowledge
+    let mut r = C::random_nonzero_F(rng);
+    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(),
+        (C::generator() * r).to_bytes().as_ref(),
+        &cached_msg,
+      ),
+    );
+    r.zeroize();
+
+    // Step 4: Broadcast
+    (
+      SecretShareMachine {
+        params: self.params,
+        context: self.context,
+        coefficients,
+        our_commitments: commitments.clone(),
+        enc_key,
+      },
+      Commitments { commitments, enc_key: pub_enc_key, cached_msg, sig },
+    )
+  }
+}
+
+fn polynomial<F: PrimeField>(coefficients: &[F], l: u16) -> F {
+  let l = F::from(u64::from(l));
+  let mut share = F::zero();
+  for (idx, coefficient) in coefficients.iter().rev().enumerate() {
+    share += coefficient;
+    if idx != (coefficients.len() - 1) {
+      share *= l;
+    }
+  }
+  share
+}
+
+/// Secret share to be sent to the party it's intended for over an authenticated channel.
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct SecretShare<F: PrimeField>(F::Repr);
+impl<F: PrimeField> Zeroize for SecretShare<F> {
+  fn zeroize(&mut self) {
+    self.0.as_mut().zeroize()
+  }
+}
+impl<F: PrimeField> Drop for SecretShare<F> {
+  fn drop(&mut self) {
+    self.zeroize();
+  }
+}
+impl<F: PrimeField> ZeroizeOnDrop for SecretShare<F> {}
+
+impl<F: PrimeField> SecretShare<F> {
+  pub fn read<R: Read>(reader: &mut R) -> io::Result<Self> {
+    let mut repr = F::Repr::default();
+    reader.read_exact(repr.as_mut())?;
+    Ok(SecretShare(repr))
+  }
+
+  pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
+    writer.write_all(self.0.as_ref())
+  }
+
+  pub fn serialize(&self) -> Vec<u8> {
+    let mut buf = vec![];
+    self.write(&mut buf).unwrap();
+    buf
+  }
+}
+
+fn create_ciphers<C: Ciphersuite>(
+  mut sender: <C::G as GroupEncoding>::Repr,
+  receiver: &mut <C::G as GroupEncoding>::Repr,
+  ecdh: &mut <C::G as GroupEncoding>::Repr,
+) -> (ChaCha20, ChaCha20) {
+  let directional = |sender: &mut <C::G as GroupEncoding>::Repr| {
+    let mut key = Cc20Key::default();
+    key.copy_from_slice(
+      &Hkdf::<C::H, SimpleHmac<C::H>>::extract(
+        Some(b"key"),
+        &[sender.as_ref(), ecdh.as_ref()].concat(),
+      )
+      .0
+      .as_ref()[.. 32],
+    );
+    let mut iv = Cc20Iv::default();
+    iv.copy_from_slice(
+      &Hkdf::<C::H, SimpleHmac<C::H>>::extract(
+        Some(b"iv"),
+        &[sender.as_ref(), ecdh.as_ref()].concat(),
+      )
+      .0
+      .as_ref()[.. 12],
+    );
+    sender.as_mut().zeroize();
+
+    let res = ChaCha20::new(&key, &iv);
+    <Cc20Key as AsMut<[u8]>>::as_mut(&mut key).zeroize();
+    <Cc20Iv as AsMut<[u8]>>::as_mut(&mut iv).zeroize();
+    res
+  };
+
+  let res = (directional(&mut sender), directional(receiver));
+  ecdh.as_mut().zeroize();
+  res
+}
+
+/// Advancement of the key generation state machine.
+#[derive(Zeroize)]
+pub struct SecretShareMachine<C: Ciphersuite> {
+  params: ThresholdParams,
+  context: String,
+  coefficients: Vec<C::F>,
+  our_commitments: Vec<C::G>,
+  enc_key: C::F,
+}
+impl<C: Ciphersuite> Drop for SecretShareMachine<C> {
+  fn drop(&mut self) {
+    self.zeroize()
+  }
+}
+impl<C: Ciphersuite> ZeroizeOnDrop for SecretShareMachine<C> {}
+
+impl<C: Ciphersuite> SecretShareMachine<C> {
+  /// Verify the data from the previous round (canonicity, PoKs, message authenticity)
+  fn verify_r1<R: RngCore + CryptoRng>(
+    &mut self,
+    rng: &mut R,
+    mut commitments: HashMap<u16, Commitments<C>>,
+  ) -> Result<(HashMap<u16, Vec<C::G>>, HashMap<u16, C::G>), DkgError> {
+    validate_map(&commitments, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;
+
+    let mut enc_keys = HashMap::new();
+    let mut batch = BatchVerifier::<u16, C::G>::new(commitments.len());
+    let mut commitments = commitments
+      .drain()
+      .map(|(l, mut msg)| {
+        enc_keys.insert(l, msg.enc_key);
+        msg.enc_key.zeroize();
+
+        // 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(DkgError::InvalidProofOfKnowledge)?;
+
+    commitments.insert(self.params.i, self.our_commitments.drain(..).collect());
+    Ok((commitments, enc_keys))
+  }
+
+  /// Continue generating a key.
+  /// Takes in everyone else's commitments. Returns a HashMap of secret shares to be sent over
+  /// authenticated channels to their relevant counterparties.
+  pub fn generate_secret_shares<R: RngCore + CryptoRng>(
+    mut self,
+    rng: &mut R,
+    commitments: HashMap<u16, Commitments<C>>,
+  ) -> Result<(KeyMachine<C>, HashMap<u16, SecretShare<C::F>>), DkgError> {
+    let (commitments, mut enc_keys) = self.verify_r1(&mut *rng, commitments)?;
+
+    // Step 1: Generate secret shares for all other parties
+    let mut sender = (C::generator() * self.enc_key).to_bytes();
+    let mut ciphers = HashMap::new();
+    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 cipher_send, cipher_recv) = {
+        let receiver = enc_keys.get_mut(&l).unwrap();
+        let mut ecdh = (*receiver * self.enc_key).to_bytes();
+
+        create_ciphers::<C>(sender, &mut receiver.to_bytes(), &mut ecdh)
+      };
+
+      let mut share = polynomial(&self.coefficients, l);
+      let mut share_bytes = share.to_repr();
+      share.zeroize();
+
+      cipher_send.apply_keystream(share_bytes.as_mut());
+      drop(cipher_send);
+
+      ciphers.insert(l, cipher_recv);
+      res.insert(l, SecretShare::<C::F>(share_bytes));
+      share_bytes.as_mut().zeroize();
+    }
+    self.enc_key.zeroize();
+    sender.as_mut().zeroize();
+
+    // Calculate our own share
+    let share = polynomial(&self.coefficients, self.params.i());
+
+    self.coefficients.zeroize();
+
+    Ok((KeyMachine { params: self.params, secret: share, commitments, ciphers }, res))
+  }
+}
+
+/// Final step of the key generation protocol.
+pub struct KeyMachine<C: Ciphersuite> {
+  params: ThresholdParams,
+  secret: C::F,
+  ciphers: HashMap<u16, ChaCha20>,
+  commitments: HashMap<u16, Vec<C::G>>,
+}
+impl<C: Ciphersuite> Zeroize for KeyMachine<C> {
+  fn zeroize(&mut self) {
+    self.params.zeroize();
+    self.secret.zeroize();
+
+    // cipher implements ZeroizeOnDrop and zeroizes on drop, yet doesn't implement Zeroize
+    // The following is redundant, as Rust should automatically handle dropping it, yet it shows
+    // awareness of this quirk and at least attempts to be comprehensive
+    for (_, cipher) in self.ciphers.drain() {
+      drop(cipher);
+    }
+
+    for (_, commitments) in self.commitments.iter_mut() {
+      commitments.zeroize();
+    }
+  }
+}
+impl<C: Ciphersuite> Drop for KeyMachine<C> {
+  fn drop(&mut self) {
+    self.zeroize()
+  }
+}
+impl<C: Ciphersuite> ZeroizeOnDrop for KeyMachine<C> {}
+
+impl<C: Ciphersuite> KeyMachine<C> {
+  /// Complete key generation.
+  /// Takes in everyone elses' shares submitted to us. Returns a ThresholdCore object representing
+  /// the generated keys. Successful protocol completion MUST be confirmed by all parties before
+  /// these keys may be safely used.
+  pub fn complete<R: RngCore + CryptoRng>(
+    mut self,
+    rng: &mut R,
+    mut shares: HashMap<u16, SecretShare<C::F>>,
+  ) -> Result<ThresholdCore<C>, DkgError> {
+    let mut secret_share = self.secret;
+    self.secret.zeroize();
+
+    validate_map(&shares, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;
+
+    // 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
+    let exponential = |i: u16, values: &[_]| {
+      let i = C::F::from(i.into());
+      let mut res = Vec::with_capacity(self.params.t().into());
+      (0 .. usize::from(self.params.t())).into_iter().fold(C::F::one(), |exp, l| {
+        res.push((exp, values[l]));
+        exp * i
+      });
+      res
+    };
+
+    let mut batch = BatchVerifier::new(shares.len());
+    for (l, mut share_bytes) in shares.drain() {
+      let mut cipher = self.ciphers.remove(&l).unwrap();
+      cipher.apply_keystream(share_bytes.0.as_mut());
+      drop(cipher);
+
+      let mut share: C::F =
+        Option::from(C::F::from_repr(share_bytes.0)).ok_or(DkgError::InvalidShare(l))?;
+      share_bytes.zeroize();
+      secret_share += share;
+
+      // 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(self.params.i, &self.commitments[&l]);
+      values.push((-share, C::generator()));
+      share.zeroize();
+
+      batch.queue(rng, l, values);
+    }
+    batch.verify_with_vartime_blame().map_err(DkgError::InvalidShare)?;
+
+    // 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, multiexp_vartime(&exponential(i, &stripes)));
+    }
+    // Removing this check would enable optimizing the above from t + (n * t) to t + ((n - 1) * t)
+    debug_assert_eq!(C::generator() * secret_share, verification_shares[&self.params.i()]);
+
+    Ok(ThresholdCore {
+      params: self.params,
+      secret_share,
+      group_key: stripes[0],
+      verification_shares,
+    })
+  }
+}