serai/crypto/dkg/src/frost.rs

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use std::{
marker::PhantomData,
ops::Deref,
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},
GroupEncoding,
};
use ciphersuite::Ciphersuite;
use multiexp::{multiexp_vartime, BatchVerifier};
use schnorr::SchnorrSignature;
use crate::{
DkgError, ThresholdParams, ThresholdCore, validate_map,
encryption::{ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption},
};
#[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"PoK 0", &transcript.challenge(b"challenge"))
}
/// Commitments message to be broadcast to all other parties.
#[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", 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
}
/// 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> AsMut<[u8]> for SecretShare<F> {
fn as_mut(&mut self) -> &mut [u8] {
self.0.as_mut()
}
}
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> 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<u16, 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>>, DkgError> {
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(DkgError::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 secret shares to be sent over
/// authenticated channels to their relevant counterparties.
#[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<SecretShare<C::F>>>), DkgError> {
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(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,
))
}
}
/// Final step of the key generation protocol.
pub struct KeyMachine<C: Ciphersuite> {
params: ThresholdParams,
secret: Zeroizing<C::F>,
commitments: HashMap<u16, Vec<C::G>>,
encryption: Encryption<u16, 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();
}
}
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, EncryptedMessage<SecretShare<C::F>>>,
) -> Result<ThresholdCore<C>, DkgError> {
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, share_bytes) in shares.drain() {
let mut share_bytes = self.encryption.decrypt(l, share_bytes);
let mut share = Zeroizing::new(
Option::<C::F>::from(C::F::from_repr(share_bytes.0)).ok_or(DkgError::InvalidShare(l))?,
);
share_bytes.zeroize();
*self.secret += share.deref();
// 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]);
// multiexp will Zeroize this when it's done with it
values.push((-*share.deref(), 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,
if i == self.params.i() {
C::generator() * self.secret.deref()
} else {
multiexp_vartime(&exponential(i, &stripes))
},
);
}
Ok(ThresholdCore {
params: self.params,
secret_share: self.secret.clone(),
group_key: stripes[0],
verification_shares,
})
}
}