2022-10-29 08:54:42 +00:00
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use std::{
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marker::PhantomData,
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2022-11-11 03:35:09 +00:00
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ops::Deref,
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2022-10-29 08:54:42 +00:00
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io::{self, Read, Write},
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collections::HashMap,
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};
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use rand_core::{RngCore, CryptoRng};
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2022-11-11 03:35:09 +00:00
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use zeroize::{Zeroize, ZeroizeOnDrop, Zeroizing};
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2022-10-29 08:54:42 +00:00
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use digest::Digest;
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use hkdf::{Hkdf, hmac::SimpleHmac};
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use chacha20::{
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cipher::{crypto_common::KeyIvInit, StreamCipher},
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Key as Cc20Key, Nonce as Cc20Iv, ChaCha20,
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};
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use group::{
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ff::{Field, PrimeField},
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GroupEncoding,
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};
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use ciphersuite::Ciphersuite;
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use multiexp::{multiexp_vartime, BatchVerifier};
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use schnorr::SchnorrSignature;
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use crate::{DkgError, ThresholdParams, ThresholdCore, validate_map};
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#[allow(non_snake_case)]
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fn challenge<C: Ciphersuite>(context: &str, l: u16, R: &[u8], Am: &[u8]) -> C::F {
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const DST: &[u8] = b"FROST Schnorr Proof of Knowledge";
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// Hashes the context to get a fixed size value out of it
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let mut transcript = C::H::digest(context.as_bytes()).as_ref().to_vec();
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transcript.extend(l.to_be_bytes());
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transcript.extend(R);
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transcript.extend(Am);
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C::hash_to_F(DST, &transcript)
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}
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/// Commitments message to be broadcast to all other parties.
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#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
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pub struct Commitments<C: Ciphersuite> {
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commitments: Vec<C::G>,
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enc_key: C::G,
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cached_msg: Vec<u8>,
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sig: SchnorrSignature<C>,
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}
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impl<C: Ciphersuite> Commitments<C> {
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pub fn read<R: Read>(reader: &mut R, params: ThresholdParams) -> io::Result<Self> {
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let mut commitments = Vec::with_capacity(params.t().into());
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let mut cached_msg = vec![];
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#[allow(non_snake_case)]
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let mut read_G = || -> io::Result<C::G> {
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let mut buf = <C::G as GroupEncoding>::Repr::default();
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reader.read_exact(buf.as_mut())?;
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let point = C::read_G(&mut buf.as_ref())?;
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cached_msg.extend(buf.as_ref());
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Ok(point)
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};
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for _ in 0 .. params.t() {
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commitments.push(read_G()?);
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}
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let enc_key = read_G()?;
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Ok(Commitments { commitments, enc_key, cached_msg, sig: SchnorrSignature::read(reader)? })
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}
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pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
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writer.write_all(&self.cached_msg)?;
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self.sig.write(writer)
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}
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pub fn serialize(&self) -> Vec<u8> {
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let mut buf = vec![];
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self.write(&mut buf).unwrap();
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buf
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}
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}
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/// State machine to begin the key generation protocol.
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pub struct KeyGenMachine<C: Ciphersuite> {
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params: ThresholdParams,
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context: String,
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_curve: PhantomData<C>,
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}
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impl<C: Ciphersuite> KeyGenMachine<C> {
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/// Creates a new machine to generate a key for the specified curve in the specified multisig.
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// The context string should be unique among multisigs.
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pub fn new(params: ThresholdParams, context: String) -> KeyGenMachine<C> {
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KeyGenMachine { params, context, _curve: PhantomData }
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}
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/// Start generating a key according to the FROST DKG spec.
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/// Returns a commitments message to be sent to all parties over an authenticated channel. If any
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/// party submits multiple sets of commitments, they MUST be treated as malicious.
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pub fn generate_coefficients<R: RngCore + CryptoRng>(
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self,
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rng: &mut R,
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) -> (SecretShareMachine<C>, Commitments<C>) {
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let t = usize::from(self.params.t);
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let mut coefficients = Vec::with_capacity(t);
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let mut commitments = Vec::with_capacity(t);
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let mut cached_msg = vec![];
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for i in 0 .. t {
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// Step 1: Generate t random values to form a polynomial with
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coefficients.push(Zeroizing::new(C::random_nonzero_F(&mut *rng)));
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// Step 3: Generate public commitments
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commitments.push(C::generator() * coefficients[i].deref());
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cached_msg.extend(commitments[i].to_bytes().as_ref());
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}
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// Generate an encryption key for transmitting the secret shares
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// It would probably be perfectly fine to use one of our polynomial elements, yet doing so
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// puts the integrity of FROST at risk. While there's almost no way it could, as it's used in
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// an ECDH with validated group elemnents, better to avoid any questions on it
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let enc_key = Zeroizing::new(C::random_nonzero_F(&mut *rng));
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let pub_enc_key = C::generator() * enc_key.deref();
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cached_msg.extend(pub_enc_key.to_bytes().as_ref());
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// Step 2: Provide a proof of knowledge
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let r = Zeroizing::new(C::random_nonzero_F(rng));
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let nonce = C::generator() * r.deref();
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let sig = SchnorrSignature::<C>::sign(
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&coefficients[0],
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// This could be deterministic as the PoK is a singleton never opened up to cooperative
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// discussion
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// There's no reason to spend the time and effort to make this deterministic besides a
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// general obsession with canonicity and determinism though
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r,
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challenge::<C>(&self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
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);
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// Step 4: Broadcast
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(
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SecretShareMachine {
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params: self.params,
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context: self.context,
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coefficients,
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our_commitments: commitments.clone(),
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enc_key,
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pub_enc_key,
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},
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Commitments { commitments, enc_key: pub_enc_key, cached_msg, sig },
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)
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}
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}
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2022-11-11 03:35:09 +00:00
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fn polynomial<F: PrimeField + Zeroize>(coefficients: &[Zeroizing<F>], l: u16) -> Zeroizing<F> {
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let l = F::from(u64::from(l));
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let mut share = Zeroizing::new(F::zero());
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for (idx, coefficient) in coefficients.iter().rev().enumerate() {
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*share += coefficient.deref();
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if idx != (coefficients.len() - 1) {
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*share *= l;
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}
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}
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share
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}
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/// Secret share to be sent to the party it's intended for over an authenticated channel.
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#[derive(Clone, PartialEq, Eq, Debug)]
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pub struct SecretShare<F: PrimeField>(F::Repr);
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impl<F: PrimeField> Zeroize for SecretShare<F> {
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fn zeroize(&mut self) {
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self.0.as_mut().zeroize()
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}
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}
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impl<F: PrimeField> Drop for SecretShare<F> {
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fn drop(&mut self) {
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self.zeroize();
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}
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}
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impl<F: PrimeField> ZeroizeOnDrop for SecretShare<F> {}
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impl<F: PrimeField> SecretShare<F> {
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pub fn read<R: Read>(reader: &mut R) -> io::Result<Self> {
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let mut repr = F::Repr::default();
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reader.read_exact(repr.as_mut())?;
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Ok(SecretShare(repr))
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}
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pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
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writer.write_all(self.0.as_ref())
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}
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pub fn serialize(&self) -> Vec<u8> {
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let mut buf = vec![];
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self.write(&mut buf).unwrap();
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buf
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}
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}
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fn create_ciphers<C: Ciphersuite>(
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mut sender: <C::G as GroupEncoding>::Repr,
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receiver: &mut <C::G as GroupEncoding>::Repr,
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ecdh: &mut <C::G as GroupEncoding>::Repr,
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) -> (ChaCha20, ChaCha20) {
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let directional = |sender: &mut <C::G as GroupEncoding>::Repr| {
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let mut key = Cc20Key::default();
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key.copy_from_slice(
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&Hkdf::<C::H, SimpleHmac<C::H>>::extract(
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Some(b"key"),
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&[sender.as_ref(), ecdh.as_ref()].concat(),
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)
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.0
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.as_ref()[.. 32],
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);
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let mut iv = Cc20Iv::default();
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iv.copy_from_slice(
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&Hkdf::<C::H, SimpleHmac<C::H>>::extract(
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Some(b"iv"),
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&[sender.as_ref(), ecdh.as_ref()].concat(),
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)
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.0
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.as_ref()[.. 12],
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);
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sender.as_mut().zeroize();
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let res = ChaCha20::new(&key, &iv);
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<Cc20Key as AsMut<[u8]>>::as_mut(&mut key).zeroize();
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<Cc20Iv as AsMut<[u8]>>::as_mut(&mut iv).zeroize();
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res
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};
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let res = (directional(&mut sender), directional(receiver));
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ecdh.as_mut().zeroize();
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res
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}
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/// Advancement of the key generation state machine.
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#[derive(Zeroize)]
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pub struct SecretShareMachine<C: Ciphersuite> {
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params: ThresholdParams,
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context: String,
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coefficients: Vec<Zeroizing<C::F>>,
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our_commitments: Vec<C::G>,
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enc_key: Zeroizing<C::F>,
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pub_enc_key: C::G,
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}
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impl<C: Ciphersuite> SecretShareMachine<C> {
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/// Verify the data from the previous round (canonicity, PoKs, message authenticity)
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2022-12-01 16:52:52 +00:00
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#[allow(clippy::type_complexity)]
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fn verify_r1<R: RngCore + CryptoRng>(
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&mut self,
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rng: &mut R,
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mut commitments: HashMap<u16, Commitments<C>>,
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) -> Result<(HashMap<u16, Vec<C::G>>, HashMap<u16, C::G>), DkgError> {
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validate_map(&commitments, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;
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let mut enc_keys = HashMap::new();
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let mut batch = BatchVerifier::<u16, C::G>::new(commitments.len());
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let mut commitments = commitments
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.drain()
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.map(|(l, mut msg)| {
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enc_keys.insert(l, msg.enc_key);
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// Step 5: Validate each proof of knowledge
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// This is solely the prep step for the latter batch verification
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msg.sig.batch_verify(
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rng,
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&mut batch,
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l,
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msg.commitments[0],
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challenge::<C>(&self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
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);
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(l, msg.commitments.drain(..).collect::<Vec<_>>())
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})
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.collect::<HashMap<_, _>>();
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batch.verify_with_vartime_blame().map_err(DkgError::InvalidProofOfKnowledge)?;
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commitments.insert(self.params.i, self.our_commitments.drain(..).collect());
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Ok((commitments, enc_keys))
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}
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/// Continue generating a key.
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/// Takes in everyone else's commitments. Returns a HashMap of secret shares to be sent over
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/// authenticated channels to their relevant counterparties.
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2022-12-01 16:52:52 +00:00
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#[allow(clippy::type_complexity)]
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pub fn generate_secret_shares<R: RngCore + CryptoRng>(
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mut self,
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rng: &mut R,
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commitments: HashMap<u16, Commitments<C>>,
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) -> Result<(KeyMachine<C>, HashMap<u16, SecretShare<C::F>>), DkgError> {
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let (commitments, mut enc_keys) = self.verify_r1(&mut *rng, commitments)?;
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// Step 1: Generate secret shares for all other parties
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let sender = self.pub_enc_key.to_bytes();
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let mut ciphers = HashMap::new();
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let mut res = HashMap::new();
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for l in 1 ..= self.params.n() {
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// Don't insert our own shares to the byte buffer which is meant to be sent around
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// An app developer could accidentally send it. Best to keep this black boxed
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if l == self.params.i() {
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continue;
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}
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let (mut cipher_send, cipher_recv) = {
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let receiver = enc_keys.get_mut(&l).unwrap();
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let mut ecdh = (*receiver * self.enc_key.deref()).to_bytes();
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create_ciphers::<C>(sender, &mut receiver.to_bytes(), &mut ecdh)
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};
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let mut share = polynomial(&self.coefficients, l);
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let mut share_bytes = share.to_repr();
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share.zeroize();
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cipher_send.apply_keystream(share_bytes.as_mut());
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drop(cipher_send);
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ciphers.insert(l, cipher_recv);
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res.insert(l, SecretShare::<C::F>(share_bytes));
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|
|
share_bytes.as_mut().zeroize();
|
|
|
|
}
|
|
|
|
self.enc_key.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,
|
2022-11-11 03:35:09 +00:00
|
|
|
secret: Zeroizing<C::F>,
|
2022-10-29 08:54:42 +00:00
|
|
|
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> {
|
|
|
|
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);
|
|
|
|
|
2022-11-11 03:35:09 +00:00
|
|
|
let mut share = Zeroizing::new(
|
|
|
|
Option::<C::F>::from(C::F::from_repr(share_bytes.0)).ok_or(DkgError::InvalidShare(l))?,
|
|
|
|
);
|
2022-10-29 08:54:42 +00:00
|
|
|
share_bytes.zeroize();
|
2022-11-11 03:35:09 +00:00
|
|
|
*self.secret += share.deref();
|
2022-10-29 08:54:42 +00:00
|
|
|
|
|
|
|
// 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]);
|
2022-11-11 03:35:09 +00:00
|
|
|
// multiexp will Zeroize this when it's done with it
|
|
|
|
values.push((-*share.deref(), C::generator()));
|
2022-10-29 08:54:42 +00:00
|
|
|
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() {
|
2022-11-11 03:35:09 +00:00
|
|
|
verification_shares.insert(
|
|
|
|
i,
|
|
|
|
if i == self.params.i() {
|
|
|
|
C::generator() * self.secret.deref()
|
|
|
|
} else {
|
|
|
|
multiexp_vartime(&exponential(i, &stripes))
|
|
|
|
},
|
|
|
|
);
|
2022-10-29 08:54:42 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
Ok(ThresholdCore {
|
|
|
|
params: self.params,
|
2022-11-11 03:35:09 +00:00
|
|
|
secret_share: self.secret.clone(),
|
2022-10-29 08:54:42 +00:00
|
|
|
group_key: stripes[0],
|
|
|
|
verification_shares,
|
|
|
|
})
|
|
|
|
}
|
|
|
|
}
|