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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2022-12-07 22:20:20 +00:00
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use transcript::{Transcript, RecommendedTranscript};
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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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use crate::{
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DkgError, ThresholdParams, ThresholdCore, validate_map,
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encryption::{ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption},
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};
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2022-10-29 08:54:42 +00:00
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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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2022-12-27 05:49:31 +00:00
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let mut transcript = RecommendedTranscript::new(b"DKG FROST v0.2");
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2022-12-07 22:20:20 +00:00
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transcript.domain_separate(b"Schnorr Proof of Knowledge");
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transcript.append_message(b"context", context.as_bytes());
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transcript.append_message(b"participant", l.to_le_bytes());
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transcript.append_message(b"nonce", R);
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transcript.append_message(b"commitments", Am);
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C::hash_to_F(b"PoK 0", &transcript.challenge(b"challenge"))
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2022-10-29 08:54:42 +00:00
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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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cached_msg: Vec<u8>,
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sig: SchnorrSignature<C>,
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}
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2022-12-07 22:20:20 +00:00
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impl<C: Ciphersuite> ReadWrite for Commitments<C> {
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fn read<R: Read>(reader: &mut R, params: ThresholdParams) -> io::Result<Self> {
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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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Ok(Commitments { commitments, cached_msg, sig: SchnorrSignature::read(reader)? })
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2022-10-29 08:54:42 +00:00
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}
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2022-12-07 22:20:20 +00:00
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fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
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2022-10-29 08:54:42 +00:00
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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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}
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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>, EncryptionKeyMessage<C, Commitments<C>>) {
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2022-10-29 08:54:42 +00:00
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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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2022-11-11 03:35:09 +00:00
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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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2022-11-11 03:35:09 +00:00
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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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// 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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2022-11-11 03:35:09 +00:00
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challenge::<C>(&self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
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2022-10-29 08:54:42 +00:00
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);
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2022-12-07 22:20:20 +00:00
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// Additionally create an encryption mechanism to protect the secret shares
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let encryption = Encryption::new(b"FROST", rng);
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// Step 4: Broadcast
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let msg =
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encryption.registration(Commitments { commitments: commitments.clone(), cached_msg, sig });
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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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our_commitments: commitments,
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encryption,
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},
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msg,
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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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2022-11-11 03:35:09 +00:00
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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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2022-11-11 03:35:09 +00:00
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*share += coefficient.deref();
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if idx != (coefficients.len() - 1) {
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2022-11-11 03:35:09 +00:00
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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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2022-12-07 22:20:20 +00:00
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impl<F: PrimeField> AsMut<[u8]> for SecretShare<F> {
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fn as_mut(&mut self) -> &mut [u8] {
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self.0.as_mut()
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}
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}
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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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2022-12-07 22:20:20 +00:00
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impl<F: PrimeField> ReadWrite for SecretShare<F> {
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fn read<R: Read>(reader: &mut R, _: ThresholdParams) -> io::Result<Self> {
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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
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2022-10-29 08:54:42 +00:00
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writer.write_all(self.0.as_ref())
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}
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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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2022-11-11 03:35:09 +00:00
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coefficients: Vec<Zeroizing<C::F>>,
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our_commitments: Vec<C::G>,
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encryption: Encryption<u16, C>,
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2022-10-29 08:54:42 +00:00
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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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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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mut commitments: HashMap<u16, EncryptionKeyMessage<C, Commitments<C>>>,
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) -> Result<HashMap<u16, Vec<C::G>>, DkgError> {
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2022-10-29 08:54:42 +00:00
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validate_map(&commitments, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;
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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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2022-12-07 22:20:20 +00:00
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.map(|(l, msg)| {
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let mut msg = self.encryption.register(l, msg);
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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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Ok(commitments)
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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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2022-10-29 08:54:42 +00:00
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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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2022-12-07 22:20:20 +00:00
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commitments: HashMap<u16, EncryptionKeyMessage<C, Commitments<C>>>,
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) -> Result<(KeyMachine<C>, HashMap<u16, EncryptedMessage<SecretShare<C::F>>>), DkgError> {
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let commitments = self.verify_r1(&mut *rng, commitments)?;
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2022-10-29 08:54:42 +00:00
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// Step 1: Generate secret shares for all other parties
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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 share = polynomial(&self.coefficients, l);
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2022-12-07 22:20:20 +00:00
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let share_bytes = Zeroizing::new(SecretShare::<C::F>(share.to_repr()));
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2022-10-29 08:54:42 +00:00
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share.zeroize();
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2022-12-07 22:20:20 +00:00
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res.insert(l, self.encryption.encrypt(l, share_bytes));
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2022-10-29 08:54:42 +00:00
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}
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// Calculate our own share
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let share = polynomial(&self.coefficients, self.params.i());
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self.coefficients.zeroize();
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2022-12-07 22:20:20 +00:00
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Ok((
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KeyMachine { params: self.params, secret: share, commitments, encryption: self.encryption },
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res,
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))
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2022-10-29 08:54:42 +00:00
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}
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}
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/// Final step of the key generation protocol.
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pub struct KeyMachine<C: Ciphersuite> {
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params: ThresholdParams,
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2022-11-11 03:35:09 +00:00
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secret: Zeroizing<C::F>,
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commitments: HashMap<u16, Vec<C::G>>,
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2022-12-07 22:20:20 +00:00
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encryption: Encryption<u16, C>,
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2022-10-29 08:54:42 +00:00
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}
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impl<C: Ciphersuite> Zeroize for KeyMachine<C> {
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fn zeroize(&mut self) {
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self.params.zeroize();
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self.secret.zeroize();
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for (_, commitments) in self.commitments.iter_mut() {
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commitments.zeroize();
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}
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2022-12-07 22:20:20 +00:00
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self.encryption.zeroize();
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}
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}
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impl<C: Ciphersuite> Drop for KeyMachine<C> {
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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<C: Ciphersuite> ZeroizeOnDrop for KeyMachine<C> {}
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impl<C: Ciphersuite> KeyMachine<C> {
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/// Complete key generation.
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/// Takes in everyone elses' shares submitted to us. Returns a ThresholdCore object representing
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/// the generated keys. Successful protocol completion MUST be confirmed by all parties before
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/// these keys may be safely used.
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pub fn complete<R: RngCore + CryptoRng>(
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mut self,
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rng: &mut R,
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2022-12-07 22:20:20 +00:00
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mut shares: HashMap<u16, EncryptedMessage<SecretShare<C::F>>>,
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2022-10-29 08:54:42 +00:00
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) -> Result<ThresholdCore<C>, DkgError> {
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validate_map(&shares, &(1 ..= self.params.n()).collect::<Vec<_>>(), self.params.i())?;
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// Calculate the exponent for a given participant and apply it to a series of commitments
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// Initially used with the actual commitments to verify the secret share, later used with
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// stripes to generate the verification shares
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let exponential = |i: u16, values: &[_]| {
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let i = C::F::from(i.into());
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let mut res = Vec::with_capacity(self.params.t().into());
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(0 .. usize::from(self.params.t())).into_iter().fold(C::F::one(), |exp, l| {
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res.push((exp, values[l]));
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exp * i
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});
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res
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};
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let mut batch = BatchVerifier::new(shares.len());
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2022-12-07 22:20:20 +00:00
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for (l, share_bytes) in shares.drain() {
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let mut share_bytes = self.encryption.decrypt(l, share_bytes);
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2022-11-11 03:35:09 +00:00
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let mut share = Zeroizing::new(
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Option::<C::F>::from(C::F::from_repr(share_bytes.0)).ok_or(DkgError::InvalidShare(l))?,
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);
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2022-10-29 08:54:42 +00:00
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share_bytes.zeroize();
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2022-11-11 03:35:09 +00:00
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*self.secret += share.deref();
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2022-10-29 08:54:42 +00:00
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// This can be insecurely linearized from n * t to just n using the below sums for a given
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// stripe. Doing so uses naive addition which is subject to malleability. The only way to
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// ensure that malleability isn't present is to use this n * t algorithm, which runs
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// per sender and not as an aggregate of all senders, which also enables blame
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let mut values = exponential(self.params.i, &self.commitments[&l]);
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2022-11-11 03:35:09 +00:00
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// multiexp will Zeroize this when it's done with it
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values.push((-*share.deref(), C::generator()));
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2022-10-29 08:54:42 +00:00
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share.zeroize();
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batch.queue(rng, l, values);
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}
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batch.verify_with_vartime_blame().map_err(DkgError::InvalidShare)?;
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// Stripe commitments per t and sum them in advance. Calculating verification shares relies on
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// these sums so preprocessing them is a massive speedup
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// If these weren't just sums, yet the tables used in multiexp, this would be further optimized
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// As of right now, each multiexp will regenerate them
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let mut stripes = Vec::with_capacity(usize::from(self.params.t()));
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for t in 0 .. usize::from(self.params.t()) {
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stripes.push(self.commitments.values().map(|commitments| commitments[t]).sum());
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}
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// Calculate each user's verification share
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let mut verification_shares = HashMap::new();
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for i in 1 ..= self.params.n() {
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2022-11-11 03:35:09 +00:00
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verification_shares.insert(
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i,
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if i == self.params.i() {
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C::generator() * self.secret.deref()
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} else {
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multiexp_vartime(&exponential(i, &stripes))
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},
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);
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2022-10-29 08:54:42 +00:00
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}
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Ok(ThresholdCore {
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params: self.params,
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2022-11-11 03:35:09 +00:00
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secret_share: self.secret.clone(),
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2022-10-29 08:54:42 +00:00
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group_key: stripes[0],
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verification_shares,
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})
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}
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}
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