Smash dkg into dkg, dkg-[recovery, promote, musig, pedpop]

promote and pedpop require dleq, which don't support no-std. All three should
be moved outside the Serai repository, per #597, as none are planned for use
and worth covering under our BBP.

crypto/dkg/promote/src/lib.rs

@@ -0,0 +1,168 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+// This crate requires `dleq` which doesn't support no-std via std-shims
+// #![cfg_attr(not(feature = "std"), no_std)]
+
+use core::{marker::PhantomData, ops::Deref};
+use std::{
+  io::{self, Read, Write},
+  collections::HashMap,
+};
+
+use rand_core::{RngCore, CryptoRng};
+
+use ciphersuite::{group::GroupEncoding, Ciphersuite};
+
+use transcript::{Transcript, RecommendedTranscript};
+use dleq::DLEqProof;
+
+pub use dkg::*;
+
+#[cfg(test)]
+mod tests;
+
+/// Errors encountered when promoting keys.
+#[derive(Clone, PartialEq, Eq, Debug, thiserror::Error)]
+pub enum PromotionError {
+  /// Invalid participant identifier.
+  #[error("invalid participant (1 <= participant <= {n}, yet participant is {participant})")]
+  InvalidParticipant {
+    /// The total amount of participants.
+    n: u16,
+    /// The specified participant.
+    participant: Participant,
+  },
+
+  /// An incorrect amount of participants was specified.
+  #[error("incorrect amount of participants. {t} <= amount <= {n}, yet amount is {amount}")]
+  IncorrectAmountOfParticipants {
+    /// The threshold required.
+    t: u16,
+    /// The total amount of participants.
+    n: u16,
+    /// The amount of participants specified.
+    amount: usize,
+  },
+
+  /// Participant provided an invalid proof.
+  #[error("invalid proof {0}")]
+  InvalidProof(Participant),
+}
+
+fn transcript<G: GroupEncoding>(key: &G, i: Participant) -> RecommendedTranscript {
+  let mut transcript = RecommendedTranscript::new(b"DKG Generator Promotion v0.2");
+  transcript.append_message(b"group_key", key.to_bytes());
+  transcript.append_message(b"participant", i.to_bytes());
+  transcript
+}
+
+/// Proof of valid promotion to another generator.
+#[derive(Clone, Copy)]
+pub struct GeneratorProof<C: Ciphersuite> {
+  share: C::G,
+  proof: DLEqProof<C::G>,
+}
+
+impl<C: Ciphersuite> GeneratorProof<C> {
+  pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
+    writer.write_all(self.share.to_bytes().as_ref())?;
+    self.proof.write(writer)
+  }
+
+  pub fn read<R: Read>(reader: &mut R) -> io::Result<GeneratorProof<C>> {
+    Ok(GeneratorProof {
+      share: <C as Ciphersuite>::read_G(reader)?,
+      proof: DLEqProof::read(reader)?,
+    })
+  }
+
+  pub fn serialize(&self) -> Vec<u8> {
+    let mut buf = vec![];
+    self.write(&mut buf).unwrap();
+    buf
+  }
+}
+
+/// Promote a set of keys from one generator to another, where the elliptic curve is the same.
+///
+/// Since the Ciphersuite trait additionally specifies a generator, this provides an O(n) way to
+/// update the generator used with keys. This outperforms the key generation protocol which is
+/// exponential.
+pub struct GeneratorPromotion<C1: Ciphersuite, C2: Ciphersuite> {
+  base: ThresholdKeys<C1>,
+  proof: GeneratorProof<C1>,
+  _c2: PhantomData<C2>,
+}
+
+impl<C1: Ciphersuite, C2: Ciphersuite<F = C1::F, G = C1::G>> GeneratorPromotion<C1, C2> {
+  /// Begin promoting keys from one generator to another.
+  ///
+  /// Returns a proof this share was properly promoted.
+  pub fn promote<R: RngCore + CryptoRng>(
+    rng: &mut R,
+    base: ThresholdKeys<C1>,
+  ) -> (GeneratorPromotion<C1, C2>, GeneratorProof<C1>) {
+    // Do a DLEqProof for the new generator
+    let proof = GeneratorProof {
+      share: C2::generator() * base.secret_share().deref(),
+      proof: DLEqProof::prove(
+        rng,
+        &mut transcript(&base.original_group_key(), base.params().i()),
+        &[C1::generator(), C2::generator()],
+        base.secret_share(),
+      ),
+    };
+
+    (GeneratorPromotion { base, proof, _c2: PhantomData::<C2> }, proof)
+  }
+
+  /// Complete promotion by taking in the proofs from all other participants.
+  pub fn complete(
+    self,
+    proofs: &HashMap<Participant, GeneratorProof<C1>>,
+  ) -> Result<ThresholdKeys<C2>, PromotionError> {
+    let params = self.base.params();
+    if proofs.len() != (usize::from(params.n()) - 1) {
+      Err(PromotionError::IncorrectAmountOfParticipants {
+        t: params.n(),
+        n: params.n(),
+        amount: proofs.len() + 1,
+      })?;
+    }
+    for i in proofs.keys().copied() {
+      if u16::from(i) > params.n() {
+        Err(PromotionError::InvalidParticipant { n: params.n(), participant: i })?;
+      }
+    }
+
+    let mut verification_shares = HashMap::new();
+    verification_shares.insert(params.i(), self.proof.share);
+    for i in 1 ..= params.n() {
+      let i = Participant::new(i).unwrap();
+      if i == params.i() {
+        continue;
+      }
+
+      let proof = proofs.get(&i).unwrap();
+      proof
+        .proof
+        .verify(
+          &mut transcript(&self.base.original_group_key(), i),
+          &[C1::generator(), C2::generator()],
+          &[self.base.original_verification_share(i), proof.share],
+        )
+        .map_err(|_| PromotionError::InvalidProof(i))?;
+      verification_shares.insert(i, proof.share);
+    }
+
+    Ok(
+      ThresholdKeys::new(
+        params,
+        self.base.interpolation().clone(),
+        self.base.secret_share().clone(),
+        verification_shares,
+      )
+      .unwrap(),
+    )
+  }
+}