Replace Interpolation::None with Interpolation::Constant

Allows the MuSig DKG to keep the secret share as the original private key,
enabling deriving FROST nonces consistently regardless of the MuSig context.

crypto/dkg/src/lib.rs

@@ -209,21 +209,16 @@ mod lib {
     }
   }
 
-  #[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
-  #[cfg_attr(feature = "borsh", derive(borsh::BorshSerialize))]
-  pub(crate) enum Interpolation {
-    None,
+  #[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+  pub(crate) enum Interpolation<F: Zeroize + PrimeField> {
+    Constant(Vec<F>),
     Lagrange,
   }
 
-  impl Interpolation {
-    pub(crate) fn interpolation_factor<F: PrimeField>(
-      self,
-      i: Participant,
-      included: &[Participant],
-    ) -> F {
+  impl<F: Zeroize + PrimeField> Interpolation<F> {
+    pub(crate) fn interpolation_factor(&self, i: Participant, included: &[Participant]) -> F {
       match self {
-        Interpolation::None => F::ONE,
+        Interpolation::Constant(c) => c[usize::from(u16::from(i) - 1)],
         Interpolation::Lagrange => {
           let i_f = F::from(u64::from(u16::from(i)));
 
@@ -254,7 +249,7 @@ mod lib {
     /// Threshold Parameters.
     pub(crate) params: ThresholdParams,
     /// The interpolation method used.
-    pub(crate) interpolation: Interpolation,
+    pub(crate) interpolation: Interpolation<C::F>,
 
     /// Secret share key.
     pub(crate) secret_share: Zeroizing<C::F>,
@@ -291,21 +286,14 @@ mod lib {
   impl<C: Ciphersuite> ThresholdCore<C> {
     pub(crate) fn new(
       params: ThresholdParams,
-      interpolation: Interpolation,
+      interpolation: Interpolation<C::F>,
       secret_share: Zeroizing<C::F>,
       verification_shares: HashMap<Participant, C::G>,
     ) -> ThresholdCore<C> {
       let t = (1 ..= params.t()).map(Participant).collect::<Vec<_>>();
-      ThresholdCore {
-        params,
-        interpolation,
-        secret_share,
-        group_key: t
-          .iter()
-          .map(|i| verification_shares[i] * interpolation.interpolation_factor::<C::F>(*i, &t))
-          .sum(),
-        verification_shares,
-      }
+      let group_key =
+        t.iter().map(|i| verification_shares[i] * interpolation.interpolation_factor(*i, &t)).sum();
+      ThresholdCore { params, interpolation, secret_share, group_key, verification_shares }
     }
 
     /// Parameters for these keys.
@@ -334,10 +322,15 @@ mod lib {
       writer.write_all(&self.params.t.to_le_bytes())?;
       writer.write_all(&self.params.n.to_le_bytes())?;
       writer.write_all(&self.params.i.to_bytes())?;
-      writer.write_all(match self.interpolation {
-        Interpolation::None => &[0],
-        Interpolation::Lagrange => &[1],
-      })?;
+      match &self.interpolation {
+        Interpolation::Constant(c) => {
+          writer.write_all(&[0])?;
+          for c in c {
+            writer.write_all(c.to_repr().as_ref())?;
+          }
+        }
+        Interpolation::Lagrange => writer.write_all(&[1])?,
+      };
       let mut share_bytes = self.secret_share.to_repr();
       writer.write_all(share_bytes.as_ref())?;
       share_bytes.as_mut().zeroize();
@@ -389,7 +382,13 @@ mod lib {
       let mut interpolation = [0];
       reader.read_exact(&mut interpolation)?;
       let interpolation = match interpolation[0] {
-        0 => Interpolation::None,
+        0 => Interpolation::Constant({
+          let mut res = Vec::with_capacity(usize::from(n));
+          for _ in 0 .. n {
+            res.push(C::read_F(reader)?);
+          }
+          res
+        }),
         1 => Interpolation::Lagrange,
         _ => Err(io::Error::other("invalid interpolation method"))?,
       };
@@ -426,7 +425,7 @@ mod lib {
   /// View of keys, interpolated and offset for usage.
   #[derive(Clone)]
   pub struct ThresholdView<C: Ciphersuite> {
-    interpolation: Interpolation,
+    interpolation: Interpolation<C::F>,
     offset: C::F,
     group_key: C::G,
     included: Vec<Participant>,
@@ -525,13 +524,13 @@ mod lib {
       included.sort();
 
       let mut secret_share = Zeroizing::new(
-        self.core.interpolation.interpolation_factor::<C::F>(self.params().i(), &included) *
+        self.core.interpolation.interpolation_factor(self.params().i(), &included) *
           self.secret_share().deref(),
       );
 
       let mut verification_shares = self.verification_shares();
       for (i, share) in &mut verification_shares {
-        *share *= self.core.interpolation.interpolation_factor::<C::F>(*i, &included);
+        *share *= self.core.interpolation.interpolation_factor(*i, &included);
       }
 
       // The offset is included by adding it to the participant with the lowest ID
@@ -542,7 +541,7 @@ mod lib {
       *verification_shares.get_mut(&included[0]).unwrap() += C::generator() * offset;
 
       Ok(ThresholdView {
-        interpolation: self.core.interpolation,
+        interpolation: self.core.interpolation.clone(),
         offset,
         group_key: self.group_key(),
         secret_share,

crypto/dkg/src/musig.rs

@@ -102,26 +102,26 @@ pub fn musig<C: Ciphersuite>(
     binding.push(binding_factor::<C>(transcript.clone(), i));
   }
 
-  // Multiply our private key by our binding factor
-  let mut secret_share = private_key.clone();
-  *secret_share *= binding[pos];
+  // Our secret share is our private key
+  let secret_share = private_key.clone();
 
   // Calculate verification shares
   let mut verification_shares = HashMap::new();
   let mut group_key = C::G::identity();
-  for (l, (key, binding)) in keys.iter().zip(binding).enumerate() {
-    let bound = *key * binding;
-    group_key += bound;
+  for l in 1 ..= keys_len {
+    let key = keys[usize::from(l) - 1];
+    group_key += key * binding[usize::from(l - 1)];
 
     // These errors also shouldn't be possible, for the same reasons as documented above
-    verification_shares.insert(
-      Participant::new(1 + u16::try_from(l).map_err(|_| DkgError::InvalidSigningSet)?)
-        .ok_or(DkgError::InvalidSigningSet)?,
-      bound,
-    );
+    verification_shares.insert(Participant::new(l).ok_or(DkgError::InvalidSigningSet)?, key);
   }
   debug_assert_eq!(C::generator() * secret_share.deref(), verification_shares[&params.i()]);
   debug_assert_eq!(musig_key::<C>(context, keys).unwrap(), group_key);
 
-  Ok(ThresholdCore::new(params, Interpolation::None, secret_share, verification_shares))
+  Ok(ThresholdCore::new(
+    params,
+    Interpolation::Constant(binding),
+    secret_share,
+    verification_shares,
+  ))
 }

crypto/dkg/src/promote.rs

@@ -113,7 +113,7 @@ impl<C1: Ciphersuite, C2: Ciphersuite<F = C1::F, G = C1::G>> GeneratorPromotion<
     Ok(ThresholdKeys {
       core: Arc::new(ThresholdCore::new(
         params,
-        self.base.core.interpolation,
+        self.base.core.interpolation.clone(),
         self.base.secret_share().clone(),
         verification_shares,
       )),

crypto/dkg/src/tests/mod.rs

@@ -47,8 +47,7 @@ pub fn recover_key<C: Ciphersuite>(keys: &HashMap<Participant, ThresholdKeys<C>>
 
   let group_private = keys.iter().fold(C::F::ZERO, |accum, (i, keys)| {
     accum +
-      (first.core.interpolation.interpolation_factor::<C::F>(*i, &included) *
-        keys.secret_share().deref())
+      (first.core.interpolation.interpolation_factor(*i, &included) * keys.secret_share().deref())
   });
   assert_eq!(C::generator() * group_private, first.group_key(), "failed to recover keys");
   group_private