Support caching preprocesses in FROST (#190)

* Remove the explicit included participants from FROST

Now, whoever submits preprocesses becomes the signing set. Better separates
preprocess from sign, at the cost of slightly more annoying integrations
(Monero needs to now independently lagrange/offset its key images).

* Support caching preprocesses

Closes https://github.com/serai-dex/serai/issues/40.

I *could* have added a serialization trait to Algorithm and written a ton of
data to disk, while requiring Algorithm implementors also accept such work.
Instead, I moved preprocess to a seeded RNG (Chacha20) which should be as
secure as the regular RNG. Rebuilding from cache simply loads the previously
used Chacha seed, making the Algorithm oblivious to the fact it's being
rebuilt from a cache. This removes any requirements for it to be modified
while guaranteeing equivalency.

This builds on the last commit which delayed determining the signing set till
post-preprocess acquisition. Unfortunately, that commit did force preprocess
from ThresholdView to ThresholdKeys which had visible effects on Monero.

Serai will actually need delayed set determination for #163, and overall,
it remains better, hence it's inclusion.

* Document FROST preprocess caching

* Update ethereum to new FROST

* Fix bug in Monero offset calculation and update processor

coins/monero/src/ringct/clsag/mod.rs

@@ -25,6 +25,8 @@ use crate::{
 mod multisig;
 #[cfg(feature = "multisig")]
 pub use multisig::{ClsagDetails, ClsagAddendum, ClsagMultisig};
+#[cfg(feature = "multisig")]
+pub(crate) use multisig::add_key_image_share;
 
 lazy_static! {
   static ref INV_EIGHT: Scalar = Scalar::from(8u8).invert();

coins/monero/src/ringct/clsag/multisig.rs

@@ -22,8 +22,9 @@ use transcript::{Transcript, RecommendedTranscript};
 use dalek_ff_group as dfg;
 use dleq::DLEqProof;
 use frost::{
+  dkg::lagrange,
   curve::Ed25519,
-  FrostError, ThresholdView,
+  FrostError, ThresholdKeys, ThresholdView,
   algorithm::{WriteAddendum, Algorithm},
 };
 
@@ -103,7 +104,7 @@ struct Interim {
 pub struct ClsagMultisig {
   transcript: RecommendedTranscript,
 
-  H: EdwardsPoint,
+  pub(crate) H: EdwardsPoint,
   // Merged here as CLSAG needs it, passing it would be a mess, yet having it beforehand requires
   // an extra round
   image: EdwardsPoint,
@@ -142,6 +143,20 @@ impl ClsagMultisig {
   }
 }
 
+pub(crate) fn add_key_image_share(
+  image: &mut EdwardsPoint,
+  generator: EdwardsPoint,
+  offset: Scalar,
+  included: &[u16],
+  participant: u16,
+  share: EdwardsPoint,
+) {
+  if image.is_identity() {
+    *image = generator * offset;
+  }
+  *image += share * lagrange::<dfg::Scalar>(participant, included).0;
+}
+
 impl Algorithm<Ed25519> for ClsagMultisig {
   type Transcript = RecommendedTranscript;
   type Addendum = ClsagAddendum;
@@ -154,10 +169,10 @@ impl Algorithm<Ed25519> for ClsagMultisig {
   fn preprocess_addendum<R: RngCore + CryptoRng>(
     &mut self,
     rng: &mut R,
-    view: &ThresholdView<Ed25519>,
+    keys: &ThresholdKeys<Ed25519>,
   ) -> ClsagAddendum {
     ClsagAddendum {
-      key_image: dfg::EdwardsPoint(self.H) * view.secret_share().deref(),
+      key_image: dfg::EdwardsPoint(self.H) * keys.secret_share().deref(),
       dleq: DLEqProof::prove(
         rng,
         // Doesn't take in a larger transcript object due to the usage of this
@@ -167,7 +182,7 @@ impl Algorithm<Ed25519> for ClsagMultisig {
         // try to merge later in some form, when it should instead just merge xH (as it does)
         &mut dleq_transcript(),
         &[dfg::EdwardsPoint::generator(), dfg::EdwardsPoint(self.H)],
-        view.secret_share(),
+        keys.secret_share(),
       ),
     }
   }
@@ -205,12 +220,19 @@ impl Algorithm<Ed25519> for ClsagMultisig {
       .verify(
         &mut dleq_transcript(),
         &[dfg::EdwardsPoint::generator(), dfg::EdwardsPoint(self.H)],
-        &[view.verification_share(l), addendum.key_image],
+        &[view.original_verification_share(l), addendum.key_image],
       )
       .map_err(|_| FrostError::InvalidPreprocess(l))?;
 
     self.transcript.append_message(b"key_image_share", addendum.key_image.compress().to_bytes());
-    self.image += addendum.key_image.0;
+    add_key_image_share(
+      &mut self.image,
+      self.H,
+      view.offset().0,
+      &view.included(),
+      l,
+      addendum.key_image.0,
+    );
 
     Ok(())
   }