Implement SyncKeyGen.

This is a _synchronous_ key generation algorithm. We will use it in
`DynamicHoneyBadger`, on top of `HoneyBadger` to satisfy the synchrony
requirements.

It can also be used independently e.g. on top of a blockchain.

mod.rs

@@ -2,7 +2,7 @@ pub mod error;
 pub mod poly;
 #[cfg(feature = "serialization-protobuf")]
 pub mod protobuf_impl;
-mod serde_impl;
+pub mod serde_impl;
 
 use std::fmt;
 use std::hash::{Hash, Hasher};
@@ -132,6 +132,10 @@ impl<E: Engine> SecretKey<E> {
         SecretKey(rng.gen())
     }
 
+    pub fn from_value(f: E::Fr) -> Self {
+        SecretKey(f)
+    }
+
     /// Returns the matching public key.
     pub fn public_key(&self) -> PublicKey<E> {
         PublicKey(E::G1Affine::one().mul(self.0))
@@ -167,7 +171,7 @@ impl<E: Engine> SecretKey<E> {
 }
 
 /// An encrypted message.
-#[derive(Deserialize, Serialize, Debug)]
+#[derive(Deserialize, Serialize, Debug, Clone)]
 pub struct Ciphertext<E: Engine>(
     #[serde(with = "serde_impl::projective")] E::G1,
     Vec<u8>,
@@ -216,13 +220,25 @@ impl<E: Engine> Hash for DecryptionShare<E> {
 }
 
 /// A public key and an associated set of public key shares.
-#[derive(Serialize, Deserialize, Clone, Debug, Hash)]
+#[derive(Serialize, Deserialize, Clone, Debug)]
 pub struct PublicKeySet<E: Engine> {
     /// The coefficients of a polynomial whose value at `0` is the "master key", and value at
     /// `i + 1` is key share number `i`.
     commit: Commitment<E>,
 }
 
+impl<E: Engine> PartialEq for PublicKeySet<E> {
+    fn eq(&self, other: &Self) -> bool {
+        self.commit == other.commit
+    }
+}
+
+impl<E: Engine> Hash for PublicKeySet<E> {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        self.commit.hash(state);
+    }
+}
+
 impl<E: Engine> From<Commitment<E>> for PublicKeySet<E> {
     fn from(commit: Commitment<E>) -> PublicKeySet<E> {
         PublicKeySet { commit }
@@ -449,7 +465,7 @@ mod tests {
 
         // Each of the shares is a valid signature matching its public key share.
         for (i, sig) in &sigs {
-            pk_set.public_key_share(*i).verify(sig, msg);
+            assert!(pk_set.public_key_share(*i).verify(sig, msg));
         }
 
         // Combined, they produce a signature matching the main public key.

poly.rs

@@ -1,23 +1,20 @@
-//! Utilities for distributed key generation.
+//! Utilities for distributed key generation: uni- and bivariate polynomials and commitments.
 //!
-//! A `BivarPoly` can be used for Verifiable Secret Sharing (VSS) and for key generation by a
-//! trusted dealer. In a perfectly synchronous setting, e.g. on a blockchain or other agreed
-//! transaction log, it works like this:
+//! If `G` is a group of prime order `r` (written additively), and `g` is a generator, then
+//! multiplication by integers factors through `r`, so the map `x -> x * g` (the sum of `x`
+//! copies of `g`) is a homomorphism from the field `Fr` of integers modulo `r` to `G`. If the
+//! _discrete logarithm_ is hard, i.e. it is infeasible to reverse this map, then `x * g` can be
+//! considered a _commitment_ to `x`: By publishing it, you can guarantee to others that you won't
+//! change your mind about the value `x`, without revealing it.
 //!
-//! The dealer generates a `BivarPoly` of degree `t` and publishes the `BivariateCommitment`,
-//! with which the polynomial's values can be publicly verified. They then send _row_ `m > 0` to
-//! node number `m`. Node `m`, in turn, sends _value_ `s` to node number `s`. Then if `2 * t + 1`
-//! nodes confirm that they received a valid row, and there are at most `t` faulty nodes, then at
-//! least `t + 1` honest nodes sent on an entry of every other node's column to that node. So we
-//! know that every node can now reconstruct its column and the value at `0` of its column. These
-//! values all lie on a univariate polynomial of degree `t`, so they can be used as secret keys.
+//! This concept extends to polynomials: If you have a polynomial `f` over `Fr`, defined as
+//! `a * X * X + b * X + c`, you can publish `a * g`, `b * g` and `c * g`. Then others will be able
+//! to verify any single value `f(x)` of the polynomial without learning the original polynomial,
+//! because `f(x) * g == x * x * (a * g) + x * (b * g) + (c * g)`. Only after learning three (in
+//! general `degree + 1`) values, they can interpolate `f` itself.
 //!
-//! For Distributed Key Generation (DKG), every node proposes a polynomial via VSS. After a fixed
-//! number (at least `N - 2 * t` if there are `N` nodes and up to `t` faulty ones) of them have
-//! successfully been distributed, every node adds up the resulting secrets. Since the sum of
-//! polynomials of degree `t` is itself a polynomial of degree `t`, these sums are still valid
-//! secret keys, but now nobody knows the master key (number `0`).
-// TODO: Expand this explanation and add examples, once the API is complete and stable.
+//! This module defines univariate polynomials (in one variable) and _symmetric_ bivariate
+//! polynomials (in two variables) over a field `Fr`, as well as their _commitments_ in `G`.
 
 use std::borrow::Borrow;
 use std::hash::{Hash, Hasher};
@@ -27,9 +24,10 @@ use pairing::{CurveAffine, CurveProjective, Engine, Field, PrimeField};
 use rand::Rng;
 
 /// A univariate polynomial in the prime field.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, Serialize, Deserialize)]
 pub struct Poly<E: Engine> {
     /// The coefficients of a polynomial.
+    #[serde(with = "super::serde_impl::field_vec")]
     coeff: Vec<E::Fr>,
 }
 

serde_impl.rs

@@ -80,3 +80,105 @@ pub mod projective_vec {
         Ok(wrap_vec.into_iter().map(|CurveWrap(c, _)| c).collect())
     }
 }
+
+/// Serialization and deserialization of vectors of field elements.
+pub mod field_vec {
+    use std::borrow::Borrow;
+    use std::marker::PhantomData;
+
+    use pairing::{PrimeField, PrimeFieldRepr};
+    use serde::de::Error as DeserializeError;
+    use serde::ser::Error as SerializeError;
+    use serde::{Deserialize, Deserializer, Serialize, Serializer};
+
+    /// A wrapper type to facilitate serialization and deserialization of field elements.
+    pub struct FieldWrap<F, B>(B, PhantomData<F>);
+
+    impl<F, B> FieldWrap<F, B> {
+        pub fn new(f: B) -> Self {
+            FieldWrap(f, PhantomData)
+        }
+    }
+
+    impl<F> FieldWrap<F, F> {
+        pub fn into_inner(self) -> F {
+            self.0
+        }
+    }
+
+    impl<F: PrimeField, B: Borrow<F>> Serialize for FieldWrap<F, B> {
+        fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
+            let mut bytes = Vec::new();
+            self.0
+                .borrow()
+                .into_repr()
+                .write_be(&mut bytes)
+                .map_err(|_| S::Error::custom("failed to write bytes"))?;
+            bytes.serialize(s)
+        }
+    }
+
+    impl<'de, F: PrimeField> Deserialize<'de> for FieldWrap<F, F> {
+        fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
+            let bytes: Vec<u8> = Deserialize::deserialize(d)?;
+            let mut repr = F::zero().into_repr();
+            repr.read_be(&bytes[..])
+                .map_err(|_| D::Error::custom("failed to write bytes"))?;
+            Ok(FieldWrap::new(F::from_repr(repr).map_err(|_| {
+                D::Error::custom("invalid field element representation")
+            })?))
+        }
+    }
+
+    pub fn serialize<S, F>(vec: &[F], s: S) -> Result<S::Ok, S::Error>
+    where
+        S: Serializer,
+        F: PrimeField,
+    {
+        let wrap_vec: Vec<FieldWrap<F, &F>> = vec.iter().map(FieldWrap::new).collect();
+        wrap_vec.serialize(s)
+    }
+
+    pub fn deserialize<'de, D, F>(d: D) -> Result<Vec<F>, D::Error>
+    where
+        D: Deserializer<'de>,
+        F: PrimeField,
+    {
+        let wrap_vec = <Vec<FieldWrap<F, F>>>::deserialize(d)?;
+        Ok(wrap_vec.into_iter().map(|FieldWrap(f, _)| f).collect())
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use bincode;
+    use pairing::bls12_381::Bls12;
+    use pairing::Engine;
+    use rand::{self, Rng};
+
+    #[derive(Debug, Serialize, Deserialize)]
+    pub struct Vecs<E: Engine> {
+        #[serde(with = "super::projective_vec")]
+        curve_points: Vec<E::G1>,
+        #[serde(with = "super::field_vec")]
+        field_elements: Vec<E::Fr>,
+    }
+
+    impl<E: Engine> PartialEq for Vecs<E> {
+        fn eq(&self, other: &Self) -> bool {
+            self.curve_points == other.curve_points && self.field_elements == other.field_elements
+        }
+    }
+
+    #[test]
+    fn vecs() {
+        let mut rng = rand::thread_rng();
+        let vecs: Vecs<Bls12> = Vecs {
+            curve_points: rng.gen_iter().take(10).collect(),
+            field_elements: rng.gen_iter().take(10).collect(),
+        };
+        let ser_vecs = bincode::serialize(&vecs).expect("serialize vecs");
+        let de_vecs = bincode::deserialize(&ser_vecs).expect("deserialize vecs");
+        assert_eq!(vecs, de_vecs);
+    }
+}