Publicly verifiable secret sharing

Signed-off-by: lovesh <lovesh.bond@gmail.com>

saver/src/commitment.rs

@@ -35,11 +35,6 @@ use dock_crypto_utils::{msm::multiply_field_elems_with_same_group_elem, serde_ut
 /// ```
 ///
 /// Since `b`, `n` and `G` are public, it can be ensured that `G_i`s are correctly created.
-///
-/// CAVEAT: Since the same blinding `r'` is used for `H` in both the chunked commitment `J` and the commitment
-/// to the full message, they can be divided to get a value that is unique to the message and thus can
-/// be used to link 2 different proofs created for the same message. One solution to this is to generate a
-/// different `G` for each proof by hashing an agreed upon string appended with a counter.
 #[serde_as]
 #[derive(
  Clone, PartialEq, Eq, Debug, CanonicalSerialize, CanonicalDeserialize, Serialize, Deserialize,
@@ -52,7 +47,7 @@ pub struct ChunkedCommitment<G: AffineRepr>(
 impl<G: AffineRepr> ChunkedCommitment<G> {
  /// Decompose a given field element `message` to `chunks_count` chunks each of size `chunk_bit_size` and
  /// create a Pedersen commitment to those chunks. say `m` is decomposed as `m_1`, `m_2`, .. `m_n`.
- /// Create commitment key as multiples of `g` as `g_n, g_{n-1}, ..., g_2, g_1` using `create_gs`. Now commit as `m_1 * g_1 + m_2 * g_2 + ... + m_n * g_n + r * h`
+ /// Create commitment key as multiples of `g` as `g_n, g_{n-1}, ..., g_2, g_1` using `Self::commitment_key`. Now commit as `m_1 * g_1 + m_2 * g_2 + ... + m_n * g_n + r * h`
  /// Return the commitment and commitment key
  pub fn new(
  message: &G::ScalarField,

schnorr_pok/src/discrete_log.rs

@@ -56,7 +56,15 @@ pub struct PokDiscreteLogProtocol<G: AffineRepr> {
 /// Proof of knowledge of discrete log
 #[serde_as]
 #[derive(
- Clone, PartialEq, Eq, Debug, CanonicalSerialize, CanonicalDeserialize, Serialize, Deserialize,
+ Default,
+ Clone,
+ PartialEq,
+ Eq,
+ Debug,
+ CanonicalSerialize,
+ CanonicalDeserialize,
+ Serialize,
+ Deserialize,
 )]
 pub struct PokDiscreteLog<G: AffineRepr> {
  #[serde_as(as = "ArkObjectBytes")]

schnorr_pok/src/discrete_log_pairing.rs

@@ -61,7 +61,7 @@ macro_rules! impl_protocol {
 
  #[serde_as]
  #[derive(
- Clone, PartialEq, Eq, Debug, CanonicalSerialize, CanonicalDeserialize, Serialize, Deserialize,
+ Default, Clone, PartialEq, Eq, Debug, CanonicalSerialize, CanonicalDeserialize, Serialize, Deserialize,
  )]
  pub struct $proof<E: Pairing> {
  #[serde_as(as = "ArkObjectBytes")]

secret_sharing_and_dkg/src/bagheri_pvss/README.md

@@ -0,0 +1,26 @@
+# Publicly verifiable secret sharing protocols
+
+These allow a dealer to share commitments to the secret shares (`commitment_key * secret_share`) with a group such that a threshold number of group
+members can get commitment to the secret. This sharing can happen on a public bulletin board as the dealer's
+shares are encrypted for the corresponding party and anyone can verify that the shares are created correctly because the dealer
+also outputs a proof. This primitive is useful for sharing secrets on a blockchain as the blockchain can verify the proof.
+
+Based on Fig. 7 of the paper [A Unified Framework for Verifiable Secret Sharing](https://eprint.iacr.org/2023/1669).
+Implements the protocol in the paper and a variation.
+
+The dealer in the protocol in Fig 7. wants to share commitments to the shares of secrets of `k` - (`k_1`, `k_2`, ..., `k_n`) as (`g * k_1`, `g * k_2`, ..., `g * k_n`)
+to `n` parties with secret and public keys (`s_i`, `h_i = g * s_i`) such that any `t` parties can reconstruct commitment to the secret `g * k`.
+Notice the base `g` is the same in the public keys, the share commitments and the reconstructed commitment to the secret. This is implemented in [same_base](./same_base.rs)
+
+Let's say the dealer wants to share `j * k` where base `j` is also a group generator and discrete log of `j` wrt. `g` is not known
+such that party `i` gets `j * k_i`
+The dealer follows a similar protocol as above and broadcasts `y'_i = j * k_i . g * k_i = (j + g) * k_i` in addition
+to `y_i = h_i * k_i` and a proof that `k_i` is the same in both `y'_i` and `y_i`. Then each party can
+compute `g * k_i` as described in the paper and compute `j * k_i = y'_i - g * k_i`. Essentially, `y'_i` is
+an Elgamal ciphertext, `g * k_i` is the ephemeral secret key (between the dealer and party `i`) and
+`j * k_i` is the message. This is implemented in [different_base](./different_base.rs). Note that both `j` and `g` must be in the same group.
+
+The proof in the protocol described in the paper contains a polynomial of degree `t-1`. This adds to the proof `t` field
+elements (polynomial coefficients) and requires evaluation of a `t-1` degree polynomial during proving and verification.
+An alternate implementation is to have the proof contain `n` fields elements and avoid the polynomial evaluation during
+proving and verification making these faster but the proofs bigger. These are implemented in [same_base_alt](./same_base_alt.rs) and [different_base_alt](./different_base_alt.rs)