Update verifier to match the last Plonk paper

src/commitment_scheme/kzg10/key.rs

@@ -225,15 +225,15 @@ pub struct OpeningKey {
     /// The generator of G2.
     #[cfg_attr(feature = "rkyv-impl", omit_bounds)]
     pub(crate) h: G2Affine,
-    /// \beta times the above generator of G2.
+    /// 'x' times the above generator of G2.
     #[cfg_attr(feature = "rkyv-impl", omit_bounds)]
-    pub(crate) beta_h: G2Affine,
+    pub(crate) x_h: G2Affine,
     /// The generator of G2, prepared for use in pairings.
     #[cfg_attr(feature = "rkyv-impl", omit_bounds)]
     pub(crate) prepared_h: G2Prepared,
-    /// \beta times the above generator of G2, prepared for use in pairings.
+    /// 'x' times the above generator of G2, prepared for use in pairings.
     #[cfg_attr(feature = "rkyv-impl", omit_bounds)]
-    pub(crate) prepared_beta_h: G2Prepared,
+    pub(crate) prepared_x_h: G2Prepared,
 }
 
 impl Serializable<{ G1Affine::SIZE + G2Affine::SIZE * 2 }> for OpeningKey {
@@ -246,7 +246,7 @@ impl Serializable<{ G1Affine::SIZE + G2Affine::SIZE * 2 }> for OpeningKey {
         // This can't fail therefore we don't care about the Result nor use it.
         writer.write(&self.g.to_bytes());
         writer.write(&self.h.to_bytes());
-        writer.write(&self.beta_h.to_bytes());
+        writer.write(&self.x_h.to_bytes());
 
         buf
     }
@@ -262,24 +262,21 @@ impl Serializable<{ G1Affine::SIZE + G2Affine::SIZE * 2 }> for OpeningKey {
 }
 
 impl OpeningKey {
-    pub(crate) fn new(
-        g: G1Affine,
-        h: G2Affine,
-        beta_h: G2Affine,
-    ) -> OpeningKey {
+    pub(crate) fn new(g: G1Affine, h: G2Affine, x_h: G2Affine) -> OpeningKey {
         let prepared_h = G2Prepared::from(h);
-        let prepared_beta_h = G2Prepared::from(beta_h);
+        let prepared_x_h = G2Prepared::from(x_h);
         OpeningKey {
             g,
             h,
-            beta_h,
+            x_h,
             prepared_h,
-            prepared_beta_h,
+            prepared_x_h,
         }
     }
 
     /// Checks whether a batch of polynomials evaluated at different points,
     /// returned their specified value.
+    #[allow(dead_code)]
     pub(crate) fn batch_check(
         &self,
         points: &[BlsScalar],
@@ -313,7 +310,7 @@ impl OpeningKey {
         let affine_total_c = G1Affine::from(total_c);
 
         let pairing = dusk_bls12_381::multi_miller_loop(&[
-            (&affine_total_w, &self.prepared_beta_h),
+            (&affine_total_w, &self.prepared_x_h),
             (&affine_total_c, &self.prepared_h),
         ])
         .final_exponentiation();
@@ -343,7 +340,7 @@ mod test {
             - (op_key.g * proof.evaluated_point))
             .into();
 
-        let inner_b: G2Affine = (op_key.beta_h - (op_key.h * point)).into();
+        let inner_b: G2Affine = (op_key.x_h - (op_key.h * point)).into();
         let prepared_inner_b = G2Prepared::from(-inner_b);
 
         let pairing = dusk_bls12_381::multi_miller_loop(&[

src/commitment_scheme/kzg10/proof.rs

@@ -34,6 +34,7 @@ pub(crate) mod alloc {
     /// Proof that multiple polynomials were correctly evaluated at a point `z`,
     /// each producing their respective evaluated points p_i(z).
     #[derive(Debug)]
+    #[allow(dead_code)]
     pub(crate) struct AggregateProof {
         /// This is a commitment to the aggregated witness polynomial.
         pub(crate) commitment_to_witness: Commitment,
@@ -45,6 +46,7 @@ pub(crate) mod alloc {
         pub(crate) commitments_to_polynomials: Vec<Commitment>,
     }
 
+    #[allow(dead_code)]
     impl AggregateProof {
         /// Initializes an `AggregatedProof` with the commitment to the witness.
         pub(crate) fn with_witness(witness: Commitment) -> AggregateProof {

src/commitment_scheme/kzg10/srs.rs

@@ -230,7 +230,7 @@ mod test {
         assert_eq!(got_pp.commit_key.powers_of_g, pp.commit_key.powers_of_g);
         assert_eq!(got_pp.opening_key.g, pp.opening_key.g);
         assert_eq!(got_pp.opening_key.h, pp.opening_key.h);
-        assert_eq!(got_pp.opening_key.beta_h, pp.opening_key.beta_h);
+        assert_eq!(got_pp.opening_key.x_h, pp.opening_key.x_h);
     }
 
     #[test]
@@ -245,6 +245,6 @@ mod test {
         assert_eq!(pp.commit_key, pp_p.commit_key);
         assert_eq!(pp.opening_key.g, pp_p.opening_key.g);
         assert_eq!(pp.opening_key.h, pp_p.opening_key.h);
-        assert_eq!(pp.opening_key.beta_h, pp_p.opening_key.beta_h);
+        assert_eq!(pp.opening_key.x_h, pp_p.opening_key.x_h);
     }
 }

src/compiler/prover.rs

@@ -515,15 +515,14 @@ impl Prover {
         );
         let w_z_chall_comm = self.commit_key.commit(&aggregate_witness)?;
 
-        // compute the shifted challenge 'v'
-        let v_challenge_shifted =
-            transcript.challenge_scalar(b"v_challenge_shifted");
+        // compute the shifted challenge 'v_w'
+        let v_w_challenge = transcript.challenge_scalar(b"v_w_challenge");
 
         // compute the shifted opening proof polynomial 'W_zw(X)'
         let shifted_aggregate_witness = CommitKey::compute_aggregate_witness(
             &[z_poly, a_w_poly, b_w_poly, d_w_poly],
             &(z_challenge * domain.group_gen),
-            &v_challenge_shifted,
+            &v_w_challenge,
         );
         let w_z_chall_w_comm =
             self.commit_key.commit(&shifted_aggregate_witness)?;