Circuit: Check pk_d_old = derived_pk_d_old only when split_flag = 0 (#64)

In the circuit derived_pk_d_old is evaluated from rivk, ak, nk and g_d_old.
rivk, ak and nk comes from the FullViewingKey stored in the spent note.
For split note, the FullViewingKey stored in the spent note is random in order to derive a random Nullifier nf_old.
Thus, the constraint pk_d_old = derived_pk_d_old must not be checked for split note (split_flag=1).

src/circuit.rs

@@ -225,6 +225,7 @@ impl plonk::Circuit<pallas::Base> for Circuit {
         // Constrain split_flag = 1 or nf_old = nf_old_pub
         // Constrain is_native_asset to be boolean
         // Constraint if is_native_asset = 1 then asset = native_asset else asset != native_asset
+        // Constraint split_flag = 1 or derived_pk_d_old = pk_d_old
         let q_orchard = meta.selector();
         meta.create_gate("Orchard circuit checks", |meta| {
             let q_orchard = meta.query_selector(q_orchard);
@@ -261,6 +262,11 @@ impl plonk::Circuit<pallas::Base> for Circuit {
             let diff_asset_x = asset_x - Expression::Constant(*native_asset.x());
             let diff_asset_y = asset_y - Expression::Constant(*native_asset.y());
 
+            let pk_d_old_x = meta.query_advice(advices[6], Rotation::next());
+            let pk_d_old_y = meta.query_advice(advices[7], Rotation::next());
+            let derived_pk_d_old_x = meta.query_advice(advices[8], Rotation::next());
+            let derived_pk_d_old_y = meta.query_advice(advices[9], Rotation::next());
+
             Constraints::with_selector(
                 q_orchard,
                 [
@@ -285,7 +291,7 @@ impl plonk::Circuit<pallas::Base> for Circuit {
                     ),
                     (
                         "split_flag = 1 or nf_old = nf_old_pub",
-                        (one.clone() - split_flag) * (nf_old - nf_old_pub),
+                        (one.clone() - split_flag.clone()) * (nf_old - nf_old_pub),
                     ),
                     (
                         "bool_check is_native_asset",
@@ -308,7 +314,22 @@ impl plonk::Circuit<pallas::Base> for Circuit {
                         "(is_native_asset = 0) => (asset != native_asset)",
                         (one.clone() - is_native_asset)
                             * (diff_asset_x * diff_asset_x_inv - one.clone())
-                            * (diff_asset_y * diff_asset_y_inv - one),
+                            * (diff_asset_y * diff_asset_y_inv - one.clone()),
+                    ),
+                    // Constrain derived pk_d_old to equal witnessed pk_d_old
+                    //
+                    // This equality constraint is technically superfluous, because the assigned
+                    // value of `derived_pk_d_old` is an equivalent witness. But it's nice to see
+                    // an explicit connection between circuit-synthesized values, and explicit
+                    // prover witnesses. We could get the best of both worlds with a write-on-copy
+                    // abstraction (https://github.com/zcash/halo2/issues/334).
+                    (
+                        "split_flag = 1 or pk_d_old_x = derived_pk_d_old_x",
+                        (one.clone() - split_flag.clone()) * (pk_d_old_x - derived_pk_d_old_x),
+                    ),
+                    (
+                        "split_flag = 1 or pk_d_old_y = derived_pk_d_old_y",
+                        (one - split_flag) * (pk_d_old_y - derived_pk_d_old_y),
                     ),
                 ],
             )
@@ -669,7 +690,7 @@ impl plonk::Circuit<pallas::Base> for Circuit {
         }
 
         // Diversified address integrity (https://p.z.cash/ZKS:action-addr-integrity?partial).
-        let pk_d_old = {
+        let (derived_pk_d_old, pk_d_old) = {
             let ivk = {
                 let ak = ak_P.extract_p().inner().clone();
                 let rivk = ScalarFixed::new(
@@ -696,22 +717,13 @@ impl plonk::Circuit<pallas::Base> for Circuit {
             let (derived_pk_d_old, _ivk) =
                 g_d_old.mul(layouter.namespace(|| "[ivk] g_d_old"), ivk)?;
 
-            // Constrain derived pk_d_old to equal witnessed pk_d_old
-            //
-            // This equality constraint is technically superfluous, because the assigned
-            // value of `derived_pk_d_old` is an equivalent witness. But it's nice to see
-            // an explicit connection between circuit-synthesized values, and explicit
-            // prover witnesses. We could get the best of both worlds with a write-on-copy
-            // abstraction (https://github.com/zcash/halo2/issues/334).
             let pk_d_old = NonIdentityPoint::new(
                 ecc_chip.clone(),
                 layouter.namespace(|| "witness pk_d_old"),
                 self.pk_d_old.map(|pk_d_old| pk_d_old.inner().to_affine()),
             )?;
-            derived_pk_d_old
-                .constrain_equal(layouter.namespace(|| "pk_d_old equality"), &pk_d_old)?;
 
-            pk_d_old
+            (derived_pk_d_old, pk_d_old)
         };
 
         // Old note commitment integrity (https://p.z.cash/ZKS:action-cm-old-integrity?partial).
@@ -933,6 +945,31 @@ impl plonk::Circuit<pallas::Base> for Circuit {
                     },
                 )?;
 
+                pk_d_old.inner().x().copy_advice(
+                    || "pk_d_old_x",
+                    &mut region,
+                    config.advices[6],
+                    1,
+                )?;
+                pk_d_old.inner().y().copy_advice(
+                    || "pk_d_old_y",
+                    &mut region,
+                    config.advices[7],
+                    1,
+                )?;
+                derived_pk_d_old.inner().x().copy_advice(
+                    || "derived_pk_d_old_x",
+                    &mut region,
+                    config.advices[8],
+                    1,
+                )?;
+                derived_pk_d_old.inner().y().copy_advice(
+                    || "derived_pk_d_old_y",
+                    &mut region,
+                    config.advices[9],
+                    1,
+                )?;
+
                 config.q_orchard.enable(&mut region, 0)
             },
         )?;