diff --git a/plonky2/src/plonk/circuit_builder.rs b/plonky2/src/plonk/circuit_builder.rs
index 5f153c637e..eaa11f2b35 100644
--- a/plonky2/src/plonk/circuit_builder.rs
+++ b/plonky2/src/plonk/circuit_builder.rs
@@ -531,6 +531,14 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         }
     }
 
+    /// If `condition`, enforces that two routable `Target` values are equal, using Plonk's permutation argument.
+    pub fn conditional_assert_eq(&mut self, condition: Target, x: Target, y: Target) {
+        let zero = self.zero();
+        let diff = self.sub(x, y);
+        let constr = self.mul(condition, diff);
+        self.connect(constr, zero);
+    }
+
     /// Enforces that a routable `Target` value is 0, using Plonk's permutation argument.
     pub fn assert_zero(&mut self, x: Target) {
         let zero = self.zero();
diff --git a/plonky2/src/recursion/conditional_recursive_verifier.rs b/plonky2/src/recursion/conditional_recursive_verifier.rs
index 2dc6966a20..c41a9b583a 100644
--- a/plonky2/src/recursion/conditional_recursive_verifier.rs
+++ b/plonky2/src/recursion/conditional_recursive_verifier.rs
@@ -34,18 +34,8 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     {
         let selected_proof =
             self.select_proof_with_pis(condition, proof_with_pis0, proof_with_pis1);
-        let selected_verifier_data = VerifierCircuitTarget {
-            constants_sigmas_cap: self.select_cap(
-                condition,
-                &inner_verifier_data0.constants_sigmas_cap,
-                &inner_verifier_data1.constants_sigmas_cap,
-            ),
-            circuit_digest: self.select_hash(
-                condition,
-                inner_verifier_data0.circuit_digest,
-                inner_verifier_data1.circuit_digest,
-            ),
-        };
+        let selected_verifier_data =
+            self.select_verifier_data(condition, inner_verifier_data0, inner_verifier_data1);
 
         self.verify_proof::<C>(&selected_proof, &selected_verifier_data, inner_common_data);
     }
@@ -75,7 +65,7 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
     }
 
     /// Computes `if b { proof_with_pis0 } else { proof_with_pis1 }`.
-    fn select_proof_with_pis(
+    pub fn select_proof_with_pis(
         &mut self,
         b: BoolTarget,
         proof_with_pis0: &ProofWithPublicInputsTarget<D>,
@@ -179,6 +169,23 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
             .collect()
     }
 
+    /// Computes `if b { vk0 } else { vk1 }`.
+    pub fn select_verifier_data(
+        &mut self,
+        b: BoolTarget,
+        vk0: &VerifierCircuitTarget,
+        vk1: &VerifierCircuitTarget,
+    ) -> VerifierCircuitTarget {
+        VerifierCircuitTarget {
+            constants_sigmas_cap: self.select_cap(
+                b,
+                &vk0.constants_sigmas_cap,
+                &vk1.constants_sigmas_cap,
+            ),
+            circuit_digest: self.select_hash(b, vk0.circuit_digest, vk1.circuit_digest),
+        }
+    }
+
     /// Computes `if b { os0 } else { os1 }`.
     fn select_opening_set(
         &mut self,
diff --git a/plonky2/src/recursion/dummy_circuit.rs b/plonky2/src/recursion/dummy_circuit.rs
index 75b3929e82..1dc872db5a 100644
--- a/plonky2/src/recursion/dummy_circuit.rs
+++ b/plonky2/src/recursion/dummy_circuit.rs
@@ -67,11 +67,7 @@ where
 /// Generate a proof for a dummy circuit. The `public_inputs` parameter let the caller specify
 /// certain public inputs (identified by their indices) which should be given specific values.
 /// The rest will default to zero.
-pub(crate) fn dummy_proof<
-    F: RichField + Extendable<D>,
-    C: GenericConfig<D, F = F>,
-    const D: usize,
->(
+pub fn dummy_proof<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>(
     circuit: &CircuitData<F, C, D>,
     nonzero_public_inputs: HashMap<usize, F>,
 ) -> anyhow::Result<ProofWithPublicInputs<F, C, D>>
@@ -86,11 +82,7 @@ where
 }
 
 /// Generate a circuit matching a given `CommonCircuitData`.
-pub(crate) fn dummy_circuit<
-    F: RichField + Extendable<D>,
-    C: GenericConfig<D, F = F>,
-    const D: usize,
->(
+pub fn dummy_circuit<F: RichField + Extendable<D>, C: GenericConfig<D, F = F>, const D: usize>(
     common_data: &CommonCircuitData<F, D>,
 ) -> CircuitData<F, C, D> {
     let config = common_data.config.clone();
@@ -143,6 +135,20 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
         Ok((dummy_proof_with_pis_target, dummy_verifier_data_target))
     }
+
+    pub fn dummy_proof_and_constant_vk_no_generator<C: GenericConfig<D, F = F> + 'static>(
+        &mut self,
+        common_data: &CommonCircuitData<F, D>,
+    ) -> anyhow::Result<(ProofWithPublicInputsTarget<D>, VerifierCircuitTarget)>
+    where
+        C::Hasher: AlgebraicHasher<F>,
+    {
+        let dummy_circuit = dummy_circuit::<F, C, D>(common_data);
+        let dummy_proof_with_pis_target = self.add_virtual_proof_with_pis(common_data);
+        let dummy_verifier_data_target = self.constant_verifier_data(&dummy_circuit.verifier_only);
+
+        Ok((dummy_proof_with_pis_target, dummy_verifier_data_target))
+    }
 }
 
 #[derive(Debug)]