diff --git a/src/backends/plonky2/basetypes.rs b/src/backends/plonky2/basetypes.rs
index d2b48500..5c32189c 100644
--- a/src/backends/plonky2/basetypes.rs
+++ b/src/backends/plonky2/basetypes.rs
@@ -68,30 +68,37 @@ pub static DEFAULT_VD_SET: LazyLock<VDSet> = LazyLock::new(|| {
 #[derive(Clone, Debug)]
 pub struct VDSet {
     root: Hash,
-    // (verifier_data, merkleproof)
+    // (verifier_data's hash, merkleproof)
     proofs_map: HashMap<HashOut<F>, MerkleClaimAndProof>,
 }
 impl VDSet {
     /// builds the verifier_datas tree, and returns the root and the proofs
     pub fn new(tree_depth: usize, vds: &[VerifierOnlyCircuitData]) -> Result<Self> {
-        // first of all, sort the vds, so that each set of verifier_datas gets
-        // the same root
-        let vds: Vec<&VerifierOnlyCircuitData> = vds
+        // compute the verifier_data's hashes
+        let vds_hashes: Vec<HashOut<F>> = vds
             .iter()
-            .sorted_by_key(|vd| RawValue(vd.circuit_digest.elements))
+            .map(crate::backends::plonky2::recursion::circuit::hash_verifier_data)
+            .collect::<Vec<_>>();
+
+        // before using the hash values, sort them, so that each set of
+        // verifier_datas gets the same VDSet root
+        let vds_hashes: Vec<&HashOut<F>> = vds_hashes
+            .iter()
+            .sorted_by_key(|vd| RawValue(vd.elements))
             .collect::<Vec<_>>();
 
         let array = Array::new(
             tree_depth,
-            vds.iter()
-                .map(|vd| Value::from(RawValue(vd.circuit_digest.elements)))
+            vds_hashes
+                .iter()
+                .map(|vd| Value::from(RawValue(vd.elements)))
                 .collect(),
         )?;
 
         let root = array.commitment();
         let mut proofs_map = HashMap::<HashOut<F>, MerkleClaimAndProof>::new();
 
-        for (i, vd) in vds.iter().enumerate() {
+        for (i, vd) in vds_hashes.iter().enumerate() {
             let (value, proof) = array.prove(i)?;
             let p = MerkleClaimAndProof {
                 root,
@@ -99,7 +106,7 @@ impl VDSet {
                 value: value.raw(),
                 proof,
             };
-            proofs_map.insert(vd.circuit_digest, p);
+            proofs_map.insert(**vd, p);
         }
         Ok(Self { root, proofs_map })
     }
@@ -113,12 +120,12 @@ impl VDSet {
     ) -> Result<Vec<MerkleClaimAndProof>> {
         let mut proofs: Vec<MerkleClaimAndProof> = vec![];
         for vd in vds {
-            let p =
-                self.proofs_map
-                    .get(&vd.circuit_digest)
-                    .ok_or(crate::middleware::Error::custom(
-                        "verifier_data not found in VDSet".to_string(),
-                    ))?;
+            let p = self
+                .proofs_map
+                .get(&crate::backends::plonky2::recursion::circuit::hash_verifier_data(vd))
+                .ok_or(crate::middleware::Error::custom(
+                    "verifier_data not found in VDSet".to_string(),
+                ))?;
             proofs.push(p.clone());
         }
         Ok(proofs)
diff --git a/src/backends/plonky2/recursion/circuit.rs b/src/backends/plonky2/recursion/circuit.rs
index fd01a8aa..664f7e6e 100644
--- a/src/backends/plonky2/recursion/circuit.rs
+++ b/src/backends/plonky2/recursion/circuit.rs
@@ -13,7 +13,10 @@ use plonky2::{
     self,
     field::{extension::quintic::QuinticExtension, types::Field},
     gates::{gate::GateRef, noop::NoopGate},
-    hash::hash_types::HashOutTarget,
+    hash::{
+        hash_types::{HashOut, HashOutTarget},
+        poseidon::PoseidonHash,
+    },
     iop::{
         target::Target,
         witness::{PartialWitness, WitnessWrite},
@@ -24,6 +27,7 @@ use plonky2::{
             CircuitConfig, CircuitData, CommonCircuitData, ProverCircuitData, VerifierCircuitData,
             VerifierCircuitTarget, VerifierOnlyCircuitData,
         },
+        config::Hasher,
         proof::{ProofWithPublicInputs, ProofWithPublicInputsTarget},
     },
     util::log2_ceil,
@@ -201,7 +205,18 @@ impl<I: InnerCircuit> RecursiveCircuit<I> {
         let verified_proofs = (0..arity)
             .map(|i| VerifiedProofTarget {
                 public_inputs: proofs_targ[i].public_inputs.clone(),
-                verifier_data_hash: verifier_datas_targ[i].circuit_digest,
+                // note: here we're hashing the verifier_data as Hash(vd.circuit_digest,
+                // vd.constant_sigmas_cap), despite the circuit_digest is already a hash containing
+                // the constant_sigmas_cap. Conceptually we would use the circuit_digest as the hash
+                // of the verifier_data, but unfortunately, the recursion verification circuit does
+                // not ensure this link.  Alternatively we could calculate an modified
+                // circuit_digest, hashing as in the original plonky2's circuit_digest but
+                // additionally checking it in-circuit. But since in terms of circuit costs would
+                // require a hash (with similar amount of elements), the approach that we do is take
+                // the already computed circuit_digest and hash it together with the
+                // constant_sigmas_cap, doing the same computation in-circuit, obtaining a new hash
+                // that we use to represent the verifier_data.
+                verifier_data_hash: hash_verifier_data_gadget(builder, &verifier_datas_targ[i]),
             })
             .collect_vec();
 
@@ -478,6 +493,38 @@ pub fn pad_circuit(builder: &mut CircuitBuilder<F, D>, common_data: &CommonCircu
     }
 }
 
+fn hash_verifier_data_gadget(
+    builder: &mut CircuitBuilder<F, D>,
+    verifier_data: &VerifierCircuitTarget,
+) -> HashOutTarget {
+    let f: Vec<Target> = [
+        verifier_data.circuit_digest.elements.to_vec(),
+        verifier_data
+            .constants_sigmas_cap
+            .0
+            .iter()
+            .flat_map(|e| e.elements)
+            .collect(),
+    ]
+    .concat();
+    builder.hash_n_to_hash_no_pad::<PoseidonHash>(f)
+}
+
+// compatible with hash_verifier_data_gadget.
+pub(crate) fn hash_verifier_data(verifier_only_data: &VerifierOnlyCircuitData<C, D>) -> HashOut<F> {
+    let f: Vec<F> = [
+        verifier_only_data.circuit_digest.elements.to_vec(),
+        verifier_only_data
+            .constants_sigmas_cap
+            .0
+            .iter()
+            .flat_map(|e| e.elements)
+            .collect(),
+    ]
+    .concat();
+    PoseidonHash::hash_no_pad(&f)
+}
+
 #[cfg(test)]
 mod tests {
     use std::time::Instant;