diff --git a/src/benches/poseidon_opt_native.rs b/src/benches/poseidon_opt_native.rs
index 5766ccc..2d9e1cd 100644
--- a/src/benches/poseidon_opt_native.rs
+++ b/src/benches/poseidon_opt_native.rs
@@ -14,7 +14,7 @@ fn poseidon_opt_native(c: &mut Criterion) {
     group.bench_function("Poseidon NATIVE Height-20 ARITY-2 MT", |b| {
         let inputs = (0..20).map(|_| Fr::rand(&mut rng)).collect::<Vec<_>>();
         b.iter(|| {
-            let mut poseidon = Poseidon::<(), NativeSpec<Fr, 3>, 3>::new(&mut (), param.clone());
+            let mut poseidon = Poseidon::<(), NativeSpec<Fr, 3>, 3>::new(&mut (), &param);
             let mut curr_hash = Fr::zero();
             for x in inputs.iter() {
                 poseidon.reset(&mut ());
diff --git a/src/benches/poseidon_opt_plonk.rs b/src/benches/poseidon_opt_plonk.rs
index 9973ded..8dbeb71 100644
--- a/src/benches/poseidon_opt_plonk.rs
+++ b/src/benches/poseidon_opt_plonk.rs
@@ -35,7 +35,7 @@ where
     const CIRCUIT_ID: [u8; 32] = [0xff; 32];
 
     fn gadget(&mut self, composer: &mut StandardComposer<F, P>) -> Result<(), Error> {
-        let mut poseidon = Poseidon::<_, PlonkSpec<3>, 3>::new(composer, self.constants.clone());
+        let mut poseidon = Poseidon::<_, PlonkSpec<3>, 3>::new(composer, &self.constants);
 
         let inputs_var = self
             .input
diff --git a/src/benches/poseidon_opt_r1cs.rs b/src/benches/poseidon_opt_r1cs.rs
index 3d15f33..d86fa4d 100644
--- a/src/benches/poseidon_opt_r1cs.rs
+++ b/src/benches/poseidon_opt_r1cs.rs
@@ -28,7 +28,7 @@ impl ConstraintSynthesizer<Fr> for TestCircuit
     fn generate_constraints(self, mut cs: ConstraintSystemRef<Fr>) -> Result<(), SynthesisError> {
         const WIDTH: usize = 3;
         let mut poseidon =
-            Poseidon::<_, R1csSpec<Fr, WIDTH>, WIDTH>::new(&mut cs, self.constants.clone());
+            Poseidon::<_, R1csSpec<Fr, WIDTH>, WIDTH>::new(&mut cs, &self.constants);
 
         let inputs_var = self
             .input
diff --git a/src/poseidon/poseidon_ref.rs b/src/poseidon/poseidon_ref.rs
index 06795d3..b804ce7 100644
--- a/src/poseidon/poseidon_ref.rs
+++ b/src/poseidon/poseidon_ref.rs
@@ -11,6 +11,7 @@ use plonk_core::prelude as plonk;
 use std::fmt::{Debug};
 use std::marker::PhantomData;
 
+/// Trait for unoptimized poseidon hash.
 pub trait PoseidonRefSpec<COM, const WIDTH: usize> {
     /// Field used as state
     type Field: Debug + Clone;
@@ -234,6 +235,8 @@ pub struct NativeSpecRef<F: PrimeField> {
 }
 
 impl<F: PrimeField, const WIDTH: usize> PoseidonRefSpec<(), WIDTH> for NativeSpecRef<F> {
+    // Field is private variables, ParameterField is public constants.
+    // In Naitve Spec, we do not distinguish these two values.
     type Field = F;
     type ParameterField = F;
 
@@ -327,6 +330,9 @@ mod r1cs {
     impl<F: PrimeField, const WIDTH: usize> PoseidonRefSpec<ConstraintSystemRef<F>, WIDTH>
         for R1csSpecRef<F, WIDTH>
     {
+        // Field is private variables, ParameterField is public constants.
+        // In R1cs Spec, these two types lead to different privacy and #constraints.
+        // See add() and addi() below.
         type Field = FpVar<F>;
         type ParameterField = F;