diff --git a/kzg/Cargo.toml b/kzg/Cargo.toml
index 6359cbc..1cd4bd0 100644
--- a/kzg/Cargo.toml
+++ b/kzg/Cargo.toml
@@ -4,6 +4,10 @@ version = "0.1.0"
 edition = "2021"
 
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+[[example]]
+name = "kzg-example"
+path = "examples/example.rs"
+
 
 [dependencies]
 ark-ff = "0.4.2"
diff --git a/kzg/examples/example.rs b/kzg/examples/example.rs
new file mode 100644
index 0000000..db91daa
--- /dev/null
+++ b/kzg/examples/example.rs
@@ -0,0 +1,26 @@
+use ark_bls12_381::Fr;
+use ark_poly::univariate::DensePolynomial;
+use ark_poly::{DenseUVPolynomial, Polynomial};
+use kzg::scheme::KzgScheme;
+use kzg::srs::Srs;
+
+fn main() {
+    // trusted setup
+    let srs = Srs::new(10);
+    let scheme = KzgScheme::new(srs);
+
+    // polynomial x^3 + 3x + 5
+
+    let coeff = vec![Fr::from(5), Fr::from(3), Fr::from(0), Fr::from(1)];
+    let poly = DensePolynomial::from_coefficients_vec(coeff);
+    let v = poly.evaluate(&Fr::from(1));
+    assert_eq!(v, Fr::from(9));
+
+    // commit poly
+    let commitment = scheme.commit(&poly);
+    // opening point at p = 4.
+    let opening_pos = Fr::from(4);
+    let opening = scheme.open(&poly, opening_pos);
+
+    assert!(scheme.verify(&commitment, &opening, opening_pos));
+}
diff --git a/kzg/src/commitment.rs b/kzg/src/commitment.rs
index 93663e1..021c78c 100644
--- a/kzg/src/commitment.rs
+++ b/kzg/src/commitment.rs
@@ -49,7 +49,7 @@ mod tests {
                 .mul(poly.evaluate(&secret))
                 .into_affine()
         );
-        let opening = scheme.open(poly, d);
+        let opening = scheme.open(&poly, d);
         assert!(scheme.verify(&commitment, &opening, d));
     }
 
@@ -111,7 +111,7 @@ mod tests {
         let openings: Vec<KzgOpening> = f
             .iter()
             .zip(z)
-            .map(|(f_i, z_i)| scheme.open(f_i.clone(), z_i))
+            .map(|(f_i, z_i)| scheme.open(f_i, z_i))
             .collect();
         let c: Vec<KzgCommitment> = f.iter().map(|f_i| scheme.commit(f_i)).collect();
         let mut rng = StdRng::from_entropy();
diff --git a/kzg/src/opening.rs b/kzg/src/opening.rs
index 49c4991..4f93531 100644
--- a/kzg/src/opening.rs
+++ b/kzg/src/opening.rs
@@ -6,7 +6,8 @@ use crate::types::G1Point;
 
 /// Represents an opening at a point with its corresponding evaluation.
 ///
-/// `KzgOpening` encapsulates a `G1Point` representing the point and an `Fr` representing the evaluation.
+/// `KzgOpening` encapsulates a `G1Point` representing the corresponding point
+/// of quotient polynomial and an `Fr` representing the evaluation.
 #[derive(Debug, Clone)]
 pub struct KzgOpening(pub G1Point, pub Fr);
 
diff --git a/kzg/src/scheme.rs b/kzg/src/scheme.rs
index 11218a7..252cfa0 100644
--- a/kzg/src/scheme.rs
+++ b/kzg/src/scheme.rs
@@ -89,14 +89,16 @@ impl KzgScheme {
     /// # Returns
     ///
     /// The opening at the specified point.
-    pub fn open(&self, mut polynomial: Poly, z: impl Into<Fr>) -> KzgOpening {
+    pub fn open(&self, polynomial: &Poly, z: impl Into<Fr>) -> KzgOpening {
         let z = z.into();
         let evaluation_at_z = polynomial.evaluate(&z);
-        let first = polynomial.coeffs.first_mut().expect("at least 1");
+        let mut new_poly = polynomial.clone();
+        let first = new_poly.coeffs.first_mut().expect("at least 1");
         *first -= evaluation_at_z;
         let root = Poly::from_coefficients_slice(&[-z, 1.into()]);
-        let new_poly = &polynomial / &root;
-        let opening = self.evaluate_in_s(&new_poly);
+        // quotient polynomial
+        let quotient_poly = &new_poly / &root;
+        let opening = self.evaluate_in_s(&quotient_poly);
 
         KzgOpening(opening, evaluation_at_z)
     }
@@ -123,7 +125,9 @@ impl KzgScheme {
         let g2 = self.0.g2();
         let a = g2s.sub(g2.mul(z.into()).into_affine());
         let b = commitment.0.sub(G1Point::generator().mul(y).into_affine());
+        // e([Q]_1, [x]_2 - G_2 ⋅ z)
         let pairing1 = Bls12_381::pairing(opening.0, a);
+        // e([P]_1 - G_1 ⋅ P(x), G_2)
         let pairing2 = Bls12_381::pairing(b, g2);
         pairing1 == pairing2
     }