diff --git a/src/pcs/id/mod.rs b/src/pcs/id/mod.rs
index b2ab83b..abd9a56 100644
--- a/src/pcs/id/mod.rs
+++ b/src/pcs/id/mod.rs
@@ -1,4 +1,3 @@
-use ark_ff::Zero;
 use ark_poly::Polynomial;
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::vec::Vec;
@@ -28,23 +27,27 @@ impl<F: PrimeField> Sub<Self> for WrappedPolynomial<F> {
     type Output = WrappedPolynomial<F>;
 
     fn sub(self, other: WrappedPolynomial<F>) -> Self::Output {
-        let mut temp = self.0;
-        temp -= &other.0; //TODO
-        WrappedPolynomial(temp)
+        WrappedPolynomial(self.0 - other.0)
     }
 }
 
-impl<F: PrimeField> core::iter::Sum<Self> for WrappedPolynomial<F> {
+impl<F: PrimeField> Sum<Self> for WrappedPolynomial<F> {
     fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
         iter.reduce(|a, b| a + b).unwrap()
     }
 }
 
+impl<F: PrimeField> Mul<F> for WrappedPolynomial<F> {
+    type Output = WrappedPolynomial<F>;
+
+    fn mul(self, by: F) -> Self {
+        (&self).mul(by)
+    }
+}
+
 impl<F: PrimeField> Commitment<F> for WrappedPolynomial<F> {
     fn mul(&self, by: F) -> Self {
-        let mut temp = Poly::zero(); //TODO
-        temp += (by, &self.0);
-        WrappedPolynomial(temp)
+        WrappedPolynomial(&self.0 * by)
     }
 
     fn combine(coeffs: &[F], commitments: &[Self]) -> Self {
diff --git a/src/pcs/kzg/commitment.rs b/src/pcs/kzg/commitment.rs
index 88da5c3..f187e0c 100644
--- a/src/pcs/kzg/commitment.rs
+++ b/src/pcs/kzg/commitment.rs
@@ -12,6 +12,14 @@ use crate::utils::ec::small_multiexp_affine;
 #[derive(Clone, Debug, PartialEq, Eq, CanonicalSerialize, CanonicalDeserialize)]
 pub struct KzgCommitment<E: Pairing>(pub E::G1Affine);
 
+impl<E: Pairing> Mul<E::ScalarField> for KzgCommitment<E> {
+    type Output = Self;
+
+    fn mul(self, by: E::ScalarField) -> Self {
+        (&self).mul(by)
+    }
+}
+
 impl<E: Pairing> Commitment<E::ScalarField> for KzgCommitment<E> {
     fn mul(&self, by: E::ScalarField) -> KzgCommitment<E> {
         KzgCommitment(self.0.mul(by).into())
diff --git a/src/pcs/mod.rs b/src/pcs/mod.rs
index 7a8f576..a2cb0b8 100644
--- a/src/pcs/mod.rs
+++ b/src/pcs/mod.rs
@@ -3,7 +3,7 @@ use ark_poly::Evaluations;
 use ark_serialize::*;
 use ark_std::fmt::Debug;
 use ark_std::iter::Sum;
-use ark_std::ops::{Add, Sub};
+use ark_std::ops::{Add, Mul, Sub};
 use ark_std::rand::Rng;
 use ark_std::vec::Vec;
 
@@ -20,6 +20,7 @@ pub trait Commitment<F: PrimeField>:
     + Clone
     + Debug
     + Add<Self, Output = Self>
+    + Mul<F, Output=Self>
     + Sub<Self, Output = Self>
     + Sum<Self>
     + CanonicalSerialize