diff --git a/src/polynomial/commitment.rs b/src/polynomial/commitment.rs
index 5ace678c..b0666a2f 100644
--- a/src/polynomial/commitment.rs
+++ b/src/polynomial/commitment.rs
@@ -30,7 +30,10 @@ impl<F: Field> ListPolynomialCommitment<F> {
     /// Creates a list polynomial commitment for the polynomials interpolating the values in `values`.
     pub fn new(values: Vec<PolynomialValues<F>>, rate_bits: usize, blinding: bool) -> Self {
         let degree = values[0].len();
-        let polynomials = values.iter().map(|v| v.clone().ifft()).collect::<Vec<_>>();
+        let polynomials = values
+            .par_iter()
+            .map(|v| v.clone().ifft())
+            .collect::<Vec<_>>();
         let lde_values = timed!(
             Self::lde_values(&polynomials, rate_bits, blinding),
             "to compute LDE"
diff --git a/src/polynomial/polynomial.rs b/src/polynomial/polynomial.rs
index 3d6c12ba..888d7af0 100644
--- a/src/polynomial/polynomial.rs
+++ b/src/polynomial/polynomial.rs
@@ -36,6 +36,7 @@ impl<F: Field> PolynomialValues<F> {
         ifft(self)
     }
 
+    /// Returns the polynomial whose evaluation on the coset `shift*H` is `self`.
     pub fn coset_ifft(self, shift: F) -> PolynomialCoeffs<F> {
         let mut shifted_coeffs = self.ifft();
         shifted_coeffs
@@ -195,6 +196,7 @@ impl<F: Field> PolynomialCoeffs<F> {
         fft(self)
     }
 
+    /// Returns the evaluation of the polynomial on the coset `shift*H`.
     pub fn coset_fft(self, shift: F) -> PolynomialValues<F> {
         let modified_poly: Self = shift
             .powers()
@@ -393,8 +395,31 @@ mod tests {
             .into_iter()
             .map(|x| poly.eval(x))
             .collect::<Vec<_>>();
-
         assert_eq!(coset_evals, naive_coset_evals);
+
+        let ifft_coeffs = PolynomialValues::new(coset_evals).coset_ifft(shift);
+        assert_eq!(poly, ifft_coeffs.into());
+    }
+
+    #[test]
+    fn test_coset_ifft() {
+        type F = CrandallField;
+
+        let k = 8;
+        let n = 1 << k;
+        let evals = PolynomialValues::new(F::rand_vec(n));
+        let shift = F::rand();
+        let coeffs = evals.clone().coset_ifft(shift);
+
+        let generator = F::primitive_root_of_unity(k);
+        let naive_coset_evals = F::cyclic_subgroup_coset_known_order(generator, shift, n)
+            .into_iter()
+            .map(|x| coeffs.eval(x))
+            .collect::<Vec<_>>();
+        assert_eq!(evals, naive_coset_evals.into());
+
+        let fft_evals = coeffs.coset_fft(shift);
+        assert_eq!(evals, fft_evals);
     }
 
     #[test]