diff --git a/src/field/field.rs b/src/field/field.rs
index 0249610f..4025c968 100644
--- a/src/field/field.rs
+++ b/src/field/field.rs
@@ -267,7 +267,7 @@ pub trait Field:
     }
 
     fn rand() -> Self {
-        Self::rand_from_rng(&mut OsRng)
+        Self::rand_from_rng(&mut rand::thread_rng())
     }
 
     fn rand_vec(n: usize) -> Vec<Self> {
diff --git a/src/polynomial/division.rs b/src/polynomial/division.rs
index a893c509..8e3c2676 100644
--- a/src/polynomial/division.rs
+++ b/src/polynomial/division.rs
@@ -128,7 +128,13 @@ impl<F: Field> PolynomialCoeffs<F> {
     /// Computes the inverse of `self` modulo `x^n`.
     pub(crate) fn inv_mod_xn(&self, n: usize) -> Self {
         assert!(self.coeffs[0].is_nonzero(), "Inverse doesn't exist.");
-        let mut h = self.padded(n);
+
+        let h = if self.len() < n {
+            self.padded(n)
+        } else {
+            self.clone()
+        };
+
         let mut a = Self::empty();
         a.coeffs.push(h.coeffs[0].inverse());
         for i in 0..log2_ceil(n) {