diff --git a/ff/src/biginteger/mod.rs b/ff/src/biginteger/mod.rs
index e0d025965..46a236fcb 100644
--- a/ff/src/biginteger/mod.rs
+++ b/ff/src/biginteger/mod.rs
@@ -444,10 +444,9 @@ impl<const N: usize> BigInteger for BigInt<N> {
     }
 
     #[inline]
-    fn mul_low(&mut self, other: &Self) {
+    fn mul_low(&self, other: &Self) -> Self {
         if self.is_zero() || other.is_zero() {
-            *self = Self::zero();
-            return;
+            return Self::zero();
         }
 
         let mut res = Self::zero();
@@ -460,7 +459,7 @@ impl<const N: usize> BigInteger for BigInt<N> {
             carry = 0;
         }
 
-        *self = res
+        res
     }
 
     #[inline]
@@ -1099,15 +1098,13 @@ pub trait BigInteger:
     /// // Basic
     /// let mut a = B::from(42u64);
     /// let b = B::from(3u64);
-    /// a.mul_low(&b);
-    /// assert_eq!(a, B::from(126u64));
+    /// assert_eq!(a.mul_low(&b), B::from(126u64));
     ///
     /// // Edge-Case
     /// let mut zero = B::from(0u64);
-    /// zero.mul_low(&B::from(5u64));
-    /// assert_eq!(zero, B::from(0u64));
+    /// assert_eq!(zero.mul_low(&B::from(5u64)), B::from(0u64));
     /// ```
-    fn mul_low(&mut self, other: &Self);
+    fn mul_low(&self, other: &Self) -> Self;
 
     /// Multiplies this [`BigInteger`] by another `BigInteger`, returning the high bits of the result.
     ///
diff --git a/ff/src/biginteger/tests.rs b/ff/src/biginteger/tests.rs
index 83767aaf5..dad4730c1 100644
--- a/ff/src/biginteger/tests.rs
+++ b/ff/src/biginteger/tests.rs
@@ -51,29 +51,21 @@ fn biginteger_arithmetic_test<B: BigInteger>(a: B, b: B, zero: B, max: B) {
     assert_eq!(a_mul2, a_plus_a);
 
     // a * 1 = a
-    let mut a_mul = a;
-    a_mul.mul_low(&B::from(1u64));
-    assert_eq!(a_mul, a);
+    assert_eq!(a.mul_low(&B::from(1u64)), a);
 
     // a * 2 = a
-    a_mul.mul_low(&B::from(2u64));
-    assert_eq!(a_mul, a_plus_a);
+    assert_eq!(a.mul_low(&B::from(2u64)), a_plus_a);
 
-    // a * 2 * b = b * 2 * a
-    a_mul.mul_low(&b);
-    let mut b_mul = b;
-    b_mul.mul_low(&B::from(2u64));
-    b_mul.mul_low(&a);
-    assert_eq!(a_mul, b_mul);
+    // a * b = b * a
+    assert_eq!(a.mul_low(&b), b.mul_low(&a));
 
     // a * 2 * b * 0 = 0
-    a_mul.mul_low(&zero);
-    assert!(a_mul.is_zero());
+    assert!(a.mul_low(&zero).is_zero());
 
     // a * 2 * ... * 2  = a * 2^n
     let mut a_mul_n = a;
     for _ in 0..20 {
-        a_mul_n.mul_low(&B::from(2u64));
+        a_mul_n = a_mul_n.mul_low(&B::from(2u64));
     }
     assert_eq!(a_mul_n, a << 20);