diff --git a/src/scalar.rs b/src/scalar.rs
index 3f8295d..931bdc7 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -464,6 +464,9 @@ impl Scalar {
             tree[i] = UnpackedScalar::montgomery_mul(&tree[2*i], &tree[2*i+1]);
         }
 
+        // tree[1] is zero iff any of the inputs are zero.
+        debug_assert!(tree[1].from_montgomery().pack() != Scalar::zero());
+
         let allinv = tree[1].montgomery_invert();
 
         for i in 0..inputs.len() {
@@ -977,6 +980,15 @@ mod test {
         let parsed: Scalar = serde_cbor::from_slice(&output).unwrap();
         assert_eq!(parsed, X);
     }
+
+    #[test]
+    #[should_panic]
+    fn batch_invert_with_a_zero_input_panics() {
+        let mut xs = vec![Scalar::one(); 16];
+        xs[3] = Scalar::zero();
+        // This should panic in debug mode.
+        Scalar::batch_invert(&mut xs);
+    }
 }
 
 #[cfg(all(test, feature = "bench"))]