diff --git a/test/recipes/91-test_pkey_check.t b/test/recipes/91-test_pkey_check.t
index c85ab5c377..4dce838d1f 100644
--- a/test/recipes/91-test_pkey_check.t
+++ b/test/recipes/91-test_pkey_check.t
@@ -46,7 +46,9 @@ push(@tests, (
 
 push(@tests, (
     # For SM2 keys the range for the secret scalar `k` is `1 <= k < n-1`
-    "sm2_bad_max.pem", # `k` set to `n-1` (invalid, because SM2 range)
+    "sm2_bad_neg1.pem", # `k` set to `n-1` (invalid, because SM2 range)
+    "sm2_bad_0.pem", # `k` set to `n` (equivalent to `0 mod n`, invalid)
+    "sm2_bad_1.pem", # `k` set to `n+1` (equivalent to `1 mod n`, invalid)
     )) unless disabled("sm2");
 
 plan skip_all => "No tests within the current enabled feature set"
diff --git a/test/recipes/91-test_pkey_check_data/sm2_bad_0.pem b/test/recipes/91-test_pkey_check_data/sm2_bad_0.pem
new file mode 100644
index 0000000000..5ad2bd184b
--- /dev/null
+++ b/test/recipes/91-test_pkey_check_data/sm2_bad_0.pem
@@ -0,0 +1,4 @@
+-----BEGIN PRIVATE KEY-----
+MEECAQAwEwYHKoZIzj0CAQYIKoEcz1UBgi0EJzAlAgEBBCD////+////////////
+////cgPfayHGBStTu/QJOdVBIw==
+-----END PRIVATE KEY-----
diff --git a/test/recipes/91-test_pkey_check_data/sm2_bad_1.pem b/test/recipes/91-test_pkey_check_data/sm2_bad_1.pem
new file mode 100644
index 0000000000..d094d4d296
--- /dev/null
+++ b/test/recipes/91-test_pkey_check_data/sm2_bad_1.pem
@@ -0,0 +1,4 @@
+-----BEGIN PRIVATE KEY-----
+MEECAQAwEwYHKoZIzj0CAQYIKoEcz1UBgi0EJzAlAgEBBCD////+////////////
+////cgPfayHGBStTu/QJOdVBJA==
+-----END PRIVATE KEY-----
diff --git a/test/recipes/91-test_pkey_check_data/sm2_bad_max.pem b/test/recipes/91-test_pkey_check_data/sm2_bad_neg1.pem
similarity index 100%
rename from test/recipes/91-test_pkey_check_data/sm2_bad_max.pem
rename to test/recipes/91-test_pkey_check_data/sm2_bad_neg1.pem