diff --git a/src/cryptography/utils.py b/src/cryptography/utils.py
index 9bf31faadbec..ef0fc44332d0 100644
--- a/src/cryptography/utils.py
+++ b/src/cryptography/utils.py
@@ -41,8 +41,8 @@ def read_only_property(name: str):
 
 
 def register_interface(iface):
-    def register_decorator(klass):
-        verify_interface(iface, klass)
+    def register_decorator(klass, *, check_annotations=False):
+        verify_interface(iface, klass, check_annotations=check_annotations)
         iface.register(klass)
         return klass
 
@@ -50,9 +50,9 @@ def register_decorator(klass):
 
 
 def register_interface_if(predicate, iface):
-    def register_decorator(klass):
+    def register_decorator(klass, *, check_annotations=False):
         if predicate:
-            verify_interface(iface, klass)
+            verify_interface(iface, klass, check_annotations=check_annotations)
             iface.register(klass)
         return klass
 
@@ -69,7 +69,16 @@ class InterfaceNotImplemented(Exception):
     pass
 
 
-def verify_interface(iface, klass):
+def strip_annotation(signature):
+    return inspect.Signature(
+        [
+            param.replace(annotation=inspect.Parameter.empty)
+            for param in signature.parameters.values()
+        ]
+    )
+
+
+def verify_interface(iface, klass, *, check_annotations=False):
     for method in iface.__abstractmethods__:
         if not hasattr(klass, method):
             raise InterfaceNotImplemented(
@@ -80,7 +89,11 @@ def verify_interface(iface, klass):
             continue
         sig = inspect.signature(getattr(iface, method))
         actual = inspect.signature(getattr(klass, method))
-        if sig != actual:
+        if check_annotations:
+            ok = sig == actual
+        else:
+            ok = strip_annotation(sig) == strip_annotation(actual)
+        if not ok:
             raise InterfaceNotImplemented(
                 "{}.{}'s signature differs from the expected. Expected: "
                 "{!r}. Received: {!r}".format(klass, method, sig, actual)
diff --git a/tests/test_interfaces.py b/tests/test_interfaces.py
index c5c579da0ca7..89d802aed017 100644
--- a/tests/test_interfaces.py
+++ b/tests/test_interfaces.py
@@ -77,3 +77,27 @@ def property(self):
         # Invoke this to ensure the line is covered
         NonImplementer().property
         verify_interface(SimpleInterface, NonImplementer)
+
+    def test_signature_mismatch(self):
+        class SimpleInterface(metaclass=abc.ABCMeta):
+            @abc.abstractmethod
+            def method(self, other: object) -> int:
+                """Method with signature"""
+
+        class ClassWithoutSignature:
+            def method(self, other):
+                """Method without signature"""
+
+        class ClassWithSignature:
+            def method(self, other: object) -> int:
+                """Method with signature"""
+
+        verify_interface(SimpleInterface, ClassWithoutSignature)
+        verify_interface(SimpleInterface, ClassWithSignature)
+        with pytest.raises(InterfaceNotImplemented):
+            verify_interface(
+                SimpleInterface, ClassWithoutSignature, check_annotations=True
+            )
+        verify_interface(
+            SimpleInterface, ClassWithSignature, check_annotations=True
+        )