diff --git a/changelog.d/4970.feature b/changelog.d/4970.feature
new file mode 100644
index 000000000000..3374ae51fe7f
--- /dev/null
+++ b/changelog.d/4970.feature
@@ -0,0 +1 @@
+Add support for cross-signing.
diff --git a/synapse/handlers/e2e_keys.py b/synapse/handlers/e2e_keys.py
index 90118ddf748b..ca33a654a33e 100644
--- a/synapse/handlers/e2e_keys.py
+++ b/synapse/handlers/e2e_keys.py
@@ -19,22 +19,24 @@
 from six import iteritems
 
 from canonicaljson import encode_canonical_json, json
-
-from twisted.internet import defer
-
 from signedjson.key import decode_verify_key_bytes, encode_verify_key_base64
 from signedjson.sign import SignatureVerifyException, verify_signed_json
+from unpaddedbase64 import decode_base64
 
-from synapse.api.errors import Codes, CodeMessageException, FederationDeniedError, \
-    SynapseError
+from twisted.internet import defer
+
+from synapse.api.errors import (
+    CodeMessageException,
+    Codes,
+    FederationDeniedError,
+    SynapseError,
+)
 from synapse.types import UserID, get_domain_from_id
 from synapse.util.async_helpers import Linearizer
 from synapse.util.caches.expiringcache import ExpiringCache
 from synapse.util.logcontext import make_deferred_yieldable, run_in_background
 from synapse.util.retryutils import NotRetryingDestination
 
-from unpaddedbase64 import decode_base64
-
 logger = logging.getLogger(__name__)
 
 
@@ -199,7 +201,7 @@ def get_self_signing_key(user_id):
             try:
                 self_signing_keys[user_id] = \
                     yield self.store.get_e2e_self_signing_key(user_id, from_user_id)
-            except Exception as e:
+            except Exception:
                 pass
 
         yield make_deferred_yieldable(defer.gatherResults([
@@ -465,7 +467,7 @@ def upload_signing_keys_for_user(self, user_id, keys):
                     )
                 try:
                     verify_signed_json(self_signing_key, user_id, old_verify_key)
-                except SignatureVerifyException as e:
+                except SignatureVerifyException:
                     raise SynapseError(
                         400,
                         "Invalid signature on self-signing key",
@@ -499,7 +501,7 @@ def upload_signing_keys_for_user(self, user_id, keys):
                 )
             try:
                 verify_signed_json(user_signing_key, user_id, verify_key)
-            except SignatureVerifyException as e:
+            except SignatureVerifyException:
                 raise SynapseError(
                     400,
                     "Invalid signature on user-signing key",
@@ -614,7 +616,7 @@ def upload_signatures_for_device_keys(self, user_id, signatures):
                         }
                         try:
                             verify_signed_json(key, user_id, self_signing_verify_key)
-                        except SignatureVerifyException as e:
+                        except SignatureVerifyException:
                             logger.error("invalid signature on key")
                             raise SynapseError(
                                 400,
@@ -745,7 +747,7 @@ def upload_signatures_for_device_keys(self, user_id, signatures):
                         }
                         try:
                             verify_signed_json(key, user_id, user_signing_verify_key)
-                        except SignatureVerifyException as e:
+                        except SignatureVerifyException:
                             logger.error("invalid signature on key")
                             raise SynapseError(
                                 400,
diff --git a/synapse/storage/end_to_end_keys.py b/synapse/storage/end_to_end_keys.py
index 33e4533f2043..0fafd2ee37a2 100644
--- a/synapse/storage/end_to_end_keys.py
+++ b/synapse/storage/end_to_end_keys.py
@@ -13,6 +13,8 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import time
+
 from six import iteritems
 
 from canonicaljson import encode_canonical_json, json
@@ -21,8 +23,6 @@
 
 from synapse.util.caches.descriptors import cached
 
-import time
-
 from ._base import SQLBaseStore, db_to_json
 
 
diff --git a/tests/handlers/test_e2e_keys.py b/tests/handlers/test_e2e_keys.py
index 081694280532..4fa95403fa5b 100644
--- a/tests/handlers/test_e2e_keys.py
+++ b/tests/handlers/test_e2e_keys.py
@@ -16,11 +16,11 @@
 
 import mock
 
-from twisted.internet import defer
-
 import signedjson.key as key
 import signedjson.sign as sign
 
+from twisted.internet import defer
+
 import synapse.api.errors
 import synapse.handlers.e2e_keys
 import synapse.storage