diff --git a/google/cloud/alloydb/connector/async_connector.py b/google/cloud/alloydb/connector/async_connector.py
index 2eb5283..0db6f3d 100644
--- a/google/cloud/alloydb/connector/async_connector.py
+++ b/google/cloud/alloydb/connector/async_connector.py
@@ -75,7 +75,7 @@ def __init__(
         ip_type: str | IPTypes = IPTypes.PRIVATE,
         user_agent: Optional[str] = None,
         refresh_strategy: str | RefreshStrategy = RefreshStrategy.BACKGROUND,
-        static_conn_info: io.TextIOBase = None,
+        static_conn_info: Optional[io.TextIOBase] = None,
     ) -> None:
         self._cache: dict[str, Union[RefreshAheadCache, LazyRefreshCache]] = {}
         # initialize default params
@@ -147,6 +147,7 @@ async def connect(
         enable_iam_auth = kwargs.pop("enable_iam_auth", self._enable_iam_auth)
 
         # use existing connection info if possible
+        cache: Union[RefreshAheadCache, LazyRefreshCache, StaticConnectionInfoCache]
         if instance_uri in self._cache:
             cache = self._cache[instance_uri]
         elif self._static_conn_info:
diff --git a/google/cloud/alloydb/connector/connection_info.py b/google/cloud/alloydb/connector/connection_info.py
index 65ca231..aed28ad 100644
--- a/google/cloud/alloydb/connector/connection_info.py
+++ b/google/cloud/alloydb/connector/connection_info.py
@@ -27,7 +27,7 @@
 if TYPE_CHECKING:
     import datetime
 
-    from cryptography.hazmat.primitives.asymmetric import rsa
+    from cryptography.hazmat.primitives.asymmetric.types import PrivateKeyTypes
 
     from google.cloud.alloydb.connector.enums import IPTypes
 
@@ -41,7 +41,7 @@ class ConnectionInfo:
 
     cert_chain: list[str]
     ca_cert: str
-    key: rsa.RSAPrivateKey
+    key: PrivateKeyTypes
     ip_addrs: dict[str, Optional[str]]
     expiration: datetime.datetime
     context: Optional[ssl.SSLContext] = None
diff --git a/google/cloud/alloydb/connector/connector.py b/google/cloud/alloydb/connector/connector.py
index bcfe2e0..755e2b6 100644
--- a/google/cloud/alloydb/connector/connector.py
+++ b/google/cloud/alloydb/connector/connector.py
@@ -87,7 +87,7 @@ def __init__(
         ip_type: str | IPTypes = IPTypes.PRIVATE,
         user_agent: Optional[str] = None,
         refresh_strategy: str | RefreshStrategy = RefreshStrategy.BACKGROUND,
-        static_conn_info: io.TextIOBase = None,
+        static_conn_info: Optional[io.TextIOBase] = None,
     ) -> None:
         # create event loop and start it in background thread
         self._loop: asyncio.AbstractEventLoop = asyncio.new_event_loop()
@@ -176,6 +176,7 @@ async def connect_async(self, instance_uri: str, driver: str, **kwargs: Any) ->
             )
         enable_iam_auth = kwargs.pop("enable_iam_auth", self._enable_iam_auth)
         # use existing connection info if possible
+        cache: Union[RefreshAheadCache, LazyRefreshCache, StaticConnectionInfoCache]
         if instance_uri in self._cache:
             cache = self._cache[instance_uri]
         elif self._static_conn_info:
diff --git a/google/cloud/alloydb/connector/static.py b/google/cloud/alloydb/connector/static.py
index 287e29b..da90245 100644
--- a/google/cloud/alloydb/connector/static.py
+++ b/google/cloud/alloydb/connector/static.py
@@ -19,7 +19,6 @@
 import json
 
 from cryptography.hazmat.primitives import serialization
-from cryptography.hazmat.primitives.asymmetric import rsa
 
 from google.cloud.alloydb.connector.connection_info import ConnectionInfo
 
@@ -70,9 +69,8 @@ def __init__(self, instance_uri: str, static_conn_info: io.TextIOBase) -> None:
         }
         expiration = datetime.now(timezone.utc) + timedelta(hours=1)
         priv_key = static_info["privateKey"]
-        priv_key_bytes: rsa.RSAPrivateKey = serialization.load_pem_private_key(
-            priv_key.encode("UTF-8"),
-            password=None,
+        priv_key_bytes = serialization.load_pem_private_key(
+            priv_key.encode("UTF-8"), password=None
         )
         self._info = ConnectionInfo(
             cert_chain, ca_cert, priv_key_bytes, ip_addrs, expiration
diff --git a/google/cloud/alloydb/connector/utils.py b/google/cloud/alloydb/connector/utils.py
index 908ce40..e4c9939 100644
--- a/google/cloud/alloydb/connector/utils.py
+++ b/google/cloud/alloydb/connector/utils.py
@@ -17,10 +17,11 @@
 import aiofiles
 from cryptography.hazmat.primitives import serialization
 from cryptography.hazmat.primitives.asymmetric import rsa
+from cryptography.hazmat.primitives.asymmetric.types import PrivateKeyTypes
 
 
 async def _write_to_file(
-    dir_path: str, ca_cert: str, cert_chain: list[str], key: rsa.RSAPrivateKey
+    dir_path: str, ca_cert: str, cert_chain: list[str], key: PrivateKeyTypes
 ) -> tuple[str, str, str]:
     """
     Helper function to write the server_ca, client certificate and