diff --git a/changelog.d/5534.feature b/changelog.d/5534.feature
new file mode 100644
index 0000000000..2e279c9b77
--- /dev/null
+++ b/changelog.d/5534.feature
@@ -0,0 +1 @@
+Split public rooms directory auth config in two settings, in order to manage client auth independently from the federation part of it. Obsoletes the "restrict_public_rooms_to_local_users" configuration setting. If "restrict_public_rooms_to_local_users" is set in the config, Synapse will act as if both new options are enabled, i.e. require authentication through the client API and deny federation requests.
diff --git a/docs/sample_config.yaml b/docs/sample_config.yaml
index d5cc3e7abc..f4fd113211 100644
--- a/docs/sample_config.yaml
+++ b/docs/sample_config.yaml
@@ -54,11 +54,15 @@ pid_file: DATADIR/homeserver.pid
 #
 #require_auth_for_profile_requests: true
 
-# If set to 'true', requires authentication to access the server's
-# public rooms directory through the client API, and forbids any other
-# homeserver to fetch it via federation. Defaults to 'false'.
+# If set to 'false', requires authentication to access the server's public rooms
+# directory through the client API. Defaults to 'true'.
 #
-#restrict_public_rooms_to_local_users: true
+#allow_public_rooms_without_auth: false
+
+# If set to 'false', forbids any other homeserver to fetch the server's public
+# rooms directory via federation. Defaults to 'true'.
+#
+#allow_public_rooms_over_federation: false
 
 # The default room version for newly created rooms.
 #
diff --git a/synapse/config/server.py b/synapse/config/server.py
index 1e58b2e91b..7cbb699a66 100644
--- a/synapse/config/server.py
+++ b/synapse/config/server.py
@@ -82,12 +82,32 @@ class ServerConfig(Config):
             "require_auth_for_profile_requests", False
         )
 
-        # If set to 'True', requires authentication to access the server's
-        # public rooms directory through the client API, and forbids any other
-        # homeserver to fetch it via federation.
-        self.restrict_public_rooms_to_local_users = config.get(
-            "restrict_public_rooms_to_local_users", False
-        )
+        if "restrict_public_rooms_to_local_users" in config and (
+            "allow_public_rooms_without_auth" in config
+            or "allow_public_rooms_over_federation" in config
+        ):
+            raise ConfigError(
+                "Can't use 'restrict_public_rooms_to_local_users' if"
+                " 'allow_public_rooms_without_auth' and/or"
+                " 'allow_public_rooms_over_federation' is set."
+            )
+
+        # Check if the legacy "restrict_public_rooms_to_local_users" flag is set. This
+        # flag is now obsolete but we need to check it for backward-compatibility.
+        if config.get("restrict_public_rooms_to_local_users", False):
+            self.allow_public_rooms_without_auth = False
+            self.allow_public_rooms_over_federation = False
+        else:
+            # If set to 'False', requires authentication to access the server's public
+            # rooms directory through the client API. Defaults to 'True'.
+            self.allow_public_rooms_without_auth = config.get(
+                "allow_public_rooms_without_auth", True
+            )
+            # If set to 'False', forbids any other homeserver to fetch the server's public
+            # rooms directory via federation. Defaults to 'True'.
+            self.allow_public_rooms_over_federation = config.get(
+                "allow_public_rooms_over_federation", True
+            )
 
         default_room_version = config.get("default_room_version", DEFAULT_ROOM_VERSION)
 
@@ -366,11 +386,15 @@ class ServerConfig(Config):
         #
         #require_auth_for_profile_requests: true
 
-        # If set to 'true', requires authentication to access the server's
-        # public rooms directory through the client API, and forbids any other
-        # homeserver to fetch it via federation. Defaults to 'false'.
+        # If set to 'false', requires authentication to access the server's public rooms
+        # directory through the client API. Defaults to 'true'.
         #
-        #restrict_public_rooms_to_local_users: true
+        #allow_public_rooms_without_auth: false
+
+        # If set to 'false', forbids any other homeserver to fetch the server's public
+        # rooms directory via federation. Defaults to 'true'.
+        #
+        #allow_public_rooms_over_federation: false
 
         # The default room version for newly created rooms.
         #
diff --git a/synapse/federation/transport/server.py b/synapse/federation/transport/server.py
index b4854e82f6..955f0f4308 100644
--- a/synapse/federation/transport/server.py
+++ b/synapse/federation/transport/server.py
@@ -721,15 +721,15 @@ class PublicRoomList(BaseFederationServlet):
 
     PATH = "/publicRooms"
 
-    def __init__(self, handler, authenticator, ratelimiter, server_name, deny_access):
+    def __init__(self, handler, authenticator, ratelimiter, server_name, allow_access):
         super(PublicRoomList, self).__init__(
             handler, authenticator, ratelimiter, server_name
         )
-        self.deny_access = deny_access
+        self.allow_access = allow_access
 
     @defer.inlineCallbacks
     def on_GET(self, origin, content, query):
-        if self.deny_access:
+        if not self.allow_access:
             raise FederationDeniedError(origin)
 
         limit = parse_integer_from_args(query, "limit", 0)
@@ -1436,7 +1436,7 @@ def register_servlets(hs, resource, authenticator, ratelimiter, servlet_groups=N
                 authenticator=authenticator,
                 ratelimiter=ratelimiter,
                 server_name=hs.hostname,
-                deny_access=hs.config.restrict_public_rooms_to_local_users,
+                allow_access=hs.config.allow_public_rooms_over_federation,
             ).register(resource)
 
     if "group_server" in servlet_groups:
diff --git a/synapse/rest/client/v1/room.py b/synapse/rest/client/v1/room.py
index a028337125..cca7e45ddb 100644
--- a/synapse/rest/client/v1/room.py
+++ b/synapse/rest/client/v1/room.py
@@ -311,7 +311,7 @@ class PublicRoomListRestServlet(TransactionRestServlet):
             # Option to allow servers to require auth when accessing
             # /publicRooms via CS API. This is especially helpful in private
             # federations.
-            if self.hs.config.restrict_public_rooms_to_local_users:
+            if not self.hs.config.allow_public_rooms_without_auth:
                 raise
 
             # We allow people to not be authed if they're just looking at our
diff --git a/tests/rest/client/v1/test_rooms.py b/tests/rest/client/v1/test_rooms.py
index 2e3a765bf3..fe741637f5 100644
--- a/tests/rest/client/v1/test_rooms.py
+++ b/tests/rest/client/v1/test_rooms.py
@@ -920,7 +920,7 @@ class PublicRoomsRestrictedTestCase(unittest.HomeserverTestCase):
         self.url = b"/_matrix/client/r0/publicRooms"
 
         config = self.default_config()
-        config["restrict_public_rooms_to_local_users"] = True
+        config["allow_public_rooms_without_auth"] = False
         self.hs = self.setup_test_homeserver(config=config)
 
         return self.hs