diff --git a/django/contrib/sessions/backends/file.py b/django/contrib/sessions/backends/file.py
index 843edca9cf..2c4e40dbc7 100644
--- a/django/contrib/sessions/backends/file.py
+++ b/django/contrib/sessions/backends/file.py
@@ -26,6 +26,8 @@ class SessionStore(SessionBase):
         self.file_prefix = settings.SESSION_COOKIE_NAME
         super(SessionStore, self).__init__(session_key)
 
+    VALID_KEY_CHARS = set("abcdef0123456789")
+
     def _key_to_file(self, session_key=None):
         """
         Get the file associated with this session key.
@@ -36,9 +38,9 @@ class SessionStore(SessionBase):
         # Make sure we're not vulnerable to directory traversal. Session keys
         # should always be md5s, so they should never contain directory
         # components.
-        if os.path.sep in session_key:
+        if not set(session_key).issubset(self.VALID_KEY_CHARS):
             raise SuspiciousOperation(
-                "Invalid characters (directory components) in session key")
+                "Invalid characters in session key")
 
         return os.path.join(self.storage_path, self.file_prefix + session_key)
 
diff --git a/django/contrib/sessions/tests.py b/django/contrib/sessions/tests.py
index 941c7e811b..afdb761816 100644
--- a/django/contrib/sessions/tests.py
+++ b/django/contrib/sessions/tests.py
@@ -11,7 +11,7 @@ from django.contrib.sessions.backends.cached_db import SessionStore as CacheDBSe
 from django.contrib.sessions.backends.file import SessionStore as FileSession
 from django.contrib.sessions.models import Session
 from django.contrib.sessions.middleware import SessionMiddleware
-from django.core.exceptions import ImproperlyConfigured
+from django.core.exceptions import ImproperlyConfigured, SuspiciousOperation
 from django.http import HttpResponse
 from django.test import TestCase, RequestFactory
 from django.utils import unittest
@@ -322,6 +322,16 @@ class FileSessionTests(SessionTestsMixin, unittest.TestCase):
         settings.SESSION_FILE_PATH = "/if/this/directory/exists/you/have/a/weird/computer"
         self.assertRaises(ImproperlyConfigured, self.backend)
 
+    def test_invalid_key_backslash(self):
+        # Ensure we don't allow directory-traversal
+        self.assertRaises(SuspiciousOperation,
+                          self.backend("a\\b\\c").load)
+
+    def test_invalid_key_forwardslash(self):
+        # Ensure we don't allow directory-traversal
+        self.assertRaises(SuspiciousOperation,
+                          self.backend("a/b/c").load)
+
 
 class CacheSessionTests(SessionTestsMixin, unittest.TestCase):