diff --git a/rsa/_compat.py b/rsa/_compat.py
index 7533c36..3c4eb81 100644
--- a/rsa/_compat.py
+++ b/rsa/_compat.py
@@ -76,6 +76,11 @@
     bytes_type = str
 
 
+# To avoid calling b() multiple times in tight loops.
+ZERO_BYTE = b('\x00')
+EMPTY_BYTE = b('')
+
+
 def is_bytes(obj):
     """
     Determines whether the given value is a byte string.
diff --git a/tests/test_common.py b/tests/test_common.py
index bad24f8..9980b15 100644
--- a/tests/test_common.py
+++ b/tests/test_common.py
@@ -34,6 +34,9 @@
         self.assertRaises(TypeError, byte_size, None)
 
 class Test_bit_size(unittest2.TestCase):
+    def test_zero(self):
+        self.assertEqual(bit_size(0), 0)
+
     def test_values(self):
         self.assertEqual(bit_size(1023), 10)
         self.assertEqual(bit_size(1024), 11)