diff --git a/lib/Crypto/Hash/CMAC.py b/lib/Crypto/Hash/CMAC.py
index 7b87ffcb..152d88a0 100644
--- a/lib/Crypto/Hash/CMAC.py
+++ b/lib/Crypto/Hash/CMAC.py
@@ -20,7 +20,9 @@
 # SOFTWARE.
 # ===================================================================
 
-from Crypto.Util.py3compat import b, bchr, bord, tobytes
+import sys
+
+from Crypto.Util.py3compat import bord, tobytes
 
 from binascii import unhexlify
 
@@ -33,6 +35,12 @@ from Crypto.Random import get_random_bytes
 digest_size = None
 
 
+if sys.version_info[0] == 2 and sys.version_info[1] < 7:
+    _memoryview = None
+else:
+    _memoryview = memoryview
+
+
 def _shift_bytes(bs, xor_lsb=0):
     num = (bytes_to_long(bs) << 1) ^ xor_lsb
     return long_to_bytes(num, len(bs))[-len(bs):]
@@ -77,7 +85,7 @@ class CMAC(object):
         self._mac_tag = None
 
         # Compute sub-keys
-        zero_block = bchr(0) * ciphermod.block_size
+        zero_block = b'\x00' * ciphermod.block_size
         cipher = ciphermod.new(key,
                                ciphermod.MODE_ECB,
                                **self._cipher_params)
@@ -98,7 +106,7 @@ class CMAC(object):
                                   **self._cipher_params)
 
         # Cache for outstanding data to authenticate
-        self._cache = b("")
+        self._cache = b""
 
         # Last two pieces of ciphertext produced
         self._last_ct = self._last_pt = zero_block
@@ -128,16 +136,19 @@ class CMAC(object):
 
             msg = msg[filler:]
             self._update(self._cache)
-            self._cache = b("")
+            self._cache = b""
 
         update_len, remain = divmod(len(msg), self.digest_size)
         update_len *= self.digest_size
         if remain > 0:
             self._update(msg[:update_len])
-            self._cache = msg[update_len:]
+            if isinstance(msg, _memoryview):
+                self._cache = msg[update_len:].tobytes()
+            else:
+                self._cache = msg[update_len:]
         else:
             self._update(msg)
-            self._cache = b("")
+            self._cache = b""
         return self
 
     def _update(self, data_block):
@@ -201,8 +212,8 @@ class CMAC(object):
             pt = strxor(strxor(self._before_last_ct, self._k1), self._last_pt)
         else:
             # Last block is partial (or message length is zero)
-            ext = self._cache + bchr(0x80) +\
-                    bchr(0) * (self.digest_size - len(self._cache) - 1)
+            ext = self._cache + b'\x80' +\
+                    b'\x00' * (self.digest_size - len(self._cache) - 1)
             pt = strxor(strxor(self._last_ct, self._k2), ext)
 
         cipher = self._factory.new(self._key,
diff --git a/lib/Crypto/SelfTest/Hash/test_CMAC.py b/lib/Crypto/SelfTest/Hash/test_CMAC.py
index fe320759..a785b313 100644
--- a/lib/Crypto/SelfTest/Hash/test_CMAC.py
+++ b/lib/Crypto/SelfTest/Hash/test_CMAC.py
@@ -33,6 +33,7 @@
 
 """Self-test suite for Crypto.Hash.CMAC"""
 
+import sys
 import unittest
 
 from Crypto.Util.py3compat import tobytes
@@ -266,6 +267,54 @@ class MultipleUpdates(unittest.TestCase):
             self.assertEqual(ref_mac, mac.digest())
 
 
+class ByteArrayTests(unittest.TestCase):
+
+    def runTest(self):
+
+        key = b"0" * 16
+        data = b"\x00\x01\x02"
+
+        key_ba = bytearray(key)
+        data_ba = bytearray(data)
+
+        # Data and key can be a bytearray (during initialization)
+        h1 = CMAC.new(key, data, ciphermod=AES)
+        h2 = CMAC.new(key_ba, data_ba, ciphermod=AES)
+        self.assertEqual(h1.digest(), h2.digest())
+
+        # Data can be a bytearray (during operation)
+        h1 = CMAC.new(key, ciphermod=AES)
+        h2 = CMAC.new(key, ciphermod=AES)
+        h1.update(data)
+        h2.update(data_ba)
+        self.assertEqual(h1.digest(), h2.digest())
+
+
+class MemoryViewTests(unittest.TestCase):
+
+    def runTest(self):
+
+        key = b"0" * 16
+        data = b"\x00\x01\x02"
+
+        mv_ro = [ memoryview(x) for x in (key, data) ]
+        mv_rw = [ memoryview(bytearray(x)) for x in (key, data) ]
+
+        for key_mv, data_mv in (mv_ro, mv_rw):
+
+            # Data and key can be a memoryview (during initialization)
+            h1 = CMAC.new(key, data, ciphermod=AES)
+            h2 = CMAC.new(key_mv, data_mv, ciphermod=AES)
+            self.assertEqual(h1.digest(), h2.digest())
+
+            # Data can be a memoryview (during operation)
+            h1 = CMAC.new(key, ciphermod=AES)
+            h2 = CMAC.new(key, ciphermod=AES)
+            h1.update(data)
+            h2.update(data_mv)
+            self.assertEqual(h1.digest(), h2.digest())
+
+
 def get_tests(config={}):
     global test_data
     from common import make_mac_tests
@@ -279,6 +328,9 @@ def get_tests(config={}):
 
     tests = make_mac_tests(CMAC, "CMAC", params_test_data)
     tests.append(MultipleUpdates())
+    tests.append(ByteArrayTests())
+    if not (sys.version_info[0] == 2 and sys.version_info[1] < 7):
+        tests.append(MemoryViewTests())
     return tests