diff --git a/paramiko/dsskey.py b/paramiko/dsskey.py
index c26966e..04281ea 100644
--- a/paramiko/dsskey.py
+++ b/paramiko/dsskey.py
@@ -20,8 +20,9 @@
 DSS keys.
 """
 
+from hashlib import sha1
+
 from Crypto.PublicKey import DSA
-from Crypto.Hash import SHA
 
 from paramiko import util
 from paramiko.common import zero_byte, rng
@@ -96,7 +97,7 @@ class DSSKey (PKey):
         return self.x is not None
 
     def sign_ssh_data(self, rng, data):
-        digest = SHA.new(data).digest()
+        digest = sha1(data).digest()
         dss = DSA.construct((long(self.y), long(self.g), long(self.p), long(self.q), long(self.x)))
         # generate a suitable k
         qsize = len(util.deflate_long(self.q, 0))
@@ -130,7 +131,7 @@ class DSSKey (PKey):
         # pull out (r, s) which are NOT encoded as mpints
         sigR = util.inflate_long(sig[:20], 1)
         sigS = util.inflate_long(sig[20:], 1)
-        sigM = util.inflate_long(SHA.new(data).digest(), 1)
+        sigM = util.inflate_long(sha1(data).digest(), 1)
 
         dss = DSA.construct((long(self.y), long(self.g), long(self.p), long(self.q)))
         return dss.verify(sigM, (sigR, sigS))
diff --git a/paramiko/ecdsakey.py b/paramiko/ecdsakey.py
index 6ae2d27..7e2ee7f 100644
--- a/paramiko/ecdsakey.py
+++ b/paramiko/ecdsakey.py
@@ -21,11 +21,12 @@ L{ECDSAKey}
 """
 
 import binascii
-from ecdsa import SigningKey, VerifyingKey, der, curves
-from Crypto.Hash import SHA256
-from ecdsa.test_pyecdsa import ECDSA
-from paramiko.common import four_byte, one_byte
+from hashlib import sha256
 
+from ecdsa import SigningKey, VerifyingKey, der, curves
+from ecdsa.test_pyecdsa import ECDSA
+
+from paramiko.common import four_byte, one_byte
 from paramiko.message import Message
 from paramiko.pkey import PKey
 from paramiko.py3compat import byte_chr, u
@@ -98,7 +99,7 @@ class ECDSAKey (PKey):
         return self.signing_key is not None
 
     def sign_ssh_data(self, rpool, data):
-        digest = SHA256.new(data).digest()
+        digest = sha256(data).digest()
         sig = self.signing_key.sign_digest(digest, entropy=rpool.read,
                                            sigencode=self._sigencode)
         m = Message()
@@ -113,7 +114,7 @@ class ECDSAKey (PKey):
 
         # verify the signature by SHA'ing the data and encrypting it
         # using the public key.
-        hash_obj = SHA256.new(data).digest()
+        hash_obj = sha256(data).digest()
         return self.verifying_key.verify_digest(sig, hash_obj,
                                                 sigdecode=self._sigdecode)
 
diff --git a/paramiko/hostkeys.py b/paramiko/hostkeys.py
index f32fbeb..e1e7a18 100644
--- a/paramiko/hostkeys.py
+++ b/paramiko/hostkeys.py
@@ -18,7 +18,9 @@
 
 
 import binascii
-from Crypto.Hash import SHA, HMAC
+from hashlib import sha1
+from hmac import HMAC
+
 from paramiko.common import rng
 from paramiko.py3compat import b, u, encodebytes, decodebytes
 
@@ -262,13 +264,13 @@ class HostKeys (MutableMapping):
         :return: the hashed hostname as a `str`
         """
         if salt is None:
-            salt = rng.read(SHA.digest_size)
+            salt = rng.read(sha1().digest_size)
         else:
             if salt.startswith('|1|'):
                 salt = salt.split('|')[2]
             salt = decodebytes(b(salt))
-        assert len(salt) == SHA.digest_size
-        hmac = HMAC.HMAC(salt, b(hostname), SHA).digest()
+        assert len(salt) == sha1().digest_size
+        hmac = HMAC(salt, b(hostname), sha1).digest()
         hostkey = '|1|%s|%s' % (u(encodebytes(salt)), u(encodebytes(hmac)))
         return hostkey.replace('\n', '')
     hash_host = staticmethod(hash_host)
diff --git a/paramiko/kex_gex.py b/paramiko/kex_gex.py
index 02e507b..26b2243 100644
--- a/paramiko/kex_gex.py
+++ b/paramiko/kex_gex.py
@@ -22,7 +22,7 @@ generator "g" are provided by the server.  A bit more work is required on the
 client side, and a B{lot} more on the server side.
 """
 
-from Crypto.Hash import SHA
+from hashlib import sha1
 
 from paramiko import util
 from paramiko.common import DEBUG
@@ -203,7 +203,7 @@ class KexGex (object):
         hm.add_mpint(self.e)
         hm.add_mpint(self.f)
         hm.add_mpint(K)
-        H = SHA.new(hm.asbytes()).digest()
+        H = sha1(hm.asbytes()).digest()
         self.transport._set_K_H(K, H)
         # sign it
         sig = self.transport.get_server_key().sign_ssh_data(self.transport.rng, H)
@@ -238,6 +238,6 @@ class KexGex (object):
         hm.add_mpint(self.e)
         hm.add_mpint(self.f)
         hm.add_mpint(K)
-        self.transport._set_K_H(K, SHA.new(hm.asbytes()).digest())
+        self.transport._set_K_H(K, sha1(hm.asbytes()).digest())
         self.transport._verify_key(host_key, sig)
         self.transport._activate_outbound()
diff --git a/paramiko/kex_group1.py b/paramiko/kex_group1.py
index 3dfb7f1..f792eff 100644
--- a/paramiko/kex_group1.py
+++ b/paramiko/kex_group1.py
@@ -21,7 +21,7 @@ Standard SSH key exchange ("kex" if you wanna sound cool).  Diffie-Hellman of
 1024 bit key halves, using a known "p" prime and "g" generator.
 """
 
-from Crypto.Hash import SHA
+from hashlib import sha1
 
 from paramiko import util
 from paramiko.common import max_byte, zero_byte
@@ -105,7 +105,7 @@ class KexGroup1(object):
         hm.add_mpint(self.e)
         hm.add_mpint(self.f)
         hm.add_mpint(K)
-        self.transport._set_K_H(K, SHA.new(hm.asbytes()).digest())
+        self.transport._set_K_H(K, sha1(hm.asbytes()).digest())
         self.transport._verify_key(host_key, sig)
         self.transport._activate_outbound()
 
@@ -124,7 +124,7 @@ class KexGroup1(object):
         hm.add_mpint(self.e)
         hm.add_mpint(self.f)
         hm.add_mpint(K)
-        H = SHA.new(hm.asbytes()).digest()
+        H = sha1(hm.asbytes()).digest()
         self.transport._set_K_H(K, H)
         # sign it
         sig = self.transport.get_server_key().sign_ssh_data(self.transport.rng, H)
diff --git a/paramiko/packet.py b/paramiko/packet.py
index 0f51df5..5cffe95 100644
--- a/paramiko/packet.py
+++ b/paramiko/packet.py
@@ -25,6 +25,7 @@ import socket
 import struct
 import threading
 import time
+from hmac import HMAC
 
 from paramiko import util
 from paramiko.common import linefeed_byte, cr_byte_value, asbytes, MSG_NAMES, \
@@ -34,12 +35,6 @@ from paramiko.ssh_exception import SSHException, ProxyCommandFailure
 from paramiko.message import Message
 
 
-try:
-    from r_hmac import HMAC
-except ImportError:
-    from Crypto.Hash.HMAC import HMAC
-
-
 def compute_hmac(key, message, digest_class):
     return HMAC(key, message, digest_class).digest()
 
@@ -359,7 +354,7 @@ class Packetizer (object):
                 raise SSHException('Mismatched MAC')
         padding = byte_ord(packet[0])
         payload = packet[1:packet_size - padding]
-        
+
         if self.__dump_packets:
             self._log(DEBUG, 'Got payload (%d bytes, %d padding)' % (packet_size, padding))
 
diff --git a/paramiko/pkey.py b/paramiko/pkey.py
index c8f84e0..7d5da40 100644
--- a/paramiko/pkey.py
+++ b/paramiko/pkey.py
@@ -23,8 +23,8 @@ Common API for all public keys.
 import base64
 from binascii import hexlify, unhexlify
 import os
+from hashlib import md5
 
-from Crypto.Hash import MD5
 from Crypto.Cipher import DES3, AES
 
 from paramiko import util
@@ -126,7 +126,7 @@ class PKey (object):
             a 16-byte `string <str>` (binary) of the MD5 fingerprint, in SSH
             format.
         """
-        return MD5.new(self.asbytes()).digest()
+        return md5(self.asbytes()).digest()
 
     def get_base64(self):
         """
@@ -300,7 +300,7 @@ class PKey (object):
         keysize = self._CIPHER_TABLE[encryption_type]['keysize']
         mode = self._CIPHER_TABLE[encryption_type]['mode']
         salt = unhexlify(b(saltstr))
-        key = util.generate_key_bytes(MD5, salt, password, keysize)
+        key = util.generate_key_bytes(md5, salt, password, keysize)
         return cipher.new(key, mode, salt).decrypt(data)
 
     def _write_private_key_file(self, tag, filename, data, password=None):
@@ -332,7 +332,7 @@ class PKey (object):
             blocksize = self._CIPHER_TABLE[cipher_name]['blocksize']
             mode = self._CIPHER_TABLE[cipher_name]['mode']
             salt = rng.read(16)
-            key = util.generate_key_bytes(MD5, salt, password, keysize)
+            key = util.generate_key_bytes(md5, salt, password, keysize)
             if len(data) % blocksize != 0:
                 n = blocksize - len(data) % blocksize
                 #data += rng.read(n)
diff --git a/paramiko/rsakey.py b/paramiko/rsakey.py
index c93f321..fc09b5c 100644
--- a/paramiko/rsakey.py
+++ b/paramiko/rsakey.py
@@ -20,8 +20,9 @@
 RSA keys.
 """
 
+from hashlib import sha1
+
 from Crypto.PublicKey import RSA
-from Crypto.Hash import SHA
 
 from paramiko import util
 from paramiko.common import rng, max_byte, zero_byte, one_byte
@@ -91,7 +92,7 @@ class RSAKey (PKey):
         return self.d is not None
 
     def sign_ssh_data(self, rpool, data):
-        digest = SHA.new(data).digest()
+        digest = sha1(data).digest()
         rsa = RSA.construct((long(self.n), long(self.e), long(self.d)))
         sig = util.deflate_long(rsa.sign(self._pkcs1imify(digest), bytes())[0], 0)
         m = Message()
@@ -106,7 +107,7 @@ class RSAKey (PKey):
         # verify the signature by SHA'ing the data and encrypting it using the
         # public key.  some wackiness ensues where we "pkcs1imify" the 20-byte
         # hash into a string as long as the RSA key.
-        hash_obj = util.inflate_long(self._pkcs1imify(SHA.new(data).digest()), True)
+        hash_obj = util.inflate_long(self._pkcs1imify(sha1(data).digest()), True)
         rsa = RSA.construct((long(self.n), long(self.e)))
         return rsa.verify(hash_obj, (sig,))
 
diff --git a/paramiko/sftp_server.py b/paramiko/sftp_server.py
index dadfd02..2d8d190 100644
--- a/paramiko/sftp_server.py
+++ b/paramiko/sftp_server.py
@@ -22,9 +22,9 @@ Server-mode SFTP support.
 
 import os
 import errno
-
-from Crypto.Hash import MD5, SHA
 import sys
+from hashlib import md5, sha1
+
 from paramiko import util
 from paramiko.sftp import BaseSFTP, Message, SFTP_FAILURE, \
     SFTP_PERMISSION_DENIED, SFTP_NO_SUCH_FILE
@@ -45,8 +45,8 @@ from paramiko.sftp import CMD_HANDLE, SFTP_DESC, CMD_STATUS, SFTP_EOF, CMD_NAME,
     CMD_READLINK, CMD_SYMLINK, CMD_REALPATH, CMD_EXTENDED, SFTP_OP_UNSUPPORTED
 
 _hash_class = {
-    'sha1': SHA,
-    'md5': MD5,
+    'sha1': sha1,
+    'md5': md5,
 }
 
 
@@ -82,14 +82,14 @@ class SFTPServer (BaseSFTP, SubsystemHandler):
         self.file_table = {}
         self.folder_table = {}
         self.server = sftp_si(server, *largs, **kwargs)
-        
+
     def _log(self, level, msg):
         if issubclass(type(msg), list):
             for m in msg:
                 super(SFTPServer, self)._log(level, "[chan " + self.sock.get_name() + "] " + m)
         else:
             super(SFTPServer, self)._log(level, "[chan " + self.sock.get_name() + "] " + msg)
-        
+
     def start_subsystem(self, name, transport, channel):
         self.sock = channel
         self._log(DEBUG, 'Started sftp server on channel %s' % repr(channel))
@@ -157,7 +157,7 @@ class SFTPServer (BaseSFTP, SubsystemHandler):
 
         This is meant to be a handy helper function for translating SFTP file
         requests into local file operations.
-        
+
         :param str filename:
             name of the file to alter (should usually be an absolute path).
         :param .SFTPAttributes attr: attributes to change.
@@ -281,7 +281,7 @@ class SFTPServer (BaseSFTP, SubsystemHandler):
             # don't try to read more than about 64KB at a time
             chunklen = min(blocklen, 65536)
             count = 0
-            hash_obj = alg.new()
+            hash_obj = alg()
             while count < blocklen:
                 data = f.read(offset, chunklen)
                 if not isinstance(data, bytes_types):
@@ -298,7 +298,7 @@ class SFTPServer (BaseSFTP, SubsystemHandler):
         msg.add_string(algname)
         msg.add_bytes(sum_out)
         self._send_packet(CMD_EXTENDED_REPLY, msg)
-    
+
     def _convert_pflags(self, pflags):
         """convert SFTP-style open() flags to Python's os.open() flags"""
         if (pflags & SFTP_FLAG_READ) and (pflags & SFTP_FLAG_WRITE):
diff --git a/paramiko/transport.py b/paramiko/transport.py
index 1471b54..437cd27 100644
--- a/paramiko/transport.py
+++ b/paramiko/transport.py
@@ -25,6 +25,7 @@ import sys
 import threading
 import time
 import weakref
+from hashlib import md5, sha1
 
 import paramiko
 from paramiko import util
@@ -59,7 +60,6 @@ from paramiko.util import retry_on_signal
 
 from Crypto import Random
 from Crypto.Cipher import Blowfish, AES, DES3, ARC4
-from Crypto.Hash import SHA, MD5
 try:
     from Crypto.Util import Counter
 except ImportError:
@@ -107,10 +107,10 @@ class Transport (threading.Thread):
     }
 
     _mac_info = {
-        'hmac-sha1': {'class': SHA, 'size': 20},
-        'hmac-sha1-96': {'class': SHA, 'size': 12},
-        'hmac-md5': {'class': MD5, 'size': 16},
-        'hmac-md5-96': {'class': MD5, 'size': 12},
+        'hmac-sha1': {'class': sha1, 'size': 20},
+        'hmac-sha1-96': {'class': sha1, 'size': 12},
+        'hmac-md5': {'class': md5, 'size': 16},
+        'hmac-md5-96': {'class': md5, 'size': 12},
     }
 
     _key_info = {
@@ -1338,13 +1338,13 @@ class Transport (threading.Thread):
         m.add_bytes(self.H)
         m.add_byte(b(id))
         m.add_bytes(self.session_id)
-        out = sofar = SHA.new(m.asbytes()).digest()
+        out = sofar = sha1(m.asbytes()).digest()
         while len(out) < nbytes:
             m = Message()
             m.add_mpint(self.K)
             m.add_bytes(self.H)
             m.add_bytes(sofar)
-            digest = SHA.new(m.asbytes()).digest()
+            digest = sha1(m.asbytes()).digest()
             out += digest
             sofar += digest
         return out[:nbytes]
@@ -1719,9 +1719,9 @@ class Transport (threading.Thread):
         # initial mac keys are done in the hash's natural size (not the potentially truncated
         # transmission size)
         if self.server_mode:
-            mac_key = self._compute_key('E', mac_engine.digest_size)
+            mac_key = self._compute_key('E', mac_engine().digest_size)
         else:
-            mac_key = self._compute_key('F', mac_engine.digest_size)
+            mac_key = self._compute_key('F', mac_engine().digest_size)
         self.packetizer.set_inbound_cipher(engine, block_size, mac_engine, mac_size, mac_key)
         compress_in = self._compression_info[self.remote_compression][1]
         if (compress_in is not None) and ((self.remote_compression != 'zlib@openssh.com') or self.authenticated):
@@ -1746,9 +1746,9 @@ class Transport (threading.Thread):
         # initial mac keys are done in the hash's natural size (not the potentially truncated
         # transmission size)
         if self.server_mode:
-            mac_key = self._compute_key('F', mac_engine.digest_size)
+            mac_key = self._compute_key('F', mac_engine().digest_size)
         else:
-            mac_key = self._compute_key('E', mac_engine.digest_size)
+            mac_key = self._compute_key('E', mac_engine().digest_size)
         sdctr = self.local_cipher.endswith('-ctr')
         self.packetizer.set_outbound_cipher(engine, block_size, mac_engine, mac_size, mac_key, sdctr)
         compress_out = self._compression_info[self.local_compression][0]
diff --git a/paramiko/util.py b/paramiko/util.py
index dbcbbae..f4ee3ad 100644
--- a/paramiko/util.py
+++ b/paramiko/util.py
@@ -143,15 +143,14 @@ def tb_strings():
     return ''.join(traceback.format_exception(*sys.exc_info())).split('\n')
 
 
-def generate_key_bytes(hashclass, salt, key, nbytes):
+def generate_key_bytes(hash_alg, salt, key, nbytes):
     """
     Given a password, passphrase, or other human-source key, scramble it
     through a secure hash into some keyworthy bytes.  This specific algorithm
     is used for encrypting/decrypting private key files.
 
-    :param class hashclass:
-        class from `Crypto.Hash` that can be used as a secure hashing function
-        (like ``MD5`` or ``SHA``).
+    :param function hash_alg: A function which creates a new hash object, such
+        as ``hashlib.sha256``.
     :param salt: data to salt the hash with.
     :type salt: byte string
     :param str key: human-entered password or passphrase.
@@ -163,7 +162,7 @@ def generate_key_bytes(hashclass, salt, key, nbytes):
     if len(salt) > 8:
         salt = salt[:8]
     while nbytes > 0:
-        hash_obj = hashclass.new()
+        hash_obj = hash_alg()
         if len(digest) > 0:
             hash_obj.update(digest)
         hash_obj.update(b(key))
diff --git a/tests/test_packetizer.py b/tests/test_packetizer.py
index d4d5544..a8c0f97 100644
--- a/tests/test_packetizer.py
+++ b/tests/test_packetizer.py
@@ -21,9 +21,12 @@ Some unit tests for the ssh2 protocol in Transport.
 """
 
 import unittest
+from hashlib import sha1
+
 from tests.loop import LoopSocket
+
 from Crypto.Cipher import AES
-from Crypto.Hash import SHA
+
 from paramiko import Message, Packetizer, util
 from paramiko.common import byte_chr, zero_byte
 
@@ -41,7 +44,7 @@ class PacketizerTest (unittest.TestCase):
         p.set_log(util.get_logger('paramiko.transport'))
         p.set_hexdump(True)
         cipher = AES.new(zero_byte * 16, AES.MODE_CBC, x55 * 16)
-        p.set_outbound_cipher(cipher, 16, SHA, 12, x1f * 20)
+        p.set_outbound_cipher(cipher, 16, sha1, 12, x1f * 20)
 
         # message has to be at least 16 bytes long, so we'll have at least one
         # block of data encrypted that contains zero random padding bytes
@@ -64,7 +67,7 @@ class PacketizerTest (unittest.TestCase):
         p.set_log(util.get_logger('paramiko.transport'))
         p.set_hexdump(True)
         cipher = AES.new(zero_byte * 16, AES.MODE_CBC, x55 * 16)
-        p.set_inbound_cipher(cipher, 16, SHA, 12, x1f * 20)
+        p.set_inbound_cipher(cipher, 16, sha1, 12, x1f * 20)
         wsock.send(b'\x43\x91\x97\xbd\x5b\x50\xac\x25\x87\xc2\xc4\x6b\xc7\xe9\x38\xc0\x90\xd2\x16\x56\x0d\x71\x73\x61\x38\x7c\x4c\x3d\xfb\x97\x7d\xe2\x6e\x03\xb1\xa0\xc2\x1c\xd6\x41\x41\x4c\xb4\x59')
         cmd, m = p.read_message()
         self.assertEqual(100, cmd)
diff --git a/tests/test_pkey.py b/tests/test_pkey.py
index 6ff68fc..c457f0e 100644
--- a/tests/test_pkey.py
+++ b/tests/test_pkey.py
@@ -20,11 +20,14 @@
 Some unit tests for public/private key objects.
 """
 
-from binascii import hexlify
 import unittest
+from binascii import hexlify
+from hashlib import md5
+
 from paramiko import RSAKey, DSSKey, ECDSAKey, Message, util
 from paramiko.py3compat import StringIO, byte_chr, b, bytes
 from paramiko.common import rng
+
 from tests.util import test_path
 
 # from openssh's ssh-keygen
@@ -90,8 +93,7 @@ class KeyTest (unittest.TestCase):
         pass
 
     def test_1_generate_key_bytes(self):
-        from Crypto.Hash import MD5
-        key = util.generate_key_bytes(MD5, x1234, 'happy birthday', 30)
+        key = util.generate_key_bytes(md5, x1234, 'happy birthday', 30)
         exp = b'\x61\xE1\xF2\x72\xF4\xC1\xC4\x56\x15\x86\xBD\x32\x24\x98\xC0\xE9\x24\x67\x27\x80\xF4\x7B\xB3\x7D\xDA\x7D\x54\x01\x9E\x64'
         self.assertEqual(exp, key)
 
diff --git a/tests/test_util.py b/tests/test_util.py
index 6bde404..af6eceb 100644
--- a/tests/test_util.py
+++ b/tests/test_util.py
@@ -23,7 +23,8 @@ Some unit tests for utility functions.
 from binascii import hexlify
 import errno
 import os
-from Crypto.Hash import SHA
+from hashlib import sha1
+
 import paramiko.util
 from paramiko.util import lookup_ssh_host_config as host_config
 from paramiko.py3compat import StringIO, byte_ord
@@ -136,7 +137,7 @@ class UtilTest(ParamikoTest):
             )
 
     def test_4_generate_key_bytes(self):
-        x = paramiko.util.generate_key_bytes(SHA, b'ABCDEFGH', 'This is my secret passphrase.', 64)
+        x = paramiko.util.generate_key_bytes(sha1, b'ABCDEFGH', 'This is my secret passphrase.', 64)
         hex = ''.join(['%02x' % byte_ord(c) for c in x])
         self.assertEqual(hex, '9110e2f6793b69363e58173e9436b13a5a4b339005741d5c680e505f57d871347b4239f14fb5c46e857d5e100424873ba849ac699cea98d729e57b3e84378e8b')