diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index e4e0481..ad69ec9 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -12,6 +12,7 @@
 import functools
 import gc
 import glob
+import hashlib
 import importlib
 import importlib.util
 import locale
@@ -646,6 +647,29 @@
     return decorator
 
 
+def requires_hashdigest(digestname):
+    """Decorator raising SkipTest if a hashing algorithm is not available
+
+    The hashing algorithm could be missing or blocked by a strict crypto
+    policy.
+
+    ValueError: [digital envelope routines: EVP_DigestInit_ex] disabled for FIPS
+    ValueError: unsupported hash type md4
+    """
+    def decorator(func):
+        @functools.wraps(func)
+        def wrapper(*args, **kwargs):
+            try:
+                hashlib.new(digestname)
+            except ValueError:
+                raise unittest.SkipTest(
+                    f"hash digest '{digestname}' is not available."
+                )
+            return func(*args, **kwargs)
+        return wrapper
+    return decorator
+
+
 HOST = "localhost"
 HOSTv4 = "127.0.0.1"
 HOSTv6 = "::1"
diff --git a/Lib/test/test_hmac.py b/Lib/test/test_hmac.py
index f2eb6d7..2c09de8 100644
--- a/Lib/test/test_hmac.py
+++ b/Lib/test/test_hmac.py
@@ -6,6 +6,8 @@
 import unittest.mock
 import warnings
 
+from test.support import requires_hashdigest
+
 
 def ignore_warning(func):
     @functools.wraps(func)
@@ -19,6 +21,7 @@
 
 class TestVectorsTestCase(unittest.TestCase):
 
+    @requires_hashdigest('md5')
     def test_md5_vectors(self):
         # Test the HMAC module against test vectors from the RFC.
 
@@ -76,6 +79,7 @@
                  b"and Larger Than One Block-Size Data"),
                 "6f630fad67cda0ee1fb1f562db3aa53e")
 
+    @requires_hashdigest('sha1')
     def test_sha_vectors(self):
         def shatest(key, data, digest):
             h = hmac.HMAC(key, data, digestmod=hashlib.sha1)
@@ -268,23 +272,28 @@
                                    '134676fb6de0446065c97440fa8c6a58',
                  })
 
+    @requires_hashdigest('sha224')
     def test_sha224_rfc4231(self):
         self._rfc4231_test_cases(hashlib.sha224, 'sha224', 28, 64)
 
+    @requires_hashdigest('sha256')
     def test_sha256_rfc4231(self):
         self._rfc4231_test_cases(hashlib.sha256, 'sha256', 32, 64)
 
+    @requires_hashdigest('sha384')
     def test_sha384_rfc4231(self):
         self._rfc4231_test_cases(hashlib.sha384, 'sha384', 48, 128)
 
+    @requires_hashdigest('sha512')
     def test_sha512_rfc4231(self):
         self._rfc4231_test_cases(hashlib.sha512, 'sha512', 64, 128)
 
+    @requires_hashdigest('sha256')
     def test_legacy_block_size_warnings(self):
         class MockCrazyHash(object):
             """Ain't no block_size attribute here."""
             def __init__(self, *args):
-                self._x = hashlib.sha1(*args)
+                self._x = hashlib.sha256(*args)
                 self.digest_size = self._x.digest_size
             def update(self, v):
                 self._x.update(v)
@@ -308,65 +317,78 @@
             data = b"Hi There"
             hmac.HMAC(key, data, digestmod=None)
 
+
 class ConstructorTestCase(unittest.TestCase):
 
+    expected = (
+        "6c845b47f52b3b47f6590c502db7825aad757bf4fadc8fa972f7cd2e76a5bdeb"
+    )
+
+    @requires_hashdigest('sha256')
     def test_normal(self):
         # Standard constructor call.
-        failed = 0
         try:
-            h = hmac.HMAC(b"key", digestmod='md5')
+            hmac.HMAC(b"key", digestmod='sha256')
         except Exception:
             self.fail("Standard constructor call raised exception.")
 
+    @requires_hashdigest('sha256')
     def test_with_str_key(self):
         # Pass a key of type str, which is an error, because it expects a key
         # of type bytes
         with self.assertRaises(TypeError):
-            h = hmac.HMAC("key", digestmod='md5')
+            h = hmac.HMAC("key", digestmod='sha256')
 
+    @requires_hashdigest('sha256')
     def test_dot_new_with_str_key(self):
         # Pass a key of type str, which is an error, because it expects a key
         # of type bytes
         with self.assertRaises(TypeError):
-            h = hmac.new("key", digestmod='md5')
+            h = hmac.new("key", digestmod='sha256')
 
+    @requires_hashdigest('sha256')
     def test_withtext(self):
         # Constructor call with text.
         try:
-            h = hmac.HMAC(b"key", b"hash this!", digestmod='md5')
+            h = hmac.HMAC(b"key", b"hash this!", digestmod='sha256')
         except Exception:
             self.fail("Constructor call with text argument raised exception.")
-        self.assertEqual(h.hexdigest(), '34325b639da4cfd95735b381e28cb864')
+        self.assertEqual(h.hexdigest(), self.expected)
 
+    @requires_hashdigest('sha256')
     def test_with_bytearray(self):
         try:
             h = hmac.HMAC(bytearray(b"key"), bytearray(b"hash this!"),
-                          digestmod="md5")
+                          digestmod="sha256")
         except Exception:
             self.fail("Constructor call with bytearray arguments raised exception.")
-        self.assertEqual(h.hexdigest(), '34325b639da4cfd95735b381e28cb864')
+            self.assertEqual(h.hexdigest(), self.expected)
 
+    @requires_hashdigest('sha256')
     def test_with_memoryview_msg(self):
         try:
-            h = hmac.HMAC(b"key", memoryview(b"hash this!"), digestmod="md5")
+            h = hmac.HMAC(b"key", memoryview(b"hash this!"), digestmod="sha256")
         except Exception:
             self.fail("Constructor call with memoryview msg raised exception.")
-        self.assertEqual(h.hexdigest(), '34325b639da4cfd95735b381e28cb864')
+            self.assertEqual(h.hexdigest(), self.expected)
 
+    @requires_hashdigest('sha256')
     def test_withmodule(self):
         # Constructor call with text and digest module.
         try:
-            h = hmac.HMAC(b"key", b"", hashlib.sha1)
+            h = hmac.HMAC(b"key", b"", hashlib.sha256)
         except Exception:
-            self.fail("Constructor call with hashlib.sha1 raised exception.")
+            self.fail("Constructor call with hashlib.sha256 raised exception.")
+
 
 class SanityTestCase(unittest.TestCase):
 
+    @requires_hashdigest('sha256')
     def test_exercise_all_methods(self):
         # Exercising all methods once.
         # This must not raise any exceptions
         try:
-            h = hmac.HMAC(b"my secret key", digestmod="md5")
+            h = hmac.HMAC(b"my secret key", digestmod="sha256")
             h.update(b"compute the hash of this text!")
             dig = h.digest()
             dig = h.hexdigest()
@@ -374,11 +396,13 @@
         except Exception:
             self.fail("Exception raised during normal usage of HMAC class.")
 
+
 class CopyTestCase(unittest.TestCase):
 
+    @requires_hashdigest('sha256')
     def test_attributes(self):
         # Testing if attributes are of same type.
-        h1 = hmac.HMAC(b"key", digestmod="md5")
+        h1 = hmac.HMAC(b"key", digestmod="sha256")
         h2 = h1.copy()
         self.assertTrue(h1.digest_cons == h2.digest_cons,
             "digest constructors don't match.")
@@ -387,9 +411,10 @@
         self.assertEqual(type(h1.outer), type(h2.outer),
             "Types of outer don't match.")
 
+    @requires_hashdigest('sha256')
     def test_realcopy(self):
         # Testing if the copy method created a real copy.
-        h1 = hmac.HMAC(b"key", digestmod="md5")
+        h1 = hmac.HMAC(b"key", digestmod="sha256")
         h2 = h1.copy()
         # Using id() in case somebody has overridden __eq__/__ne__.
         self.assertTrue(id(h1) != id(h2), "No real copy of the HMAC instance.")
@@ -398,9 +423,10 @@
         self.assertTrue(id(h1.outer) != id(h2.outer),
             "No real copy of the attribute 'outer'.")
 
+    @requires_hashdigest('sha256')
     def test_equality(self):
         # Testing if the copy has the same digests.
-        h1 = hmac.HMAC(b"key", digestmod="md5")
+        h1 = hmac.HMAC(b"key", digestmod="sha256")
         h1.update(b"some random text")
         h2 = h1.copy()
         self.assertEqual(h1.digest(), h2.digest(),
diff --git a/Lib/test/test_imaplib.py b/Lib/test/test_imaplib.py
index 8ab532a..03cffbe 100644
--- a/Lib/test/test_imaplib.py
+++ b/Lib/test/test_imaplib.py
@@ -10,7 +10,8 @@
 import socket
 
 from test.support import (reap_threads, verbose, transient_internet,
-                          run_with_tz, run_with_locale, cpython_only)
+                          run_with_tz, run_with_locale, cpython_only,
+                          requires_hashdigest)
 import unittest
 from unittest import mock
 from datetime import datetime, timezone, timedelta
@@ -370,6 +371,7 @@
         self.assertEqual(code, 'OK')
         self.assertEqual(server.response, b'ZmFrZQ==\r\n')  # b64 encoded 'fake'
 
+    @requires_hashdigest('md5')
     def test_login_cram_md5_bytes(self):
         class AuthHandler(SimpleIMAPHandler):
             capabilities = 'LOGINDISABLED AUTH=CRAM-MD5'
@@ -387,6 +389,7 @@
         ret, _ = client.login_cram_md5("tim", b"tanstaaftanstaaf")
         self.assertEqual(ret, "OK")
 
+    @requires_hashdigest('md5')
     def test_login_cram_md5_plain_text(self):
         class AuthHandler(SimpleIMAPHandler):
             capabilities = 'LOGINDISABLED AUTH=CRAM-MD5'
@@ -797,6 +800,7 @@
                              b'ZmFrZQ==\r\n')  # b64 encoded 'fake'
 
     @reap_threads
+    @requires_hashdigest('md5')
     def test_login_cram_md5(self):
 
         class AuthHandler(SimpleIMAPHandler):
diff --git a/Lib/test/test_poplib.py b/Lib/test/test_poplib.py
index 20d4eea..7b1d854 100644
--- a/Lib/test/test_poplib.py
+++ b/Lib/test/test_poplib.py
@@ -309,9 +309,11 @@
     def test_rpop(self):
         self.assertOK(self.client.rpop('foo'))
 
+    @test_support.requires_hashdigest('md5')
     def test_apop_normal(self):
         self.assertOK(self.client.apop('foo', 'dummypassword'))
 
+    @test_support.requires_hashdigest('md5')
     def test_apop_REDOS(self):
         # Replace welcome with very long evil welcome.
         # NB The upper bound on welcome length is currently 2048.
diff --git a/Lib/test/test_smtplib.py b/Lib/test/test_smtplib.py
index f1332e9..d0c9862 100644
--- a/Lib/test/test_smtplib.py
+++ b/Lib/test/test_smtplib.py
@@ -4,6 +4,7 @@
 from email.message import EmailMessage
 from email.base64mime import body_encode as encode_base64
 import email.utils
+import hashlib
 import hmac
 import socket
 import smtpd
@@ -21,6 +22,7 @@
 from test import support, mock_socket
 from test.support import HOST
 from test.support import threading_setup, threading_cleanup, join_thread
+from test.support import requires_hashdigest
 from unittest.mock import Mock
 
 
@@ -1009,6 +1011,7 @@
         self.assertEqual(resp, (235, b'Authentication Succeeded'))
         smtp.close()
 
+    @requires_hashdigest('md5')
     def testAUTH_CRAM_MD5(self):
         self.serv.add_feature("AUTH CRAM-MD5")
         smtp = smtplib.SMTP(HOST, self.port, local_hostname='localhost', timeout=15)
@@ -1025,7 +1028,13 @@
         smtp.close()
 
     def test_auth_function(self):
-        supported = {'CRAM-MD5', 'PLAIN', 'LOGIN'}
+        supported = {'PLAIN', 'LOGIN'}
+        try:
+            hashlib.md5()
+        except ValueError:
+            pass
+        else:
+            supported.add('CRAM-MD5')
         for mechanism in supported:
             self.serv.add_feature("AUTH {}".format(mechanism))
         for mechanism in supported:
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 7e32cbc..15324a4 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -1,7 +1,7 @@
 import sys
 import os
 import io
-from hashlib import md5
+from hashlib import sha256
 from contextlib import contextmanager
 from random import Random
 import pathlib
@@ -11,7 +11,7 @@
 import tarfile
 
 from test import support
-from test.support import script_helper
+from test.support import script_helper, requires_hashdigest
 
 # Check for our compression modules.
 try:
@@ -27,8 +27,8 @@
 except ImportError:
     lzma = None
 
-def md5sum(data):
-    return md5(data).hexdigest()
+def sha256sum(data):
+    return sha256(data).hexdigest()
 
 TEMPDIR = os.path.abspath(support.TESTFN) + "-tardir"
 tarextdir = TEMPDIR + '-extract-test'
@@ -39,8 +39,12 @@
 tmpname = os.path.join(TEMPDIR, "tmp.tar")
 dotlessname = os.path.join(TEMPDIR, "testtar")
 
-md5_regtype = "65f477c818ad9e15f7feab0c6d37742f"
-md5_sparse = "a54fbc4ca4f4399a90e1b27164012fc6"
+sha256_regtype = (
+    "e09e4bc8b3c9d9177e77256353b36c159f5f040531bbd4b024a8f9b9196c71ce"
+)
+sha256_sparse = (
+    "4f05a776071146756345ceee937b33fc5644f5a96b9780d1c7d6a32cdf164d7b"
+)
 
 
 class TarTest:
@@ -95,7 +99,7 @@
             data = fobj.read()
             self.assertEqual(len(data), tarinfo.size,
                     "regular file extraction failed")
-            self.assertEqual(md5sum(data), md5_regtype,
+            self.assertEqual(sha256sum(data), sha256_regtype,
                     "regular file extraction failed")
 
     def test_fileobj_readlines(self):
@@ -178,7 +182,7 @@
         with self.tar.extractfile("ustar/regtype") as fobj:
             fobj = io.TextIOWrapper(fobj)
             data = fobj.read().encode("iso8859-1")
-            self.assertEqual(md5sum(data), md5_regtype)
+            self.assertEqual(sha256sum(data), sha256_regtype)
             try:
                 fobj.seek(100)
             except AttributeError:
@@ -543,13 +547,13 @@
             self.addCleanup(support.unlink, os.path.join(TEMPDIR, "ustar/lnktype"))
             with open(os.path.join(TEMPDIR, "ustar/lnktype"), "rb") as f:
                 data = f.read()
-            self.assertEqual(md5sum(data), md5_regtype)
+            self.assertEqual(sha256sum(data), sha256_regtype)
 
             tar.extract("ustar/symtype", TEMPDIR)
             self.addCleanup(support.unlink, os.path.join(TEMPDIR, "ustar/symtype"))
             with open(os.path.join(TEMPDIR, "ustar/symtype"), "rb") as f:
                 data = f.read()
-            self.assertEqual(md5sum(data), md5_regtype)
+            self.assertEqual(sha256sum(data), sha256_regtype)
 
     def test_extractall(self):
         # Test if extractall() correctly restores directory permissions
@@ -684,7 +688,7 @@
             data = fobj.read()
         self.assertEqual(len(data), tarinfo.size,
                 "regular file extraction failed")
-        self.assertEqual(md5sum(data), md5_regtype,
+        self.assertEqual(sha256sum(data), sha256_regtype,
                 "regular file extraction failed")
 
     def test_provoke_stream_error(self):
@@ -796,8 +800,8 @@
     def _test_member(self, tarinfo, chksum=None, **kwargs):
         if chksum is not None:
             with self.tar.extractfile(tarinfo) as f:
-                self.assertEqual(md5sum(f.read()), chksum,
-                        "wrong md5sum for %s" % tarinfo.name)
+                self.assertEqual(sha256sum(f.read()), chksum,
+                        "wrong sha256sum for %s" % tarinfo.name)
 
         kwargs["mtime"] = 0o7606136617
         kwargs["uid"] = 1000
@@ -812,11 +816,11 @@
 
     def test_find_regtype(self):
         tarinfo = self.tar.getmember("ustar/regtype")
-        self._test_member(tarinfo, size=7011, chksum=md5_regtype)
+        self._test_member(tarinfo, size=7011, chksum=sha256_regtype)
 
     def test_find_conttype(self):
         tarinfo = self.tar.getmember("ustar/conttype")
-        self._test_member(tarinfo, size=7011, chksum=md5_regtype)
+        self._test_member(tarinfo, size=7011, chksum=sha256_regtype)
 
     def test_find_dirtype(self):
         tarinfo = self.tar.getmember("ustar/dirtype")
@@ -848,28 +852,28 @@
 
     def test_find_sparse(self):
         tarinfo = self.tar.getmember("ustar/sparse")
-        self._test_member(tarinfo, size=86016, chksum=md5_sparse)
+        self._test_member(tarinfo, size=86016, chksum=sha256_sparse)
 
     def test_find_gnusparse(self):
         tarinfo = self.tar.getmember("gnu/sparse")
-        self._test_member(tarinfo, size=86016, chksum=md5_sparse)
+        self._test_member(tarinfo, size=86016, chksum=sha256_sparse)
 
     def test_find_gnusparse_00(self):
         tarinfo = self.tar.getmember("gnu/sparse-0.0")
-        self._test_member(tarinfo, size=86016, chksum=md5_sparse)
+        self._test_member(tarinfo, size=86016, chksum=sha256_sparse)
 
     def test_find_gnusparse_01(self):
         tarinfo = self.tar.getmember("gnu/sparse-0.1")
-        self._test_member(tarinfo, size=86016, chksum=md5_sparse)
+        self._test_member(tarinfo, size=86016, chksum=sha256_sparse)
 
     def test_find_gnusparse_10(self):
         tarinfo = self.tar.getmember("gnu/sparse-1.0")
-        self._test_member(tarinfo, size=86016, chksum=md5_sparse)
+        self._test_member(tarinfo, size=86016, chksum=sha256_sparse)
 
     def test_find_umlauts(self):
         tarinfo = self.tar.getmember("ustar/umlauts-"
                                      "\xc4\xd6\xdc\xe4\xf6\xfc\xdf")
-        self._test_member(tarinfo, size=7011, chksum=md5_regtype)
+        self._test_member(tarinfo, size=7011, chksum=sha256_regtype)
 
     def test_find_ustar_longname(self):
         name = "ustar/" + "12345/" * 39 + "1234567/longname"
@@ -877,7 +881,7 @@
 
     def test_find_regtype_oldv7(self):
         tarinfo = self.tar.getmember("misc/regtype-old-v7")
-        self._test_member(tarinfo, size=7011, chksum=md5_regtype)
+        self._test_member(tarinfo, size=7011, chksum=sha256_regtype)
 
     def test_find_pax_umlauts(self):
         self.tar.close()
@@ -885,7 +889,7 @@
                                 encoding="iso8859-1")
         tarinfo = self.tar.getmember("pax/umlauts-"
                                      "\xc4\xd6\xdc\xe4\xf6\xfc\xdf")
-        self._test_member(tarinfo, size=7011, chksum=md5_regtype)
+        self._test_member(tarinfo, size=7011, chksum=sha256_regtype)
 
 
 class LongnameTest:
@@ -947,8 +951,8 @@
         filename = os.path.join(TEMPDIR, name)
         with open(filename, "rb") as fobj:
             data = fobj.read()
-        self.assertEqual(md5sum(data), md5_sparse,
-                "wrong md5sum for %s" % name)
+        self.assertEqual(sha256sum(data), sha256_sparse,
+                "wrong sha256sum for %s" % name)
 
         if self._fs_supports_holes():
             s = os.stat(filename)
@@ -2443,7 +2447,7 @@
         self.tar.extract(name, TEMPDIR)
         with open(os.path.join(TEMPDIR, name), "rb") as f:
             data = f.read()
-        self.assertEqual(md5sum(data), md5_regtype)
+        self.assertEqual(sha256sum(data), sha256_regtype)
 
     # See issues #1578269, #8879, and #17689 for some history on these skips
     @unittest.skipIf(hasattr(os.path, "islink"),
diff --git a/Lib/test/test_urllib2_localnet.py b/Lib/test/test_urllib2_localnet.py
index 591b48d..1cb358f 100644
--- a/Lib/test/test_urllib2_localnet.py
+++ b/Lib/test/test_urllib2_localnet.py
@@ -322,6 +322,7 @@
     PASSWD = "test123"
     REALM = "TestRealm"
 
+    @support.requires_hashdigest("md5")
     def setUp(self):
         super(ProxyAuthTests, self).setUp()
         # Ignore proxy bypass settings in the environment.
diff --git a/Misc/NEWS.d/next/Tests/2019-09-25-12-18-31.bpo-38270._x-9uH.rst b/Misc/NEWS.d/next/Tests/2019-09-25-12-18-31.bpo-38270._x-9uH.rst
new file mode 100644
index 0000000..efb1b98
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-09-25-12-18-31.bpo-38270._x-9uH.rst
@@ -0,0 +1,4 @@
+test.support now has a helper function to check for availibility of a
+hash digest function. Several tests are refactored avoid MD5 and use
+SHA256 instead. Other tests are marked to use MD5 and skipped when MD5 is
+disabled.