diff --git a/Lib/hashlib.py b/Lib/hashlib.py
index 58c340d..ffa3be0 100644
--- a/Lib/hashlib.py
+++ b/Lib/hashlib.py
@@ -173,6 +173,7 @@ def __hash_new(name, data=b'', **kwargs):
     algorithms_available = algorithms_available.union(
             _hashlib.openssl_md_meth_names)
 except ImportError:
+    _hashlib = None
     new = __py_new
     __get_hash = __get_builtin_constructor
 
diff --git a/Lib/hmac.py b/Lib/hmac.py
index 180bc37..8b4f920 100644
--- a/Lib/hmac.py
+++ b/Lib/hmac.py
@@ -8,11 +8,12 @@
     import _hashlib as _hashopenssl
 except ImportError:
     _hashopenssl = None
-    _openssl_md_meths = None
+    _functype = None
     from _operator import _compare_digest as compare_digest
 else:
-    _openssl_md_meths = frozenset(_hashopenssl.openssl_md_meth_names)
     compare_digest = _hashopenssl.compare_digest
+    _functype = type(_hashopenssl.openssl_sha256)  # builtin type
+
 import hashlib as _hashlib
 
 trans_5C = bytes((x ^ 0x5C) for x in range(256))
@@ -23,7 +24,6 @@
 digest_size = None
 
 
-
 class HMAC:
     """RFC 2104 HMAC class.  Also complies with RFC 4231.
 
@@ -32,7 +32,7 @@ class HMAC:
     blocksize = 64  # 512-bit HMAC; can be changed in subclasses.
 
     __slots__ = (
-        "_digest_cons", "_inner", "_outer", "block_size", "digest_size"
+        "_hmac", "_inner", "_outer", "block_size", "digest_size"
     )
 
     def __init__(self, key, msg=None, digestmod=''):
@@ -55,15 +55,30 @@ def __init__(self, key, msg=None, digestmod=''):
         if not digestmod:
             raise TypeError("Missing required parameter 'digestmod'.")
 
-        if callable(digestmod):
-            self._digest_cons = digestmod
-        elif isinstance(digestmod, str):
-            self._digest_cons = lambda d=b'': _hashlib.new(digestmod, d)
+        if _hashopenssl and isinstance(digestmod, (str, _functype)):
+            try:
+                self._init_hmac(key, msg, digestmod)
+            except _hashopenssl.UnsupportedDigestmodError:
+                self._init_old(key, msg, digestmod)
         else:
-            self._digest_cons = lambda d=b'': digestmod.new(d)
+            self._init_old(key, msg, digestmod)
 
-        self._outer = self._digest_cons()
-        self._inner = self._digest_cons()
+    def _init_hmac(self, key, msg, digestmod):
+        self._hmac = _hashopenssl.hmac_new(key, msg, digestmod=digestmod)
+        self.digest_size = self._hmac.digest_size
+        self.block_size = self._hmac.block_size
+
+    def _init_old(self, key, msg, digestmod):
+        if callable(digestmod):
+            digest_cons = digestmod
+        elif isinstance(digestmod, str):
+            digest_cons = lambda d=b'': _hashlib.new(digestmod, d)
+        else:
+            digest_cons = lambda d=b'': digestmod.new(d)
+
+        self._hmac = None
+        self._outer = digest_cons()
+        self._inner = digest_cons()
         self.digest_size = self._inner.digest_size
 
         if hasattr(self._inner, 'block_size'):
@@ -79,13 +94,13 @@ def __init__(self, key, msg=None, digestmod=''):
                            RuntimeWarning, 2)
             blocksize = self.blocksize
 
+        if len(key) > blocksize:
+            key = digest_cons(key).digest()
+
         # self.blocksize is the default blocksize. self.block_size is
         # effective block size as well as the public API attribute.
         self.block_size = blocksize
 
-        if len(key) > blocksize:
-            key = self._digest_cons(key).digest()
-
         key = key.ljust(blocksize, b'\0')
         self._outer.update(key.translate(trans_5C))
         self._inner.update(key.translate(trans_36))
@@ -94,23 +109,15 @@ def __init__(self, key, msg=None, digestmod=''):
 
     @property
     def name(self):
-        return "hmac-" + self._inner.name
-
-    @property
-    def digest_cons(self):
-        return self._digest_cons
-
-    @property
-    def inner(self):
-        return self._inner
-
-    @property
-    def outer(self):
-        return self._outer
+        if self._hmac:
+            return self._hmac.name
+        else:
+            return f"hmac-{self._inner.name}"
 
     def update(self, msg):
         """Feed data from msg into this hashing object."""
-        self._inner.update(msg)
+        inst = self._hmac or self._inner
+        inst.update(msg)
 
     def copy(self):
         """Return a separate copy of this hashing object.
@@ -119,10 +126,14 @@ def copy(self):
         """
         # Call __new__ directly to avoid the expensive __init__.
         other = self.__class__.__new__(self.__class__)
-        other._digest_cons = self._digest_cons
         other.digest_size = self.digest_size
-        other._inner = self._inner.copy()
-        other._outer = self._outer.copy()
+        if self._hmac:
+            other._hmac = self._hmac.copy()
+            other._inner = other._outer = None
+        else:
+            other._hmac = None
+            other._inner = self._inner.copy()
+            other._outer = self._outer.copy()
         return other
 
     def _current(self):
@@ -130,9 +141,12 @@ def _current(self):
 
         To be used only internally with digest() and hexdigest().
         """
-        h = self._outer.copy()
-        h.update(self._inner.digest())
-        return h
+        if self._hmac:
+            return self._hmac
+        else:
+            h = self._outer.copy()
+            h.update(self._inner.digest())
+            return h
 
     def digest(self):
         """Return the hash value of this hashing object.
@@ -179,9 +193,11 @@ def digest(key, msg, digest):
             A hashlib constructor returning a new hash object. *OR*
             A module supporting PEP 247.
     """
-    if (_hashopenssl is not None and
-            isinstance(digest, str) and digest in _openssl_md_meths):
-        return _hashopenssl.hmac_digest(key, msg, digest)
+    if _hashopenssl is not None and isinstance(digest, (str, _functype)):
+        try:
+            return _hashopenssl.hmac_digest(key, msg, digest)
+        except _hashopenssl.UnsupportedDigestmodError:
+            pass
 
     if callable(digest):
         digest_cons = digest
diff --git a/Lib/test/test_hmac.py b/Lib/test/test_hmac.py
index 6daf22c..adf52ad 100644
--- a/Lib/test/test_hmac.py
+++ b/Lib/test/test_hmac.py
@@ -11,14 +11,21 @@
 from _operator import _compare_digest as operator_compare_digest
 
 try:
+    import _hashlib as _hashopenssl
     from _hashlib import HMAC as C_HMAC
     from _hashlib import hmac_new as c_hmac_new
     from _hashlib import compare_digest as openssl_compare_digest
 except ImportError:
+    _hashopenssl = None
     C_HMAC = None
     c_hmac_new = None
     openssl_compare_digest = None
 
+try:
+    import _sha256 as sha256_module
+except ImportError:
+    sha256_module = None
+
 
 def ignore_warning(func):
     @functools.wraps(func)
@@ -32,22 +39,27 @@ def wrapper(*args, **kwargs):
 
 class TestVectorsTestCase(unittest.TestCase):
 
-    def asssert_hmac(
-        self, key, data, digest, hashfunc, hashname, digest_size, block_size
+    def assert_hmac_internals(
+            self, h, digest, hashname, digest_size, block_size
     ):
-        h = hmac.HMAC(key, data, digestmod=hashfunc)
         self.assertEqual(h.hexdigest().upper(), digest.upper())
         self.assertEqual(h.digest(), binascii.unhexlify(digest))
         self.assertEqual(h.name, f"hmac-{hashname}")
         self.assertEqual(h.digest_size, digest_size)
         self.assertEqual(h.block_size, block_size)
 
+    def assert_hmac(
+        self, key, data, digest, hashfunc, hashname, digest_size, block_size
+    ):
+        h = hmac.HMAC(key, data, digestmod=hashfunc)
+        self.assert_hmac_internals(
+            h, digest, hashname, digest_size, block_size
+        )
+
         h = hmac.HMAC(key, data, digestmod=hashname)
-        self.assertEqual(h.hexdigest().upper(), digest.upper())
-        self.assertEqual(h.digest(), binascii.unhexlify(digest))
-        self.assertEqual(h.name, f"hmac-{hashname}")
-        self.assertEqual(h.digest_size, digest_size)
-        self.assertEqual(h.block_size, block_size)
+        self.assert_hmac_internals(
+            h, digest, hashname, digest_size, block_size
+        )
 
         h = hmac.HMAC(key, digestmod=hashname)
         h2 = h.copy()
@@ -56,11 +68,9 @@ def asssert_hmac(
         self.assertEqual(h.hexdigest().upper(), digest.upper())
 
         h = hmac.new(key, data, digestmod=hashname)
-        self.assertEqual(h.hexdigest().upper(), digest.upper())
-        self.assertEqual(h.digest(), binascii.unhexlify(digest))
-        self.assertEqual(h.name, f"hmac-{hashname}")
-        self.assertEqual(h.digest_size, digest_size)
-        self.assertEqual(h.block_size, block_size)
+        self.assert_hmac_internals(
+            h, digest, hashname, digest_size, block_size
+        )
 
         h = hmac.new(key, None, digestmod=hashname)
         h.update(data)
@@ -81,23 +91,18 @@ def asssert_hmac(
             hmac.digest(key, data, digest=hashfunc),
             binascii.unhexlify(digest)
         )
-        with unittest.mock.patch('hmac._openssl_md_meths', {}):
-            self.assertEqual(
-                hmac.digest(key, data, digest=hashname),
-                binascii.unhexlify(digest)
-            )
-            self.assertEqual(
-                hmac.digest(key, data, digest=hashfunc),
-                binascii.unhexlify(digest)
-            )
+
+        h = hmac.HMAC.__new__(hmac.HMAC)
+        h._init_old(key, data, digestmod=hashname)
+        self.assert_hmac_internals(
+            h, digest, hashname, digest_size, block_size
+        )
 
         if c_hmac_new is not None:
             h = c_hmac_new(key, data, digestmod=hashname)
-            self.assertEqual(h.hexdigest().upper(), digest.upper())
-            self.assertEqual(h.digest(), binascii.unhexlify(digest))
-            self.assertEqual(h.name, f"hmac-{hashname}")
-            self.assertEqual(h.digest_size, digest_size)
-            self.assertEqual(h.block_size, block_size)
+            self.assert_hmac_internals(
+                h, digest, hashname, digest_size, block_size
+            )
 
             h = c_hmac_new(key, digestmod=hashname)
             h2 = h.copy()
@@ -105,12 +110,24 @@ def asssert_hmac(
             h.update(data)
             self.assertEqual(h.hexdigest().upper(), digest.upper())
 
+            func = getattr(_hashopenssl, f"openssl_{hashname}")
+            h = c_hmac_new(key, data, digestmod=func)
+            self.assert_hmac_internals(
+                h, digest, hashname, digest_size, block_size
+            )
+
+            h = hmac.HMAC.__new__(hmac.HMAC)
+            h._init_hmac(key, data, digestmod=hashname)
+            self.assert_hmac_internals(
+                h, digest, hashname, digest_size, block_size
+            )
+
     @hashlib_helper.requires_hashdigest('md5', openssl=True)
     def test_md5_vectors(self):
         # Test the HMAC module against test vectors from the RFC.
 
         def md5test(key, data, digest):
-            self.asssert_hmac(
+            self.assert_hmac(
                 key, data, digest,
                 hashfunc=hashlib.md5,
                 hashname="md5",
@@ -150,7 +167,7 @@ def md5test(key, data, digest):
     @hashlib_helper.requires_hashdigest('sha1', openssl=True)
     def test_sha_vectors(self):
         def shatest(key, data, digest):
-            self.asssert_hmac(
+            self.assert_hmac(
                 key, data, digest,
                 hashfunc=hashlib.sha1,
                 hashname="sha1",
@@ -191,7 +208,7 @@ def _rfc4231_test_cases(self, hashfunc, hash_name, digest_size, block_size):
         def hmactest(key, data, hexdigests):
             digest = hexdigests[hashfunc]
 
-            self.asssert_hmac(
+            self.assert_hmac(
                 key, data, digest,
                 hashfunc=hashfunc,
                 hashname=hash_name,
@@ -427,6 +444,15 @@ def test_internal_types(self):
         ):
             C_HMAC()
 
+    @unittest.skipUnless(sha256_module is not None, 'need _sha256')
+    def test_with_sha256_module(self):
+        h = hmac.HMAC(b"key", b"hash this!", digestmod=sha256_module.sha256)
+        self.assertEqual(h.hexdigest(), self.expected)
+        self.assertEqual(h.name, "hmac-sha256")
+
+        digest = hmac.digest(b"key", b"hash this!", sha256_module.sha256)
+        self.assertEqual(digest, binascii.unhexlify(self.expected))
+
 
 class SanityTestCase(unittest.TestCase):
 
@@ -447,21 +473,21 @@ def test_exercise_all_methods(self):
 class CopyTestCase(unittest.TestCase):
 
     @hashlib_helper.requires_hashdigest('sha256')
-    def test_attributes(self):
+    def test_attributes_old(self):
         # Testing if attributes are of same type.
-        h1 = hmac.HMAC(b"key", digestmod="sha256")
+        h1 = hmac.HMAC.__new__(hmac.HMAC)
+        h1._init_old(b"key", b"msg", digestmod="sha256")
         h2 = h1.copy()
-        self.assertTrue(h1._digest_cons == h2._digest_cons,
-            "digest constructors don't match.")
         self.assertEqual(type(h1._inner), type(h2._inner),
             "Types of inner don't match.")
         self.assertEqual(type(h1._outer), type(h2._outer),
             "Types of outer don't match.")
 
     @hashlib_helper.requires_hashdigest('sha256')
-    def test_realcopy(self):
+    def test_realcopy_old(self):
         # Testing if the copy method created a real copy.
-        h1 = hmac.HMAC(b"key", digestmod="sha256")
+        h1 = hmac.HMAC.__new__(hmac.HMAC)
+        h1._init_old(b"key", b"msg", 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.")
@@ -469,17 +495,15 @@ def test_realcopy(self):
             "No real copy of the attribute 'inner'.")
         self.assertTrue(id(h1._outer) != id(h2._outer),
             "No real copy of the attribute 'outer'.")
-        self.assertEqual(h1._inner, h1.inner)
-        self.assertEqual(h1._outer, h1.outer)
-        self.assertEqual(h1._digest_cons, h1.digest_cons)
+        self.assertIs(h1._hmac, None)
 
+    @unittest.skipIf(_hashopenssl is None, "test requires _hashopenssl")
     @hashlib_helper.requires_hashdigest('sha256')
-    def test_properties(self):
-        # deprecated properties
-        h1 = hmac.HMAC(b"key", digestmod="sha256")
-        self.assertEqual(h1._inner, h1.inner)
-        self.assertEqual(h1._outer, h1.outer)
-        self.assertEqual(h1._digest_cons, h1.digest_cons)
+    def test_realcopy_hmac(self):
+        h1 = hmac.HMAC.__new__(hmac.HMAC)
+        h1._init_hmac(b"key", b"msg", digestmod="sha256")
+        h2 = h1.copy()
+        self.assertTrue(id(h1._hmac) != id(h2._hmac))
 
     @hashlib_helper.requires_hashdigest('sha256')
     def test_equality(self):
diff --git a/Misc/NEWS.d/next/Library/2021-03-19-10-22-17.bpo-40645.5pXhb-.rst b/Misc/NEWS.d/next/Library/2021-03-19-10-22-17.bpo-40645.5pXhb-.rst
new file mode 100644
index 0000000..a9ab1c0
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2021-03-19-10-22-17.bpo-40645.5pXhb-.rst
@@ -0,0 +1,2 @@
+The :mod:`hmac` module now uses OpenSSL's HMAC implementation when digestmod
+argument is a hash name or builtin hash function.
diff --git a/Modules/_hashopenssl.c b/Modules/_hashopenssl.c
index d4295d7..6c83b9e 100644
--- a/Modules/_hashopenssl.c
+++ b/Modules/_hashopenssl.c
@@ -86,6 +86,8 @@ typedef struct {
 #ifdef PY_OPENSSL_HAS_SHAKE
     PyTypeObject *EVPXOFtype;
 #endif
+    PyObject *constructs;
+    PyObject *unsupported_digestmod_error;
 } _hashlibstate;
 
 static inline _hashlibstate*
@@ -289,9 +291,56 @@ py_digest_by_name(const char *name)
 #endif
     }
 
+    if (digest == NULL) {
+        PyErr_Format(PyExc_ValueError, "unsupported hash type %s", name);
+        return NULL;
+    }
+
     return digest;
 }
 
+/* Get digest EVP from object
+ *
+ * * string
+ * * _hashopenssl builtin function
+ *
+ * on error returns NULL with exception set.
+ */
+static const EVP_MD*
+py_digest_by_digestmod(PyObject *module, PyObject *digestmod) {
+    const EVP_MD* evp;
+    PyObject *name_obj = NULL;
+    const char *name;
+
+    if (PyUnicode_Check(digestmod)) {
+        name_obj = digestmod;
+    } else {
+        _hashlibstate *state = get_hashlib_state(module);
+        // borrowed ref
+        name_obj = PyDict_GetItem(state->constructs, digestmod);
+    }
+    if (name_obj == NULL) {
+        _hashlibstate *state = get_hashlib_state(module);
+        PyErr_Clear();
+        PyErr_Format(
+            state->unsupported_digestmod_error,
+            "Unsupported digestmod %R", digestmod);
+        return NULL;
+    }
+
+    name = PyUnicode_AsUTF8(name_obj);
+    if (name == NULL) {
+        return NULL;
+    }
+
+    evp = py_digest_by_name(name);
+    if (evp == NULL) {
+        return NULL;
+    }
+
+    return evp;
+}
+
 static EVPobject *
 newEVPobject(PyTypeObject *type)
 {
@@ -829,6 +878,9 @@ EVP_new_impl(PyObject *module, PyObject *name_obj, PyObject *data_obj,
         GET_BUFFER_VIEW_OR_ERROUT(data_obj, &view);
 
     digest = py_digest_by_name(name);
+    if (digest == NULL) {
+        return NULL;
+    }
 
     ret_obj = EVPnew(module, digest,
                      (unsigned char*)view.buf, view.len,
@@ -1124,7 +1176,6 @@ pbkdf2_hmac_impl(PyObject *module, const char *hash_name,
 
     digest = py_digest_by_name(hash_name);
     if (digest == NULL) {
-        PyErr_SetString(PyExc_ValueError, "unsupported hash type");
         goto end;
     }
 
@@ -1328,26 +1379,26 @@ _hashlib.hmac_digest as _hashlib_hmac_singleshot
 
     key: Py_buffer
     msg: Py_buffer
-    digest: str
+    digest: object
 
 Single-shot HMAC.
 [clinic start generated code]*/
 
 static PyObject *
 _hashlib_hmac_singleshot_impl(PyObject *module, Py_buffer *key,
-                              Py_buffer *msg, const char *digest)
-/*[clinic end generated code: output=15658ede5ab98185 input=019dffc571909a46]*/
+                              Py_buffer *msg, PyObject *digest)
+/*[clinic end generated code: output=82f19965d12706ac input=0a0790cc3db45c2e]*/
 {
     unsigned char md[EVP_MAX_MD_SIZE] = {0};
     unsigned int md_len = 0;
     unsigned char *result;
     const EVP_MD *evp;
 
-    evp = py_digest_by_name(digest);
+    evp = py_digest_by_digestmod(module, digest);
     if (evp == NULL) {
-        PyErr_SetString(PyExc_ValueError, "unsupported hash type");
         return NULL;
     }
+
     if (key->len > INT_MAX) {
         PyErr_SetString(PyExc_OverflowError,
                         "key is too long.");
@@ -1385,15 +1436,15 @@ _hashlib.hmac_new
 
     key: Py_buffer
     msg as msg_obj: object(c_default="NULL") = b''
-    digestmod: str(c_default="NULL") = None
+    digestmod: object(c_default="NULL") = None
 
 Return a new hmac object.
 [clinic start generated code]*/
 
 static PyObject *
 _hashlib_hmac_new_impl(PyObject *module, Py_buffer *key, PyObject *msg_obj,
-                       const char *digestmod)
-/*[clinic end generated code: output=9a35673be0cbea1b input=a0878868eb190134]*/
+                       PyObject *digestmod)
+/*[clinic end generated code: output=c20d9e4d9ed6d219 input=5f4071dcc7f34362]*/
 {
     PyTypeObject *type = get_hashlib_state(module)->HMACtype;
     const EVP_MD *digest;
@@ -1407,15 +1458,14 @@ _hashlib_hmac_new_impl(PyObject *module, Py_buffer *key, PyObject *msg_obj,
         return NULL;
     }
 
-    if ((digestmod == NULL) || !strlen(digestmod)) {
+    if (digestmod == NULL) {
         PyErr_SetString(
             PyExc_TypeError, "Missing required parameter 'digestmod'.");
         return NULL;
     }
 
-    digest = py_digest_by_name(digestmod);
-    if (!digest) {
-        PyErr_SetString(PyExc_ValueError, "unknown hash function");
+    digest = py_digest_by_digestmod(module, digestmod);
+    if (digest == NULL) {
         return NULL;
     }
 
@@ -1985,6 +2035,8 @@ hashlib_traverse(PyObject *m, visitproc visit, void *arg)
 #ifdef PY_OPENSSL_HAS_SHAKE
     Py_VISIT(state->EVPXOFtype);
 #endif
+    Py_VISIT(state->constructs);
+    Py_VISIT(state->unsupported_digestmod_error);
     return 0;
 }
 
@@ -1997,6 +2049,8 @@ hashlib_clear(PyObject *m)
 #ifdef PY_OPENSSL_HAS_SHAKE
     Py_CLEAR(state->EVPXOFtype);
 #endif
+    Py_CLEAR(state->constructs);
+    Py_CLEAR(state->unsupported_digestmod_error);
     return 0;
 }
 
@@ -2071,6 +2125,74 @@ hashlib_init_hmactype(PyObject *module)
     return 0;
 }
 
+static int
+hashlib_init_constructors(PyObject *module)
+{
+    /* Create dict from builtin openssl_hash functions to name
+     * {_hashlib.openssl_sha256: "sha256", ...}
+     */
+    PyModuleDef *mdef;
+    PyMethodDef *fdef;
+    PyObject *proxy;
+    PyObject *func, *name_obj;
+    _hashlibstate *state = get_hashlib_state(module);
+
+    mdef = PyModule_GetDef(module);
+    if (mdef == NULL) {
+        return -1;
+    }
+
+    state->constructs = PyDict_New();
+    if (state->constructs == NULL) {
+        return -1;
+    }
+
+    for (fdef = mdef->m_methods; fdef->ml_name != NULL; fdef++) {
+        if (strncmp(fdef->ml_name, "openssl_", 8)) {
+            continue;
+        }
+        name_obj = PyUnicode_FromString(fdef->ml_name + 8);
+        if (name_obj == NULL) {
+            return -1;
+        }
+        func  = PyObject_GetAttrString(module, fdef->ml_name);
+        if (func == NULL) {
+            return -1;
+        }
+        if (PyDict_SetItem(state->constructs, func, name_obj) < 0) {
+            return -1;
+        }
+        Py_DECREF(func);
+        Py_DECREF(name_obj);
+    }
+
+    proxy = PyDictProxy_New(state->constructs);
+    if (proxy == NULL) {
+        return -1;
+    }
+    if (PyModule_AddObjectRef(module, "_constructors", proxy) < 0) {
+        return -1;
+    }
+    return 0;
+}
+
+static int
+hashlib_exception(PyObject *module)
+{
+    _hashlibstate *state = get_hashlib_state(module);
+    state->unsupported_digestmod_error = PyErr_NewException(
+        "_hashlib.UnsupportedDigestmodError", PyExc_ValueError, NULL);
+    if (state->unsupported_digestmod_error == NULL) {
+        return -1;
+    }
+    if (PyModule_AddObjectRef(module, "UnsupportedDigestmodError",
+                              state->unsupported_digestmod_error) < 0) {
+        return -1;
+    }
+    return 0;
+}
+
+
 static PyModuleDef_Slot hashlib_slots[] = {
     /* OpenSSL 1.0.2 and LibreSSL */
     {Py_mod_exec, hashlib_openssl_legacy_init},
@@ -2078,6 +2200,8 @@ static PyModuleDef_Slot hashlib_slots[] = {
     {Py_mod_exec, hashlib_init_evpxoftype},
     {Py_mod_exec, hashlib_init_hmactype},
     {Py_mod_exec, hashlib_md_meth_names},
+    {Py_mod_exec, hashlib_init_constructors},
+    {Py_mod_exec, hashlib_exception},
     {0, NULL}
 };
 
diff --git a/Modules/clinic/_hashopenssl.c.h b/Modules/clinic/_hashopenssl.c.h
index e72b558..fbdff26 100644
--- a/Modules/clinic/_hashopenssl.c.h
+++ b/Modules/clinic/_hashopenssl.c.h
@@ -1081,7 +1081,7 @@ PyDoc_STRVAR(_hashlib_hmac_singleshot__doc__,
 
 static PyObject *
 _hashlib_hmac_singleshot_impl(PyObject *module, Py_buffer *key,
-                              Py_buffer *msg, const char *digest);
+                              Py_buffer *msg, PyObject *digest);
 
 static PyObject *
 _hashlib_hmac_singleshot(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
@@ -1092,7 +1092,7 @@ _hashlib_hmac_singleshot(PyObject *module, PyObject *const *args, Py_ssize_t nar
     PyObject *argsbuf[3];
     Py_buffer key = {NULL, NULL};
     Py_buffer msg = {NULL, NULL};
-    const char *digest;
+    PyObject *digest;
 
     args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 3, 3, 0, argsbuf);
     if (!args) {
@@ -1112,19 +1112,7 @@ _hashlib_hmac_singleshot(PyObject *module, PyObject *const *args, Py_ssize_t nar
         _PyArg_BadArgument("hmac_digest", "argument 'msg'", "contiguous buffer", args[1]);
         goto exit;
     }
-    if (!PyUnicode_Check(args[2])) {
-        _PyArg_BadArgument("hmac_digest", "argument 'digest'", "str", args[2]);
-        goto exit;
-    }
-    Py_ssize_t digest_length;
-    digest = PyUnicode_AsUTF8AndSize(args[2], &digest_length);
-    if (digest == NULL) {
-        goto exit;
-    }
-    if (strlen(digest) != (size_t)digest_length) {
-        PyErr_SetString(PyExc_ValueError, "embedded null character");
-        goto exit;
-    }
+    digest = args[2];
     return_value = _hashlib_hmac_singleshot_impl(module, &key, &msg, digest);
 
 exit:
@@ -1151,7 +1139,7 @@ PyDoc_STRVAR(_hashlib_hmac_new__doc__,
 
 static PyObject *
 _hashlib_hmac_new_impl(PyObject *module, Py_buffer *key, PyObject *msg_obj,
-                       const char *digestmod);
+                       PyObject *digestmod);
 
 static PyObject *
 _hashlib_hmac_new(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames)
@@ -1163,7 +1151,7 @@ _hashlib_hmac_new(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyO
     Py_ssize_t noptargs = nargs + (kwnames ? PyTuple_GET_SIZE(kwnames) : 0) - 1;
     Py_buffer key = {NULL, NULL};
     PyObject *msg_obj = NULL;
-    const char *digestmod = NULL;
+    PyObject *digestmod = NULL;
 
     args = _PyArg_UnpackKeywords(args, nargs, NULL, kwnames, &_parser, 1, 3, 0, argsbuf);
     if (!args) {
@@ -1185,19 +1173,7 @@ _hashlib_hmac_new(PyObject *module, PyObject *const *args, Py_ssize_t nargs, PyO
             goto skip_optional_pos;
         }
     }
-    if (!PyUnicode_Check(args[2])) {
-        _PyArg_BadArgument("hmac_new", "argument 'digestmod'", "str", args[2]);
-        goto exit;
-    }
-    Py_ssize_t digestmod_length;
-    digestmod = PyUnicode_AsUTF8AndSize(args[2], &digestmod_length);
-    if (digestmod == NULL) {
-        goto exit;
-    }
-    if (strlen(digestmod) != (size_t)digestmod_length) {
-        PyErr_SetString(PyExc_ValueError, "embedded null character");
-        goto exit;
-    }
+    digestmod = args[2];
 skip_optional_pos:
     return_value = _hashlib_hmac_new_impl(module, &key, msg_obj, digestmod);
 
@@ -1417,4 +1393,4 @@ _hashlib_compare_digest(PyObject *module, PyObject *const *args, Py_ssize_t narg
 #ifndef _HASHLIB_GET_FIPS_MODE_METHODDEF
     #define _HASHLIB_GET_FIPS_MODE_METHODDEF
 #endif /* !defined(_HASHLIB_GET_FIPS_MODE_METHODDEF) */
-/*[clinic end generated code: output=2bbd6159493f44ea input=a9049054013a1b77]*/
+/*[clinic end generated code: output=980087de1b03ad42 input=a9049054013a1b77]*/