diff --git a/sphinx/builders/html.py b/sphinx/builders/html.py

index 8b63352..1a95c77 100644

--- a/sphinx/builders/html.py

+++ b/sphinx/builders/html.py

@@ -14,7 +14,6 @@ import posixpath

 import re

 import sys

 import warnings

-from hashlib import md5

 from os import path

 import docutils

@@ -40,7 +39,7 @@ from sphinx.highlighting import PygmentsBridge

 from sphinx.locale import _, __, l_

 from sphinx.search import js_index

 from sphinx.theming import HTMLThemeFactory

-from sphinx.util import jsonimpl, logging, status_iterator

+from sphinx.util import jsonimpl, logging, status_iterator, md5

 from sphinx.util.console import bold, darkgreen  # type: ignore

 from sphinx.util.docutils import is_html5_writer_available, new_document

 from sphinx.util.fileutil import copy_asset

diff --git a/sphinx/ext/graphviz.py b/sphinx/ext/graphviz.py

index 08707b7..9d53a0e 100644

--- a/sphinx/ext/graphviz.py

+++ b/sphinx/ext/graphviz.py

@@ -13,7 +13,6 @@

 import codecs

 import posixpath

 import re

-from hashlib import sha1

 from os import path

 from subprocess import Popen, PIPE

@@ -25,7 +24,7 @@ from six import text_type

 import sphinx

 from sphinx.errors import SphinxError

 from sphinx.locale import _, __

-from sphinx.util import logging

+from sphinx.util import logging, sha1

 from sphinx.util.i18n import search_image_for_language

 from sphinx.util.osutil import ensuredir, ENOENT, EPIPE, EINVAL

diff --git a/sphinx/ext/imgmath.py b/sphinx/ext/imgmath.py

index 5f9d7a1..23f89ed 100644

--- a/sphinx/ext/imgmath.py

+++ b/sphinx/ext/imgmath.py

@@ -14,7 +14,6 @@ import posixpath

 import re

 import shutil

 import tempfile

-from hashlib import sha1

 from os import path

 from subprocess import Popen, PIPE

@@ -26,7 +25,7 @@ from sphinx.errors import SphinxError, ExtensionError

 from sphinx.ext.mathbase import get_node_equation_number

 from sphinx.ext.mathbase import setup_math as mathbase_setup, wrap_displaymath

 from sphinx.locale import _

-from sphinx.util import logging

+from sphinx.util import logging, sha1

 from sphinx.util.osutil import ensuredir, ENOENT, cd

 from sphinx.util.png import read_png_depth, write_png_depth

 from sphinx.util.pycompat import sys_encoding

diff --git a/sphinx/ext/inheritance_diagram.py b/sphinx/ext/inheritance_diagram.py

index 14593ac..9576d07 100644

--- a/sphinx/ext/inheritance_diagram.py

+++ b/sphinx/ext/inheritance_diagram.py

@@ -39,7 +39,6 @@ r"""

 import inspect

 import re

 import sys

-from hashlib import md5

 from docutils import nodes

 from docutils.parsers.rst import Directive, directives

@@ -50,7 +49,7 @@ import sphinx

 from sphinx.ext.graphviz import render_dot_html, render_dot_latex, \

     render_dot_texinfo, figure_wrapper

 from sphinx.pycode import ModuleAnalyzer

-from sphinx.util import force_decode

+from sphinx.util import force_decode, md5

 if False:

     # For type annotation

diff --git a/sphinx/transforms/post_transforms/images.py b/sphinx/transforms/post_transforms/images.py

index 6dd135e..d1c50bd 100644

--- a/sphinx/transforms/post_transforms/images.py

+++ b/sphinx/transforms/post_transforms/images.py

@@ -10,14 +10,13 @@

 """

 import os

-from hashlib import sha1

 from math import ceil

 from docutils import nodes

 from six import text_type

 from sphinx.transforms import SphinxTransform

-from sphinx.util import epoch_to_rfc1123, rfc1123_to_epoch

+from sphinx.util import epoch_to_rfc1123, rfc1123_to_epoch, sha1

 from sphinx.util import logging, requests

 from sphinx.util.images import guess_mimetype, get_image_extension, parse_data_uri

 from sphinx.util.osutil import ensuredir, movefile

diff --git a/sphinx/util/__init__.py b/sphinx/util/__init__.py

index dda3fb0..9c1c441 100644

--- a/sphinx/util/__init__.py

+++ b/sphinx/util/__init__.py

@@ -11,6 +11,7 @@

 from __future__ import absolute_import

 import fnmatch

+import hashlib

 import os

 import posixpath

 import re

@@ -164,6 +165,32 @@ class FilenameUniqDict(dict):

         # type: (Set[unicode]) -> None

         self._existing = state

+def md5(data=b'', **kwargs):

+    """Wrapper around hashlib.md5

+    Attempt call with 'usedforsecurity=False' if we get a ValueError, which happens when

+    OpenSSL FIPS mode is enabled:

+    ValueError: error:060800A3:digital envelope routines:EVP_DigestInit_ex:disabled for fips

+    See: https://github.com/sphinx-doc/sphinx/issues/7611

+    """

+

+    try:

+        return hashlib.md5(data, **kwargs)  # type: ignore

+    except ValueError:

+        return hashlib.md5(data, **kwargs, usedforsecurity=False)  # type: ignore

+

+

+def sha1(data=b'', **kwargs):

+    """Wrapper around hashlib.sha1

+    Attempt call with 'usedforsecurity=False' if we get a ValueError

+    See: https://github.com/sphinx-doc/sphinx/issues/7611

+    """

+

+    try:

+        return hashlib.sha1(data, **kwargs)  # type: ignore

+    except ValueError:

+        return hashlib.sha1(data, **kwargs, usedforsecurity=False)  # type: ignore

+

+

 def copy_static_entry(source, targetdir, builder, context={},

                       exclude_matchers=(), level=0):