@@ -215,6 +215,25 @@ purposes.
       :data:`VERIFY_X509_STRICT` in its default verify flags.
 
 
+Signature algorithms
+^^^^^^^^^^^^^^^^^^^^
+
+.. function:: get_sigalgs()
+
+   Return a list of available TLS signature algorithm names used
+   by servers to complete the TLS handshake or clients requesting
+   certificate-based authentication. For example::
+
+       >>> ssl.get_sigalgs()  # doctest: +SKIP
+       ['ecdsa_secp256r1_sha256', 'ecdsa_secp384r1_sha384', ...]
+
+   These names can be used when building string values to pass to the
+   :meth:`SSLContext.set_client_sigalgs` and
+   :meth:`SSLContext.set_server_sigalgs` methods.
+
+   .. versionadded:: next
+
+
 Exceptions
 ^^^^^^^^^^
 
@@ -1297,6 +1316,22 @@ SSL sockets also have the following additional methods and attributes:
 
    .. versionadded:: next
 
+.. method:: SSLSocket.client_sigalg()
+
+   Return the signature algorithm used for performing certificate-based client
+   authentication on this connection, or ``None`` if no connection has been
+   established or client authentication didn't occur.
+
+   .. versionadded:: next
+
+.. method:: SSLSocket.server_sigalg()
+
+   Return the signature algorithm used by the server to complete the TLS
+   handshake on this connection, or ``None`` if no connection has been
+   established or the cipher suite has no signature.
+
+   .. versionadded:: next
+
 .. method:: SSLSocket.compression()
 
    Return the compression algorithm being used as a string, or ``None``
@@ -1725,6 +1760,35 @@ to speed up repeated connections from the same clients.
 
    .. versionadded:: next
 
+.. method:: SSLContext.set_client_sigalgs(sigalgs)
+
+   Set the signature algorithms allowed for certificate-based client
+   authentication. It should be a string in the `OpenSSL client sigalgs
+   list format
+   <https://docs.openssl.org/master/man3/SSL_CTX_set1_client_sigalgs_list/>`_.
+
+   .. note::
+
+      When connected, the :meth:`SSLSocket.client_sigalg` method of SSL
+      sockets will return the signature algorithm used for performing
+      certificate-based client authentication on that connection.
+
+   .. versionadded:: next
+
+.. method:: SSLContext.set_server_sigalgs(sigalgs)
+
+   Set the signature algorithms allowed for the server to complete the TLS
+   handshake. It should be a string in the `OpenSSL sigalgs list format
+   <https://docs.openssl.org/master/man3/SSL_CTX_set1_sigalgs_list/>`_.
+
+   .. note::
+
+      When connected, the :meth:`SSLSocket.server_sigalg` method of SSL
+      sockets will return the signature algorithm used by the server to
+      complete the TLS handshake on that connection.
+
+   .. versionadded:: next
+
 .. method:: SSLContext.set_alpn_protocols(protocols)
 
    Specify which protocols the socket should advertise during the SSL/TLS
@@ -2876,7 +2940,7 @@ of TLS/SSL. Some new TLS 1.3 features are not yet available.
   process certificate requests while they send or receive application data
   from the server.
 - TLS 1.3 features like early data, deferred TLS client cert request,
-  signature algorithm configuration, and rekeying are not supported yet.
+  and rekeying are not supported yet.
 
 
 .. seealso::
 
@@ -442,6 +442,23 @@ ssl
   connection is made.
   (Contributed by Ron Frederick in :gh:`137197`.)
 
+* Added new methods for managing signature algorithms:
+
+  * :func:`ssl.get_sigalgs` returns a list of all available TLS signature
+    algorithms. This call requires OpenSSL 3.4 or later.
+  * :meth:`ssl.SSLContext.set_client_sigalgs` sets the signature algorithms
+    allowed for certificate-based client authentication.
+  * :meth:`ssl.SSLContext.set_server_sigalgs` sets the signature algorithms
+    allowed for the server to complete the TLS handshake.
+  * :meth:`ssl.SSLSocket.client_sigalg` returns the signature algorithm
+    selected for client authentication on the current connection. This call
+    requires OpenSSL 3.5 or later.
+  * :meth:`ssl.SSLSocket.server_sigalg` returns the signature algorithm
+    selected for the server to complete the TLS handshake on the current
+    connection. This call requires OpenSSL 3.5 or later.
+
+   (Contributed by Ron Frederick in :gh:`138252`.)
+
 
 tarfile
 -------
 
@@ -13,6 +13,9 @@
 
 Functions:
 
+  get_sigalgs          -- return a list of all available TLS signature
+                          algorithms (requires OpenSSL 3.4 or later)
+
   cert_time_to_seconds -- convert time string used for certificate
                           notBefore and notAfter functions to integer
                           seconds past the Epoch (the time values
@@ -112,6 +115,7 @@
 except ImportError:
     # RAND_egd is not supported on some platforms
     pass
+from _ssl import get_sigalgs
 
 
 from _ssl import (
@@ -935,6 +939,14 @@ def group(self):
         """Return the currently selected key agreement group name."""
         return self._sslobj.group()
 
+    def client_sigalg(self):
+        """Return the selected client authentication signature algorithm."""
+        return self._sslobj.client_sigalg()
+
+    def server_sigalg(self):
+        """Return the selected server handshake signature algorithm."""
+        return self._sslobj.server_sigalg()
+
     def shared_ciphers(self):
         """Return a list of ciphers shared by the client during the handshake or
         None if this is not a valid server connection.
@@ -1222,6 +1234,22 @@ def group(self):
         else:
             return self._sslobj.group()
 
+    @_sslcopydoc
+    def client_sigalg(self):
+        self._checkClosed()
+        if self._sslobj is None:
+            return None
+        else:
+            return self._sslobj.client_sigalg()
+
+    @_sslcopydoc
+    def server_sigalg(self):
+        self._checkClosed()
+        if self._sslobj is None:
+            return None
+        else:
+            return self._sslobj.server_sigalg()
+
     @_sslcopydoc
     def shared_ciphers(self):
         self._checkClosed()
 
@@ -51,6 +51,10 @@
 CAN_GET_SELECTED_OPENSSL_GROUP = ssl.OPENSSL_VERSION_INFO >= (3, 2)
 CAN_IGNORE_UNKNOWN_OPENSSL_GROUPS = ssl.OPENSSL_VERSION_INFO >= (3, 3)
 CAN_GET_AVAILABLE_OPENSSL_GROUPS = ssl.OPENSSL_VERSION_INFO >= (3, 5)
+CAN_GET_AVAILABLE_OPENSSL_SIGALGS = ssl.OPENSSL_VERSION_INFO >= (3, 4)
+CAN_SET_CLIENT_SIGALGS = "AWS-LC" not in ssl.OPENSSL_VERSION
+CAN_IGNORE_UNKNOWN_OPENSSL_SIGALGS = ssl.OPENSSL_VERSION_INFO >= (3, 3)
+CAN_GET_SELECTED_OPENSSL_SIGALG = ssl.OPENSSL_VERSION_INFO >= (3, 5)
 PY_SSL_DEFAULT_CIPHERS = sysconfig.get_config_var('PY_SSL_DEFAULT_CIPHERS')
 
 PROTOCOL_TO_TLS_VERSION = {}
@@ -294,7 +298,8 @@ def test_wrap_socket(sock, *,
 USE_SAME_TEST_CONTEXT = False
 _TEST_CONTEXT = None
 
-def testing_context(server_cert=SIGNED_CERTFILE, *, server_chain=True):
+def testing_context(server_cert=SIGNED_CERTFILE, *, server_chain=True,
+                    client_cert=None):
     """Create context
 
     client_context, server_context, hostname = testing_context()
@@ -321,6 +326,10 @@ def testing_context(server_cert=SIGNED_CERTFILE, *, server_chain=True):
     if server_chain:
         server_context.load_verify_locations(SIGNING_CA)
 
+    if client_cert:
+        client_context.load_cert_chain(client_cert)
+        server_context.verify_mode = ssl.CERT_REQUIRED
+
     if USE_SAME_TEST_CONTEXT:
         if _TEST_CONTEXT is not None:
             _TEST_CONTEXT = client_context, server_context, hostname
@@ -990,6 +999,37 @@ def test_get_groups(self):
         self.assertNotIn('P-256', ctx.get_groups())
         self.assertIn('P-256', ctx.get_groups(include_aliases=True))
 
+    @unittest.skipUnless(CAN_GET_AVAILABLE_OPENSSL_SIGALGS,
+                         "SSL library doesn't support getting sigalgs")
+    def test_get_sigalgs(self):
+        self.assertIn('rsa_pss_rsae_sha256', ssl.get_sigalgs())
+
+    @unittest.skipUnless(CAN_SET_CLIENT_SIGALGS,
+                         "SSL library doesn't support setting client sigalgs")
+    def test_set_client_sigalgs(self):
+        ctx = ssl.create_default_context()
+
+        self.assertIsNone(ctx.set_client_sigalgs('rsa_pss_rsae_sha256'))
+
+        self.assertRaises(ssl.SSLError, ctx.set_client_sigalgs,
+                          'rsa_pss_rsae_sha256:foo')
+
+        # Ignoring unknown sigalgs is only supported since OpenSSL 3.3.
+        if CAN_IGNORE_UNKNOWN_OPENSSL_SIGALGS:
+            self.assertIsNone(ctx.set_client_sigalgs('rsa_pss_rsae_sha256:?foo'))
+
+    def test_set_server_sigalgs(self):
+        ctx = ssl.create_default_context()
+
+        self.assertIsNone(ctx.set_server_sigalgs('rsa_pss_rsae_sha256'))
+
+        self.assertRaises(ssl.SSLError, ctx.set_server_sigalgs,
+                          'rsa_pss_rsae_sha256:foo')
+
+        # Ignoring unknown sigalgs is only supported since OpenSSL 3.3.
+        if CAN_IGNORE_UNKNOWN_OPENSSL_SIGALGS:
+            self.assertIsNone(ctx.set_server_sigalgs('rsa_pss_rsae_sha256:?foo'))
+
     def test_options(self):
         # Test default SSLContext options
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLS_CLIENT)
@@ -2814,6 +2854,9 @@ def server_params_test(client_context, server_context, indata=b"FOO\n",
             })
             if CAN_GET_SELECTED_OPENSSL_GROUP:
                 stats.update({'group': s.group()})
+            if CAN_GET_SELECTED_OPENSSL_SIGALG:
+                stats.update({'client_sigalg': s.client_sigalg()})
+                stats.update({'server_sigalg': s.server_sigalg()})
             s.close()
         stats['server_alpn_protocols'] = server.selected_alpn_protocols
         stats['server_shared_ciphers'] = server.shared_ciphers
@@ -4273,6 +4316,71 @@ def test_groups(self):
                                chatty=True, connectionchatty=True,
                                sni_name=hostname)
 
+    @unittest.skipUnless(CAN_SET_CLIENT_SIGALGS,
+                         "SSL library doesn't support setting client sigalgs")
+    def test_client_sigalgs(self):
+        # no mutual auth, so cient_sigalg should be None
+        client_context, server_context, hostname = testing_context()
+        stats = server_params_test(client_context, server_context,
+                                   chatty=True, connectionchatty=True,
+                                   sni_name=hostname)
+        if CAN_GET_SELECTED_OPENSSL_SIGALG:
+            self.assertIsNone(stats['client_sigalg'])
+
+        # server auto, client rsa_pss_rsae_sha384
+        sigalg = "rsa_pss_rsae_sha384"
+        client_context, server_context, hostname = \
+            testing_context(client_cert=SIGNED_CERTFILE)
+        client_context.set_client_sigalgs(sigalg)
+        stats = server_params_test(client_context, server_context,
+                                   chatty=True, connectionchatty=True,
+                                   sni_name=hostname)
+        if CAN_GET_SELECTED_OPENSSL_SIGALG:
+            self.assertEqual(stats['client_sigalg'], sigalg)
+
+    @unittest.skipUnless(CAN_SET_CLIENT_SIGALGS,
+                         "SSL library doesn't support setting client sigalgs")
+    def test_client_sigalgs_mismatch(self):
+        client_context, server_context, hostname = \
+            testing_context(client_cert=SIGNED_CERTFILE)
+        client_context.set_client_sigalgs("rsa_pss_rsae_sha256")
+        server_context.set_client_sigalgs("rsa_pss_rsae_sha384")
+
+        # Some systems return ConnectionResetError on handshake failures
+        with self.assertRaises((ssl.SSLError, ConnectionResetError)):
+            server_params_test(client_context, server_context,
+                               chatty=True, connectionchatty=True,
+                               sni_name=hostname)
+
+    def test_server_sigalgs(self):
+        # server rsa_pss_rsae_sha384, client auto
+        sigalg = "rsa_pss_rsae_sha384"
+        client_context, server_context, hostname = testing_context()
+        server_context.set_server_sigalgs(sigalg)
+        stats = server_params_test(client_context, server_context,
+                                   chatty=True, connectionchatty=True,
+                                   sni_name=hostname)
+        if CAN_GET_SELECTED_OPENSSL_SIGALG:
+            self.assertEqual(stats['server_sigalg'], sigalg)
+
+        # server auto, client rsa_pss_rsae_sha384
+        client_context, server_context, hostname = testing_context()
+        client_context.set_server_sigalgs(sigalg)
+        stats = server_params_test(client_context, server_context,
+                                   chatty=True, connectionchatty=True,
+                                   sni_name=hostname)
+        if CAN_GET_SELECTED_OPENSSL_SIGALG:
+            self.assertEqual(stats['server_sigalg'], sigalg)
+
+    def test_server_sigalgs_mismatch(self):
+        client_context, server_context, hostname = testing_context()
+        client_context.set_server_sigalgs("rsa_pss_rsae_sha256")
+        server_context.set_server_sigalgs("rsa_pss_rsae_sha384")
+        with self.assertRaises(ssl.SSLError):
+            server_params_test(client_context, server_context,
+                               chatty=True, connectionchatty=True,
+                               sni_name=hostname)
+
     def test_selected_alpn_protocol(self):
         # selected_alpn_protocol() is None unless ALPN is used.
         client_context, server_context, hostname = testing_context()
 
@@ -0,0 +1,4 @@
+:mod:`ssl`: :class:`~ssl.SSLContext` objects can now set client and server
+TLS signature algorithms. If Python has been built with OpenSSL 3.5 or later,
+:class:`~ssl.SSLSocket` objects can return the signature algorithms selected
+on a connection.