diff --git a/pyproject.toml b/pyproject.toml
index 430c563f..4512943c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -26,7 +26,7 @@ dependencies = [
   "pydantic>=2.3.0,!=1.7.*,!=1.8.*,!=1.9.*",
   "pyOpenSSL>=22.0.0",
   "pytz>=2019.3",
-  "signxml>=3.1.0",
+  "signxml>=4.0.0",
 ]
 requires-python = ">=3.8, <3.11"
 authors = [
diff --git a/requirements.in b/requirements.in
index e7cbcac2..d900e90e 100644
--- a/requirements.in
+++ b/requirements.in
@@ -18,4 +18,4 @@ marshmallow==3.22.0
 pydantic==2.10.3
 pyOpenSSL==24.2.1
 pytz==2024.2
-signxml==3.2.2
+signxml==4.0.3
diff --git a/requirements.txt b/requirements.txt
index 0397d4cb..dd5cf8cc 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -64,9 +64,7 @@ pydantic==2.10.3
 pydantic-core==2.27.1
     # via pydantic
 pyopenssl==24.2.1
-    # via
-    #   -r requirements.in
-    #   signxml
+    # via -r requirements.in
 pytz==2024.2
     # via -r requirements.in
 referencing==0.35.1
@@ -77,7 +75,7 @@ rpds-py==0.19.0
     # via
     #   jsonschema
     #   referencing
-signxml==3.2.2
+signxml==4.0.3
     # via -r requirements.in
 sqlparse==0.5.0
     # via django
diff --git a/src/cl_sii/libs/crypto_utils.py b/src/cl_sii/libs/crypto_utils.py
index 776cd8a4..cd20233d 100644
--- a/src/cl_sii/libs/crypto_utils.py
+++ b/src/cl_sii/libs/crypto_utils.py
@@ -157,8 +157,7 @@ def add_pem_cert_header_footer(pem_cert: bytes) -> bytes:
     """
     pem_value_str = pem_cert.decode('ascii')
     # note: it would be great if 'add_pem_header' did not forcefully convert bytes to str.
-    mod_pem_value_str = signxml.util.add_pem_header(pem_value_str)
-    mod_pem_value: bytes = mod_pem_value_str.encode('ascii')
+    mod_pem_value: bytes = signxml.util.add_pem_header(pem_value_str)
     return mod_pem_value
 
 
diff --git a/src/cl_sii/libs/xml_utils.py b/src/cl_sii/libs/xml_utils.py
index da4be0fd..381ebc51 100644
--- a/src/cl_sii/libs/xml_utils.py
+++ b/src/cl_sii/libs/xml_utils.py
@@ -440,14 +440,8 @@ def verify_xml_signature(
         )
 
     if isinstance(trusted_x509_cert, crypto_utils._X509CertOpenSsl):
-        trusted_x509_cert_open_ssl = trusted_x509_cert
-    elif isinstance(trusted_x509_cert, crypto_utils.X509Cert):
-        trusted_x509_cert_open_ssl = crypto_utils._X509CertOpenSsl.from_cryptography(
-            trusted_x509_cert
-        )
-    elif trusted_x509_cert is None:
-        trusted_x509_cert_open_ssl = None
-    else:
+        trusted_x509_cert = trusted_x509_cert.to_cryptography()
+    elif not (isinstance(trusted_x509_cert, crypto_utils.X509Cert) or trusted_x509_cert is None):
         # A 'crypto_utils._X509CertOpenSsl' is ok but we prefer 'crypto_utils.X509Cert'.
         raise TypeError("'trusted_x509_cert' must be a 'crypto_utils.X509Cert' instance, or None.")
 
@@ -481,10 +475,10 @@ def verify_xml_signature(
         #   https://github.com/XML-Security/signxml/commit/ef15da8dbb904f1dedfdd210ae3e0df5da535612
         result = xml_verifier.verify(
             data=tmp_bytes,
-            require_x509=True,
-            x509_cert=trusted_x509_cert_open_ssl,
-            ignore_ambiguous_key_info=True,
+            x509_cert=trusted_x509_cert,
             expect_config=signxml.verifier.SignatureConfiguration(
+                require_x509=True,
+                ignore_ambiguous_key_info=True,
                 signature_methods=frozenset([signxml.algorithms.SignatureMethod.RSA_SHA1]),
                 digest_algorithms=frozenset([signxml.algorithms.DigestAlgorithm.SHA1]),
             ),
diff --git a/src/tests/test_data/sii-dte/DTE--76354771-K--33--170--cleaned-mod-replaced-cert.xml b/src/tests/test_data/sii-dte/DTE--76354771-K--33--170--cleaned-mod-replaced-cert.xml
index ded4f5c2..3abb9f87 100644
--- a/src/tests/test_data/sii-dte/DTE--76354771-K--33--170--cleaned-mod-replaced-cert.xml
+++ b/src/tests/test_data/sii-dte/DTE--76354771-K--33--170--cleaned-mod-replaced-cert.xml
@@ -70,9 +70,11 @@
 </Reference>
 </SignedInfo>
 <SignatureValue>
-fsYP5p/lNfofAz8POShrJjqXdBTNNtvv4/TWCxbvwTIAXr7BLrlvX3C/Hpfo4viqaxSu1OGFgPnk
-ddDIFwj/ZsVdbdB+MhpKkyha83RxhJpYBVBY3c+y9J6oMfdIdMAYXhEkFw8w63KHyhdf2E9dnbKi
-wqSxDcYjTT6vXsLPrZk=
+wwOMQuFqa6c5gzYSJ5PWfo0OiAf+yNcJK6wx4xJ3VNehlAcMrUB2q+rK/DDhCvjxAoX4NxBACiFD
+MrTMIfvxrwXjLd1oX37lSFOtsWX6JxL0SV+tLF7qvWCu1Yzw8ypUf7GDkbymJkoTYDF9JFF8kYU4
+FdU2wttiwne9XH8QFHgXsocKP/aygwiOeGqiNX9o/O5XS2GWpt+KM20jrvtYn7UFMED/3aPacCb1
+GABizr8mlVEZggZgJunMDChpFQyEigSXMK5I737Ac8D2bw7WB47Wj1WBL3sCFRDlXUXtnMvChBVp
+0HRUXYuKHyfpCzqIBXygYrIZexxXgOSnKu/yGg==
 </SignatureValue>
 <KeyInfo>
 <KeyValue>
@@ -87,50 +89,35 @@ Uavs/9J+gR9BBMs/eYE=
 </KeyValue>
 <X509Data>
 <X509Certificate>
-MIIIDTCCBvWgAwIBAgIQXD9eCvh/44P1ET5RI1LuJjANBgkqhkiG9w0BAQsFADBU
-MQswCQYDVQQGEwJVUzEeMBwGA1UEChMVR29vZ2xlIFRydXN0IFNlcnZpY2VzMSUw
-IwYDVQQDExxHb29nbGUgSW50ZXJuZXQgQXV0aG9yaXR5IEczMB4XDTE5MDMyNjEz
-NDA0MFoXDTE5MDYxODEzMjQwMFowZjELMAkGA1UEBhMCVVMxEzARBgNVBAgMCkNh
-bGlmb3JuaWExFjAUBgNVBAcMDU1vdW50YWluIFZpZXcxEzARBgNVBAoMCkdvb2ds
-ZSBMTEMxFTATBgNVBAMMDCouZ29vZ2xlLmNvbTBZMBMGByqGSM49AgEGCCqGSM49
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-BBYEFM8C2hpNgJL/BEX/yzeB408dhba2MAwGA1UdEwEB/wQCMAAwHwYDVR0jBBgw
-FoAUd8K4UJpndnaxLcKG0IOgfqZ+ukswIQYDVR0gBBowGDAMBgorBgEEAdZ5AgUD
-MAgGBmeBDAECAjAxBgNVHR8EKjAoMCagJKAihiBodHRwOi8vY3JsLnBraS5nb29n
-L0dUU0dJQUczLmNybDANBgkqhkiG9w0BAQsFAAOCAQEAF9PM41ShwCbhtJG7tj2y
-ZvF2sHbQ5YuZrMfJc6eeCG+nCKm1U5iJzXnXctFGvfJnUCZpj9YrfwDswdEddWyZ
-IG6m6wONF3ZiQifQrcDi0oDA+0BwjEuzYGCGkbfE+Xxb30bVEyDRe51DpJf+cqsb
-+DW2pYdikbdrPem5/hwdNerc7nqrQOJ93sqwbVNGktuyJsTOGNKkSwSaejxdN7yl
-g5aa4CJsE94gy4+mCywWjnnsjcLGJM3RBUxDdAdTGMldU/r33HCUCXl33Qxc4nvP
-MlE9LyFOTIJoajWcpGOsbKWiL3Zr19DKNBSn4Xof0onbtCH7dbpyMwP8XcA2O1dA
-ow==
+MIIGVDCCBTygAwIBAgIKMUWmvgAAAAjUHTANBgkqhkiG9w0BAQUFADCB0jELMAkGA1UEBhMCQ0wx
+HTAbBgNVBAgTFFJlZ2lvbiBNZXRyb3BvbGl0YW5hMREwDwYDVQQHEwhTYW50aWFnbzEUMBIGA1UE
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+MS8wLQYDVQQKEyZTZXJ2aWNpb3MgQm9uaWxsYSB5IExvcGV6IHkgQ2lhLiBMdGRhLjEkMCIGA1UE
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+qXR4lHGl8d/Yq4yoJzDD3Ceez8qenY3JwGUhPzw9oDpg4mXWvxQDXSFeW/u/BgdadhfGnpwx61Un
++/fU24ZgU1dDJ4GKj5oIPHUIjmoSBhnstEhIr6GJWSTcDKTyzRdqBlaVhenH2Qs6Mw6FrOvRPuud
+B7lo1+OgxMb/Gjyu6XnEaPu7Vq4XlLYMoCD2xrV7WEADaDTm7KcNLczVAYqWSF1WUqYSxmPoQDFY
++kMTThJyCXBlE0NADInrkwWgLLygkKI7zXkwaw==
 </X509Certificate>
 </X509Data>
 </KeyInfo>
diff --git a/src/tests/test_libs_xml_utils.py b/src/tests/test_libs_xml_utils.py
index e30c7f45..a503f2d5 100644
--- a/src/tests/test_libs_xml_utils.py
+++ b/src/tests/test_libs_xml_utils.py
@@ -1,9 +1,15 @@
+import datetime
 import io
 import unittest
+from typing import Any
+from unittest import mock
 
 import lxml.etree
+import signxml
 
-from cl_sii.libs.crypto_utils import load_pem_x509_cert
+from cl_sii.base.constants import SII_OFFICIAL_TZ
+from cl_sii.libs.crypto_utils import _X509CertOpenSsl, load_pem_x509_cert
+from cl_sii.libs.tz_utils import convert_naive_dt_to_tz_aware
 from cl_sii.libs.xml_utils import (  # noqa: F401
     XmlElement,
     XmlFeatureForbidden,
@@ -185,6 +191,28 @@ def test_ok_external_trusted_cert(self) -> None:
         signature_xml_bytes = f.getvalue()
         self.assertEqual(signature_xml_bytes, self.with_valid_signature_signature_xml)
 
+    def test_ok_external_trusted_open_ssl_cert_with_signature(self) -> None:
+        xml_doc = parse_untrusted_xml(self.with_valid_signature)
+        cert = load_pem_x509_cert(self.xml_doc_cert_pem_bytes)
+
+        open_ssl_cert = _X509CertOpenSsl.from_cryptography(cert)
+
+        signed_data, signed_xml, signature_xml = verify_xml_signature(
+            xml_doc, trusted_x509_cert=open_ssl_cert
+        )
+
+        self.assertEqual(signed_data, self.with_valid_signature_signed_data)
+
+        f = io.BytesIO()
+        write_xml_doc(signed_xml, f)
+        signed_xml_bytes = f.getvalue()
+        self.assertEqual(signed_xml_bytes, self.with_valid_signature_signed_xml)
+
+        f = io.BytesIO()
+        write_xml_doc(signature_xml, f)
+        signature_xml_bytes = f.getvalue()
+        self.assertEqual(signature_xml_bytes, self.with_valid_signature_signature_xml)
+
     def test_ok_cert_in_signature(self) -> None:
         # TODO: implement!
 
@@ -221,7 +249,7 @@ def test_fail_verify_with_other_cert(self) -> None:
             verify_xml_signature(xml_doc, trusted_x509_cert=cert)
         self.assertEqual(
             cm.exception.args,
-            ("Signature verification failed: wrong signature length",),
+            ("Signature verification failed: ",),
         )
 
     def test_bad_cert_included(self) -> None:
@@ -244,26 +272,58 @@ def test_bad_cert_included(self) -> None:
         )
 
     def test_fail_replaced_cert(self) -> None:
+        """
+        Tests that the signature verification fails
+        when the certificate is not the one that was used to sign the document.
+        """
         xml_doc = parse_untrusted_xml(self.with_replaced_cert)
-        cert = load_pem_x509_cert(self.any_x509_cert_pem_file)
+        cert = load_pem_x509_cert(self.xml_doc_cert_pem_bytes)
 
         with self.assertRaises(XmlSignatureInvalid) as cm:
             verify_xml_signature(xml_doc, trusted_x509_cert=cert)
         self.assertEqual(
             cm.exception.args,
-            ("Signature verification failed: []",),
+            ("Signature verification failed: ",),
         )
 
     def test_fail_included_cert_not_from_a_known_ca(self) -> None:
         xml_doc = parse_untrusted_xml(self.with_valid_signature)
+        xml_doc_signature_timestamp = convert_naive_dt_to_tz_aware(
+            dt=datetime.datetime.fromisoformat('2019-04-01T01:36:40'),  # From XML doc’s <TmstFirma>
+            tz=SII_OFFICIAL_TZ,
+        )
+
+        def _get_cert_chain_verifier(
+            *args: Any, **kwargs: Any
+        ) -> signxml.util.X509CertChainVerifier:
+            # The default signature verification time is the current time (see
+            # https://cryptography.io/en/43.0.3/x509/verification/#cryptography.x509.verification.PolicyBuilder.time
+            # ), but that causes verification to fail with the message
+            # “validation failed: cert is not valid at validation time”.
+            # To avoid that, we set the verification time to the time of the signature.
+            return signxml.util.X509CertChainVerifier(
+                ca_pem_file=kwargs['ca_pem_file'], verification_time=xml_doc_signature_timestamp
+            )
 
         # Without cert: fails because the issuer of the cert in the signature is not a known CA.
-        with self.assertRaises(XmlSignatureInvalidCertificate) as cm:
+        with self.assertRaises(XmlSignatureInvalidCertificate) as cm, mock.patch.object(
+            signxml.verifier.XMLVerifier,
+            'get_cert_chain_verifier',
+            side_effect=_get_cert_chain_verifier,
+        ) as mock_get_cert_chain_verifier:
             verify_xml_signature(xml_doc, trusted_x509_cert=None)
         self.assertEqual(
             cm.exception.args,
-            ('unable to get local issuer certificate',),
+            # According to some test cases from https://x509-limbo.com/, OpenSSL’s error message
+            # “unable to get local issuer certificate” seems to be equivalent to PyCA Cryptography’s
+            # error message below:
+            (
+                'validation failed:'
+                ' candidates exhausted:'
+                ' all candidates exhausted with no interior errors',
+            ),
         )
+        mock_get_cert_chain_verifier.assert_called_once_with(ca_pem_file=None)
 
     def test_fail_signed_data_modified(self) -> None:
         xml_doc = parse_untrusted_xml(self.with_signature_and_modified)