diff --git a/docs/development/test-vectors.rst b/docs/development/test-vectors.rst
index 15c3be9..5ab1d44 100644
--- a/docs/development/test-vectors.rst
+++ b/docs/development/test-vectors.rst
@@ -148,6 +148,9 @@
   certificate containing a subject alternative name extension with the
   following general names: ``rfc822Name``, ``dNSName``, ``iPAddress``,
   ``directoryName``, and ``uniformResourceIdentifier``.
+* ``san_empty_hostname.pem`` - An RSA 2048 bit self-signed certificate
+  containing a subject alternative extension with an empty ``dNSName``
+  general name.
 * ``san_other_name.pem`` - An RSA 2048 bit self-signed certificate containing
   a subject alternative name extension with the ``otherName`` general name.
 * ``san_registered_id.pem`` - An RSA 1024 bit certificate containing a
@@ -193,6 +196,9 @@
   containing an authority information access extension with an OCSP entry.
 * ``aia_ca_issuers.pem`` - An RSA 2048 bit self-signed certificate
   containing an authority information access extension with a CA issuers entry.
+* ``cdp_empty_hostname.pem`` - An RSA 2048 bit self-signed certificate
+  containing a CRL distribution point extension with ``fullName`` URI without
+  a hostname.
 * ``cdp_fullname_reasons_crl_issuer.pem`` - An RSA 1024 bit certificate
   containing a CRL distribution points extension with ``fullName``,
   ``cRLIssuer``, and ``reasons`` data.
diff --git a/src/cryptography/hazmat/backends/openssl/x509.py b/src/cryptography/hazmat/backends/openssl/x509.py
index 80f32e2..fd32bd0 100644
--- a/src/cryptography/hazmat/backends/openssl/x509.py
+++ b/src/cryptography/hazmat/backends/openssl/x509.py
@@ -64,7 +64,9 @@
 def _decode_general_name(backend, gn):
     if gn.type == backend._lib.GEN_DNS:
         data = backend._asn1_string_to_bytes(gn.d.dNSName)
-        if data.startswith(b"*."):
+        if not data:
+            decoded = u""
+        elif data.startswith(b"*."):
             # This is a wildcard name. We need to remove the leading wildcard,
             # IDNA decode, then re-add the wildcard. Wildcard characters should
             # always be left-most (RFC 2595 section 2.4).
@@ -82,7 +84,10 @@
     elif gn.type == backend._lib.GEN_URI:
         data = backend._asn1_string_to_ascii(gn.d.uniformResourceIdentifier)
         parsed = urllib_parse.urlparse(data)
-        hostname = idna.decode(parsed.hostname)
+        if parsed.hostname:
+            hostname = idna.decode(parsed.hostname)
+        else:
+            hostname = ""
         if parsed.port:
             netloc = hostname + u":" + six.text_type(parsed.port)
         else:
diff --git a/tests/test_x509_ext.py b/tests/test_x509_ext.py
index 8537397..1bc1462 100644
--- a/tests/test_x509_ext.py
+++ b/tests/test_x509_ext.py
@@ -1555,6 +1555,21 @@
             u'saseliminator.com'
         ]
 
+    def test_san_empty_hostname(self, backend):
+        cert = _load_cert(
+            os.path.join(
+                "x509", "custom", "san_empty_hostname.pem"
+            ),
+            x509.load_pem_x509_certificate,
+            backend
+        )
+        san = cert.extensions.get_extension_for_oid(
+            ExtensionOID.SUBJECT_ALTERNATIVE_NAME
+        )
+
+        dns = san.value.get_values_for_type(x509.DNSName)
+        assert dns == [u'']
+
     def test_san_wildcard_idna_dns_name(self, backend):
         cert = _load_cert(
             os.path.join("x509", "custom", "san_wildcard_idna.pem"),
@@ -2903,6 +2918,30 @@
             )
         ])
 
+    def test_crl_empty_hostname(self, backend):
+        cert = _load_cert(
+            os.path.join(
+                "x509", "custom", "cdp_empty_hostname.pem"
+            ),
+            x509.load_pem_x509_certificate,
+            backend
+        )
+
+        cdps = cert.extensions.get_extension_for_oid(
+            ExtensionOID.CRL_DISTRIBUTION_POINTS
+        ).value
+
+        assert cdps == x509.CRLDistributionPoints([
+            x509.DistributionPoint(
+                full_name=[x509.UniformResourceIdentifier(
+                    u"ldap:/CN=A,OU=B,dc=C,DC=D?E?F?G?H=I"
+                )],
+                relative_name=None,
+                reasons=None,
+                crl_issuer=None
+            )
+        ])
+
 
 @pytest.mark.requires_backend_interface(interface=RSABackend)
 @pytest.mark.requires_backend_interface(interface=X509Backend)
diff --git a/vectors/cryptography_vectors/x509/custom/cdp_empty_hostname.pem b/vectors/cryptography_vectors/x509/custom/cdp_empty_hostname.pem
new file mode 100644
index 0000000..8a97ea2
--- /dev/null
+++ b/vectors/cryptography_vectors/x509/custom/cdp_empty_hostname.pem
@@ -0,0 +1,33 @@
+-----BEGIN CERTIFICATE-----
+MIIFsDCCA5igAwIBAgICEAAwDQYJKoZIhvcNAQELBQAwDzENMAsGA1UECgwEUHlD
+QTAeFw0xNTEwMTAwNDQ3MTVaFw0xNjEwMDkwNDQ3MTVaMA8xDTALBgNVBAoMBFB5
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+uuurBKYHWFOtfjThSEOqTSBMDEzRtk/d3n7aXGD1xOEYti6U5o3gASv7wQDIVKkv
+xpil5fmrmwEjU0dcjU5AtSZt0rLXJGywT2hTrCL7Ua8BtKwzp0KKVXLAo7O+1Vau
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+Mb7IyeivYBRJP4cqh4LdUaBIEHI=
+-----END CERTIFICATE-----
diff --git a/vectors/cryptography_vectors/x509/custom/san_empty_hostname.pem b/vectors/cryptography_vectors/x509/custom/san_empty_hostname.pem
new file mode 100644
index 0000000..90b678b
--- /dev/null
+++ b/vectors/cryptography_vectors/x509/custom/san_empty_hostname.pem
@@ -0,0 +1,32 @@
+-----BEGIN CERTIFICATE-----
+MIIFgzCCA2ugAwIBAgICEAAwDQYJKoZIhvcNAQELBQAwDzENMAsGA1UECgwEUHlD
+QTAeFw0xNTEwMTAwNDQ2MTRaFw0xNjEwMDkwNDQ2MTRaMA8xDTALBgNVBAoMBFB5
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+cHZkH9okuLpO5zNsYPEWjg1NoF4wwxw=
+-----END CERTIFICATE-----