implement signature_hash_algorithm instead
diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index df78acd..f903b7f 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -9,7 +9,7 @@
 * :func:`~cryptography.hazmat.primitives.serialization.load_ssh_public_key` can
   now load elliptic curve public keys.
 * Added
-  :attr:`~cryptography.x509.Certificate.signature_algorithm` support to
+  :attr:`~cryptography.x509.Certificate.signature_hash_algorithm` support to
   :class:`~cryptography.x509.Certificate`.
 * Added
   :func:`~cryptography.hazmat.primitives.asymmetric.rsa.rsa_recover_prime_factors`
diff --git a/docs/spelling_wordlist.txt b/docs/spelling_wordlist.txt
index fefd26b..ddd3789 100644
--- a/docs/spelling_wordlist.txt
+++ b/docs/spelling_wordlist.txt
@@ -51,3 +51,4 @@
 unencrypted
 unpadded
 unpadding
+Verisign
diff --git a/docs/x509.rst b/docs/x509.rst
index 8043b36..193b845 100644
--- a/docs/x509.rst
+++ b/docs/x509.rst
@@ -182,18 +182,19 @@
 
         The :class:`Name` of the subject.
 
-    .. attribute:: signature_algorithm
+    .. attribute:: signature_hash_algorithm
 
-        :type: :class:`ObjectIdentifier`
+        :type: :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`
 
-        An :class:`ObjectIdentifier` instance corresponding to the signature
-        algorithm used to sign the certificate. This is both the digest
-        used as well as the asymmetric type.
+        A :class:`~cryptography.hazmat.primitives.hashes.HashAlgorithm`
+        corresponding to the hash algorithm used within the certificate
+        signature.
 
         .. doctest::
 
-            >>> cert.signature_algorithm
-            <ObjectIdentifier(oid=1.2.840.113549.1.1.11, name=sha256WithRSAEncryption)>
+            >>> from cryptography.hazmat.primitives import hashes
+            >>> isinstance(cert.signature_hash_algorithm, hashes.SHA256)
+            True
 
 .. class:: Name
 
diff --git a/src/cryptography/hazmat/backends/openssl/x509.py b/src/cryptography/hazmat/backends/openssl/x509.py
index a3dddc4..989a9dd 100644
--- a/src/cryptography/hazmat/backends/openssl/x509.py
+++ b/src/cryptography/hazmat/backends/openssl/x509.py
@@ -16,6 +16,7 @@
 import datetime
 
 from cryptography import utils, x509
+from cryptography.exceptions import UnsupportedAlgorithm
 from cryptography.hazmat.primitives import hashes
 
 
@@ -138,7 +139,16 @@
         return x509.Name(attributes)
 
     @property
-    def signature_algorithm(self):
+    def signature_hash_algorithm(self):
+        oid = self._signature_algorithm()
+        try:
+            return x509._SIG_OIDS_TO_HASH[oid.dotted_string]
+        except KeyError:
+            raise UnsupportedAlgorithm(
+                "Signature algorithm {0} not recognized".format(oid)
+            )
+
+    def _signature_algorithm(self):
         buf_len = 50
         buf = self._backend._ffi.new("char[]", buf_len)
         res = self._backend._lib.OBJ_obj2txt(
diff --git a/src/cryptography/x509.py b/src/cryptography/x509.py
index c4d87bb..c6ce61d 100644
--- a/src/cryptography/x509.py
+++ b/src/cryptography/x509.py
@@ -10,6 +10,7 @@
 import six
 
 from cryptography import utils
+from cryptography.hazmat.primitives import hashes
 
 
 _OID_NAMES = {
@@ -170,6 +171,22 @@
 OID_DSA_WITH_SHA224 = ObjectIdentifier("2.16.840.1.101.3.4.3.1")
 OID_DSA_WITH_SHA256 = ObjectIdentifier("2.16.840.1.101.3.4.3.2")
 
+_SIG_OIDS_TO_HASH = {
+    "1.2.840.113549.1.1.4": hashes.MD5(),
+    "1.2.840.113549.1.1.5": hashes.SHA1(),
+    "1.2.840.113549.1.1.14": hashes.SHA224(),
+    "1.2.840.113549.1.1.11": hashes.SHA256(),
+    "1.2.840.113549.1.1.12": hashes.SHA384(),
+    "1.2.840.113549.1.1.13": hashes.SHA512(),
+    "1.2.840.10045.4.3.1": hashes.SHA224(),
+    "1.2.840.10045.4.3.2": hashes.SHA256(),
+    "1.2.840.10045.4.3.3": hashes.SHA384(),
+    "1.2.840.10045.4.3.4": hashes.SHA512(),
+    "1.2.840.10040.4.3": hashes.SHA1(),
+    "2.16.840.1.101.3.4.3.1": hashes.SHA224(),
+    "2.16.840.1.101.3.4.3.2": hashes.SHA256()
+}
+
 
 @six.add_metaclass(abc.ABCMeta)
 class Certificate(object):
@@ -222,8 +239,8 @@
         """
 
     @abc.abstractproperty
-    def signature_algorithm(self):
+    def signature_hash_algorithm(self):
         """
-        Returns an ObjectIdentifier corresponding to the signature algorithm of
-        the certificate.
+        Returns a HashAlgorithm corresponding to the type of the digest signed
+        in the certificate.
         """
diff --git a/tests/test_x509.py b/tests/test_x509.py
index 613263d..8f00eee 100644
--- a/tests/test_x509.py
+++ b/tests/test_x509.py
@@ -13,6 +13,7 @@
 import six
 
 from cryptography import x509
+from cryptography.exceptions import UnsupportedAlgorithm
 from cryptography.hazmat.backends.interfaces import (
     DSABackend, EllipticCurveBackend, RSABackend, X509Backend
 )
@@ -45,7 +46,7 @@
         assert cert.serial == 11559813051657483483
         fingerprint = binascii.hexlify(cert.fingerprint(hashes.SHA1()))
         assert fingerprint == b"2b619ed04bfc9c3b08eb677d272192286a0947a8"
-        assert cert.signature_algorithm == x509.OID_SHA1_WITH_RSA
+        assert isinstance(cert.signature_hash_algorithm, hashes.SHA1)
 
     def test_load_der_cert(self, backend):
         cert = _load_cert(
@@ -57,7 +58,7 @@
         assert cert.serial == 2
         fingerprint = binascii.hexlify(cert.fingerprint(hashes.SHA1()))
         assert fingerprint == b"6f49779533d565e8b7c1062503eab41492c38e4d"
-        assert cert.signature_algorithm == x509.OID_SHA256_WITH_RSA
+        assert isinstance(cert.signature_hash_algorithm, hashes.SHA256)
 
     def test_issuer(self, backend):
         cert = _load_cert(
@@ -330,6 +331,15 @@
         with pytest.raises(ValueError):
             x509.load_der_x509_certificate(b"notacert", backend)
 
+    def test_unsupported_signature_hash_algorithm_cert(self, backend):
+        cert = _load_cert(
+            os.path.join("x509", "verisign_md2_root.pem"),
+            x509.load_pem_x509_certificate,
+            backend
+        )
+        with pytest.raises(UnsupportedAlgorithm):
+            cert.signature_hash_algorithm
+
 
 @pytest.mark.requires_backend_interface(interface=DSABackend)
 @pytest.mark.requires_backend_interface(interface=X509Backend)
@@ -340,7 +350,7 @@
             x509.load_pem_x509_certificate,
             backend
         )
-        assert cert.signature_algorithm == x509.OID_DSA_WITH_SHA1
+        assert isinstance(cert.signature_hash_algorithm, hashes.SHA1)
         public_key = cert.public_key()
         assert isinstance(public_key, interfaces.DSAPublicKey)
         if isinstance(public_key, interfaces.DSAPublicKeyWithNumbers):
@@ -393,7 +403,7 @@
             x509.load_pem_x509_certificate,
             backend
         )
-        assert cert.signature_algorithm == x509.OID_ECDSA_WITH_SHA384
+        assert isinstance(cert.signature_hash_algorithm, hashes.SHA384)
         public_key = cert.public_key()
         assert isinstance(public_key, interfaces.EllipticCurvePublicKey)
         if isinstance(