diff --git a/cryptography/hazmat/backends/openssl/backend.py b/cryptography/hazmat/backends/openssl/backend.py
index 2540a51..9a36674 100644
--- a/cryptography/hazmat/backends/openssl/backend.py
+++ b/cryptography/hazmat/backends/openssl/backend.py
@@ -1065,28 +1065,6 @@
             )
         return curve_nid
 
-    def _ec_key_curve_sn(self, ec_key):
-        group = self._lib.EC_KEY_get0_group(ec_key)
-        assert group != self._ffi.NULL
-
-        nid = self._lib.EC_GROUP_get_curve_name(group)
-        assert nid != self._lib.NID_undef
-
-        curve_name = self._lib.OBJ_nid2sn(nid)
-        assert curve_name != self._ffi.NULL
-
-        sn = self._ffi.string(curve_name).decode('ascii')
-        return sn
-
-    def _sn_to_elliptic_curve(self, sn):
-        try:
-            return ec._CURVE_TYPES[sn]()
-        except KeyError:
-            raise UnsupportedAlgorithm(
-                "{0} is not a supported elliptic curve".format(sn),
-                _Reasons.UNSUPPORTED_ELLIPTIC_CURVE
-            )
-
     @contextmanager
     def _tmp_bn_ctx(self):
         bn_ctx = self._lib.BN_CTX_new()
diff --git a/cryptography/hazmat/backends/openssl/ec.py b/cryptography/hazmat/backends/openssl/ec.py
index 7b0fd9d..9371a9a 100644
--- a/cryptography/hazmat/backends/openssl/ec.py
+++ b/cryptography/hazmat/backends/openssl/ec.py
@@ -63,6 +63,30 @@
     return digest
 
 
+def _ec_key_curve_sn(backend, ec_key):
+    group = backend._lib.EC_KEY_get0_group(ec_key)
+    assert group != backend._ffi.NULL
+
+    nid = backend._lib.EC_GROUP_get_curve_name(group)
+    assert nid != backend._lib.NID_undef
+
+    curve_name = backend._lib.OBJ_nid2sn(nid)
+    assert curve_name != backend._ffi.NULL
+
+    sn = backend._ffi.string(curve_name).decode('ascii')
+    return sn
+
+
+def _sn_to_elliptic_curve(backend, sn):
+    try:
+        return ec._CURVE_TYPES[sn]()
+    except KeyError:
+        raise UnsupportedAlgorithm(
+            "{0} is not a supported elliptic curve".format(sn),
+            _Reasons.UNSUPPORTED_ELLIPTIC_CURVE
+        )
+
+
 @utils.register_interface(interfaces.AsymmetricSignatureContext)
 class _ECDSASignatureContext(object):
     def __init__(self, backend, private_key, algorithm):
@@ -135,8 +159,8 @@
         self._backend = backend
         self._ec_key = ec_key_cdata
 
-        sn = backend._ec_key_curve_sn(ec_key_cdata)
-        self._curve = backend._sn_to_elliptic_curve(sn)
+        sn = _ec_key_curve_sn(backend, ec_key_cdata)
+        self._curve = _sn_to_elliptic_curve(backend, sn)
 
     @property
     def curve(self):
@@ -189,8 +213,8 @@
         self._backend = backend
         self._ec_key = ec_key_cdata
 
-        sn = backend._ec_key_curve_sn(ec_key_cdata)
-        self._curve = backend._sn_to_elliptic_curve(sn)
+        sn = _ec_key_curve_sn(backend, ec_key_cdata)
+        self._curve = _sn_to_elliptic_curve(backend, sn)
 
     @property
     def curve(self):
diff --git a/tests/hazmat/backends/test_openssl.py b/tests/hazmat/backends/test_openssl.py
index bfe6040..b00543f 100644
--- a/tests/hazmat/backends/test_openssl.py
+++ b/tests/hazmat/backends/test_openssl.py
@@ -27,6 +27,7 @@
 from cryptography.hazmat.backends.openssl.backend import (
     Backend, backend
 )
+from cryptography.hazmat.backends.openssl.ec import _sn_to_elliptic_curve
 from cryptography.hazmat.primitives import hashes, interfaces
 from cryptography.hazmat.primitives.asymmetric import dsa, ec, padding, rsa
 from cryptography.hazmat.primitives.ciphers import Cipher
@@ -509,7 +510,7 @@
 
     def test_sn_to_elliptic_curve_not_supported(self):
         with raises_unsupported_algorithm(_Reasons.UNSUPPORTED_ELLIPTIC_CURVE):
-            backend._sn_to_elliptic_curve(b"fake")
+            _sn_to_elliptic_curve(backend, b"fake")
 
 
 class TestDeprecatedRSABackendMethods(object):