diff --git a/cryptography/hazmat/backends/openssl/backend.py b/cryptography/hazmat/backends/openssl/backend.py
index 900d25c..bbcfa32 100644
--- a/cryptography/hazmat/backends/openssl/backend.py
+++ b/cryptography/hazmat/backends/openssl/backend.py
@@ -346,9 +346,6 @@
         evp_pkey = self._new_evp_pkey()
         rsa_cdata = self._rsa_cdata_from_private_key(private_key)
 
-        res = self._lib.RSA_blinding_on(rsa_cdata, self._ffi.NULL)
-        assert res == 1
-
         res = self._lib.EVP_PKEY_assign_RSA(evp_pkey, rsa_cdata)
         assert res == 1
 
@@ -358,9 +355,6 @@
         evp_pkey = self._new_evp_pkey()
         rsa_cdata = self._rsa_cdata_from_public_key(public_key)
 
-        res = self._lib.RSA_blinding_on(rsa_cdata, self._ffi.NULL)
-        assert res == 1
-
         res = self._lib.EVP_PKEY_assign_RSA(evp_pkey, rsa_cdata)
         assert res == 1
 
@@ -391,6 +385,9 @@
         ctx.dmp1 = self._int_to_bn(private_key.dmp1)
         ctx.dmq1 = self._int_to_bn(private_key.dmq1)
         ctx.iqmp = self._int_to_bn(private_key.iqmp)
+        res = self._lib.RSA_blinding_on(ctx, self._ffi.NULL)
+        assert res == 1
+
         return ctx
 
     def _rsa_cdata_from_public_key(self, public_key):
@@ -401,6 +398,9 @@
         assert ctx != self._ffi.NULL
         ctx.e = self._int_to_bn(public_key.e)
         ctx.n = self._int_to_bn(public_key.n)
+        res = self._lib.RSA_blinding_on(ctx, self._ffi.NULL)
+        assert res == 1
+
         return ctx
 
     def create_rsa_signature_ctx(self, private_key, padding, algorithm):
@@ -843,6 +843,8 @@
             evp_pkey, self._backend._ffi.NULL
         )
         assert pkey_ctx != self._backend._ffi.NULL
+        pkey_ctx = self._backend._ffi.gc(pkey_ctx,
+                                         self._backend._lib.EVP_PKEY_CTX_free)
         res = self._backend._lib.EVP_PKEY_sign_init(pkey_ctx)
         assert res == 1
         res = self._backend._lib.EVP_PKEY_CTX_set_signature_md(
@@ -1028,6 +1030,8 @@
             evp_pkey, self._backend._ffi.NULL
         )
         assert pkey_ctx != self._backend._ffi.NULL
+        pkey_ctx = self._backend._ffi.gc(pkey_ctx,
+                                         self._backend._lib.EVP_PKEY_CTX_free)
         res = self._backend._lib.EVP_PKEY_verify_init(pkey_ctx)
         assert res == 1
         res = self._backend._lib.EVP_PKEY_CTX_set_signature_md(
diff --git a/cryptography/hazmat/bindings/openssl/ec.py b/cryptography/hazmat/bindings/openssl/ec.py
index 669490d..8ae2ae9 100644
--- a/cryptography/hazmat/bindings/openssl/ec.py
+++ b/cryptography/hazmat/bindings/openssl/ec.py
@@ -240,9 +240,6 @@
 EC_GROUP *(*EC_GROUP_new_curve_GFp)(
     const BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
 
-EC_GROUP *(*EC_GROUP_new_curve_GF2m)(
-    const BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
-
 EC_GROUP *(*EC_GROUP_new_by_curve_name)(int);
 
 int (*EC_GROUP_set_curve_GFp)(
@@ -251,12 +248,6 @@
 int (*EC_GROUP_get_curve_GFp)(
     const EC_GROUP *, BIGNUM *, BIGNUM *, BIGNUM *, BN_CTX *);
 
-int (*EC_GROUP_set_curve_GF2m)(
-    EC_GROUP *, const BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
-
-int (*EC_GROUP_get_curve_GF2m)(
-    const EC_GROUP *, BIGNUM *, BIGNUM *, BIGNUM *, BN_CTX *);
-
 const EC_METHOD *(*EC_GROUP_method_of)(const EC_GROUP *) = NULL;
 const EC_POINT *(*EC_GROUP_get0_generator)(const EC_GROUP *) = NULL;
 int (*EC_GROUP_get_curve_name)(const EC_GROUP *) = NULL;
@@ -283,15 +274,6 @@
 int (*EC_POINT_set_compressed_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
     const BIGNUM *, int, BN_CTX *) = NULL;
 
-int (*EC_POINT_set_affine_coordinates_GF2m)(const EC_GROUP *, EC_POINT *,
-    const BIGNUM *, const BIGNUM *, BN_CTX *) = NULL;
-
-int (*EC_POINT_get_affine_coordinates_GF2m)(const EC_GROUP *,
-    const EC_POINT *, BIGNUM *, BIGNUM *, BN_CTX *) = NULL;
-
-int (*EC_POINT_set_compressed_coordinates_GF2m)(const EC_GROUP *, EC_POINT *,
-    const BIGNUM *, int, BN_CTX *) = NULL;
-
 size_t (*EC_POINT_point2oct)(const EC_GROUP *, const EC_POINT *,
     point_conversion_form_t,
     unsigned char *, size_t, BN_CTX *) = NULL;
@@ -380,6 +362,24 @@
 static const long Cryptography_HAS_EC2M = 0;
 
 const EC_METHOD *(*EC_GF2m_simple_method)() = NULL;
+
+int (*EC_POINT_set_affine_coordinates_GF2m)(const EC_GROUP *, EC_POINT *,
+    const BIGNUM *, const BIGNUM *, BN_CTX *) = NULL;
+
+int (*EC_POINT_get_affine_coordinates_GF2m)(const EC_GROUP *,
+    const EC_POINT *, BIGNUM *, BIGNUM *, BN_CTX *) = NULL;
+
+int (*EC_POINT_set_compressed_coordinates_GF2m)(const EC_GROUP *, EC_POINT *,
+    const BIGNUM *, int, BN_CTX *) = NULL;
+
+int (*EC_GROUP_set_curve_GF2m)(
+    EC_GROUP *, const BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
+
+int (*EC_GROUP_get_curve_GF2m)(
+    const EC_GROUP *, BIGNUM *, BIGNUM *, BIGNUM *, BN_CTX *);
+
+EC_GROUP *(*EC_GROUP_new_curve_GF2m)(
+    const BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *);
 #else
 static const long Cryptography_HAS_EC2M = 1;
 #endif
@@ -391,12 +391,9 @@
         "EC_GROUP_free",
         "EC_GROUP_clear_free",
         "EC_GROUP_new_curve_GFp",
-        "EC_GROUP_new_curve_GF2m",
         "EC_GROUP_new_by_curve_name",
         "EC_GROUP_set_curve_GFp",
         "EC_GROUP_get_curve_GFp",
-        "EC_GROUP_set_curve_GF2m",
-        "EC_GROUP_get_curve_GF2m",
         "EC_GROUP_method_of",
         "EC_GROUP_get0_generator",
         "EC_GROUP_get_curve_name",
@@ -431,9 +428,6 @@
         "EC_POINT_set_affine_coordinates_GFp",
         "EC_POINT_get_affine_coordinates_GFp",
         "EC_POINT_set_compressed_coordinates_GFp",
-        "EC_POINT_set_affine_coordinates_GF2m",
-        "EC_POINT_get_affine_coordinates_GF2m",
-        "EC_POINT_set_compressed_coordinates_GF2m",
         "EC_POINT_point2oct",
         "EC_POINT_oct2point",
         "EC_POINT_point2bn",
@@ -473,5 +467,11 @@
 
     "Cryptography_HAS_EC2M": [
         "EC_GF2m_simple_method",
+        "EC_POINT_set_affine_coordinates_GF2m",
+        "EC_POINT_get_affine_coordinates_GF2m",
+        "EC_POINT_set_compressed_coordinates_GF2m",
+        "EC_GROUP_set_curve_GF2m",
+        "EC_GROUP_get_curve_GF2m",
+        "EC_GROUP_new_curve_GF2m",
     ],
 }