Expose EC group order

src/_cffi_src/openssl/ec.py

@@ -15,6 +15,7 @@
     int nid;
     const char *comment;
 } EC_builtin_curve;
+typedef ... EC_GROUP;
 """
 
 FUNCTIONS = """
@@ -23,6 +24,12 @@
 void EC_KEY_free(EC_KEY *);
 
 EC_KEY *EC_KEY_new_by_curve_name(int);
+
+EC_GROUP *EC_GROUP_new_by_curve_name(int);
+
+int EC_GROUP_get_order(const EC_GROUP *, BIGNUM *, BN_CTX *);
+
+void EC_GROUP_free(EC_GROUP *);
 """
 
 CUSTOMIZATIONS = """

src/cryptography/hazmat/backends/openssl/backend.py

@@ -318,6 +318,31 @@ def elliptic_curve_exchange_algorithm_supported(
             algorithm, ec.ECDH
         )
 
+    def elliptic_curve_group_order(self, curve: ec.EllipticCurve) -> int:
+        group = self._lib.EC_GROUP_new_by_curve_name(
+            self._lib.OBJ_txt2nid(curve.name.encode())
+        )
+
+        if not group:
+            raise Exception("EC_GROUP_new_by_curve_name failed")
+
+        bn = self._lib.BN_new()
+
+        if not bn:
+            self._lib.EC_GROUP_free(group)
+            raise Exception("BN_new failed")
+
+        if self._lib.EC_GROUP_get_order(group, bn, self._ffi.NULL) != 1:
+            self._lib.BN_free(bn)
+            self._lib.EC_GROUP_free(group)
+            raise Exception("EC_GROUP_get_order failed")
+
+        group_order = int(backend._ffi.string(self._lib.BN_bn2hex(bn)), 16)
+
+        self._lib.BN_free(bn)
+        self._lib.EC_GROUP_free(group)
+        return group_order
+
     def dh_supported(self) -> bool:
         return not rust_openssl.CRYPTOGRAPHY_IS_BORINGSSL
 

src/cryptography/hazmat/primitives/asymmetric/ec.py

@@ -52,6 +52,15 @@ def key_size(self) -> int:
         Bit size of a secret scalar for the curve.
         """
 
+    @property
+    def group_order(self) -> int:
+        """
+        The order of the curve's group
+        """
+        from cryptography.hazmat.backends.openssl.backend import backend
+
+        return backend.elliptic_curve_group_order(self)
+
 
 class EllipticCurveSignatureAlgorithm(metaclass=abc.ABCMeta):
     @property