diff --git a/src/lib/sslcrypto/_ecc.py b/src/lib/sslcrypto/_ecc.py
index 9831d688..3dbc56cd 100644
--- a/src/lib/sslcrypto/_ecc.py
+++ b/src/lib/sslcrypto/_ecc.py
@@ -18,23 +18,176 @@ else:
 
 
 class ECC:
+    # pylint: disable=line-too-long
+    # name: (nid, p, n, a, b, (Gx, Gy)),
     CURVES = {
-        "secp112r1": 704,
-        "secp112r2": 705,
-        "secp128r1": 706,
-        "secp128r2": 707,
-        "secp160k1": 708,
-        "secp160r1": 709,
-        "secp160r2": 710,
-        "secp192k1": 711,
-        "prime192v1": 409,
-        "secp224k1": 712,
-        "secp224r1": 713,
-        "secp256k1": 714,
-        "prime256v1": 415,
-        "secp384r1": 715,
-        "secp521r1": 716
+        "secp112r1": (
+            704,
+            0xDB7C2ABF62E35E668076BEAD208B,
+            0xDB7C2ABF62E35E7628DFAC6561C5,
+            0xDB7C2ABF62E35E668076BEAD2088,
+            0x659EF8BA043916EEDE8911702B22,
+            (
+                0x09487239995A5EE76B55F9C2F098,
+                0xA89CE5AF8724C0A23E0E0FF77500
+            )
+        ),
+        "secp112r2": (
+            705,
+            0xDB7C2ABF62E35E668076BEAD208B,
+            0x36DF0AAFD8B8D7597CA10520D04B,
+            0x6127C24C05F38A0AAAF65C0EF02C,
+            0x51DEF1815DB5ED74FCC34C85D709,
+            (
+                0x4BA30AB5E892B4E1649DD0928643,
+                0xADCD46F5882E3747DEF36E956E97
+            )
+        ),
+        "secp128r1": (
+            706,
+            0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF,
+            0xFFFFFFFE0000000075A30D1B9038A115,
+            0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC,
+            0xE87579C11079F43DD824993C2CEE5ED3,
+            (
+                0x161FF7528B899B2D0C28607CA52C5B86,
+                0xCF5AC8395BAFEB13C02DA292DDED7A83
+            )
+        ),
+        "secp128r2": (
+            707,
+            0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF,
+            0x3FFFFFFF7FFFFFFFBE0024720613B5A3,
+            0xD6031998D1B3BBFEBF59CC9BBFF9AEE1,
+            0x5EEEFCA380D02919DC2C6558BB6D8A5D,
+            (
+                0x7B6AA5D85E572983E6FB32A7CDEBC140,
+                0x27B6916A894D3AEE7106FE805FC34B44
+            )
+        ),
+        "secp160k1": (
+            708,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73,
+            0x0100000000000000000001B8FA16DFAB9ACA16B6B3,
+            0,
+            7,
+            (
+                0x3B4C382CE37AA192A4019E763036F4F5DD4D7EBB,
+                0x938CF935318FDCED6BC28286531733C3F03C4FEE
+            )
+        ),
+        "secp160r1": (
+            709,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF,
+            0x0100000000000000000001F4C8F927AED3CA752257,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC,
+            0x001C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45,
+            (
+                0x4A96B5688EF573284664698968C38BB913CBFC82,
+                0x23A628553168947D59DCC912042351377AC5FB32
+            )
+        ),
+        "secp160r2": (
+            710,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73,
+            0x0100000000000000000000351EE786A818F3A1A16B,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70,
+            0x00B4E134D3FB59EB8BAB57274904664D5AF50388BA,
+            (
+                0x52DCB034293A117E1F4FF11B30F7199D3144CE6D,
+                0xFEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E
+            )
+        ),
+        "secp192k1": (
+            711,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37,
+            0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D,
+            0,
+            3,
+            (
+                0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D,
+                0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D
+            )
+        ),
+        "prime192v1": (
+            409,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF,
+            0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC,
+            0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1,
+            (
+                0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012,
+                0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811
+            )
+        ),
+        "secp224k1": (
+            712,
+            0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D,
+            0x010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7,
+            0,
+            5,
+            (
+                0xA1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C,
+                0x7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5
+            )
+        ),
+        "secp224r1": (
+            713,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE,
+            0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4,
+            (
+                0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21,
+                0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34
+            )
+        ),
+        "secp256k1": (
+            714,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
+            0,
+            7,
+            (
+                0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
+                0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
+            )
+        ),
+        "prime256v1": (
+            715,
+            0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF,
+            0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551,
+            0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC,
+            0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B,
+            (
+                0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296,
+                0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5
+            )
+        ),
+        "secp384r1": (
+            716,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973,
+            0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC,
+            0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF,
+            (
+                0xAA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7,
+                0x3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F
+            )
+        ),
+        "secp521r1": (
+            717,
+            0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,
+            0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409,
+            0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC,
+            0x0051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00,
+            (
+                0x00C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66,
+                0x011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650
+            )
+        )
     }
+    # pylint: enable=line-too-long
 
     def __init__(self, backend, aes):
         self._backend = backend
@@ -44,8 +197,8 @@ class ECC:
     def get_curve(self, name):
         if name not in self.CURVES:
             raise ValueError("Unknown curve {}".format(name))
-        nid = self.CURVES[name]
-        return EllipticCurve(self._backend(nid), self._aes, nid)
+        nid, p, n, a, b, g = self.CURVES[name]
+        return EllipticCurve(self._backend(p, n, a, b, g), self._aes, nid)
 
 
     def get_backend(self):
diff --git a/src/lib/sslcrypto/fallback/ecc.py b/src/lib/sslcrypto/fallback/ecc.py
index 3a438d4d..6ca9a498 100644
--- a/src/lib/sslcrypto/fallback/ecc.py
+++ b/src/lib/sslcrypto/fallback/ecc.py
@@ -6,185 +6,13 @@ from .aes import aes
 from ._util import int_to_bytes, bytes_to_int, inverse, square_root_mod_prime
 
 
-# pylint: disable=line-too-long
-CURVES = {
-    # nid: (p, n, a, b, (Gx, Gy)),
-    704: (
-        # secp112r1
-        0xDB7C2ABF62E35E668076BEAD208B,
-        0xDB7C2ABF62E35E7628DFAC6561C5,
-        0xDB7C2ABF62E35E668076BEAD2088,
-        0x659EF8BA043916EEDE8911702B22,
-        (
-            0x09487239995A5EE76B55F9C2F098,
-            0xA89CE5AF8724C0A23E0E0FF77500
-        )
-    ),
-    705: (
-        # secp112r2
-        0xDB7C2ABF62E35E668076BEAD208B,
-        0x36DF0AAFD8B8D7597CA10520D04B,
-        0x6127C24C05F38A0AAAF65C0EF02C,
-        0x51DEF1815DB5ED74FCC34C85D709,
-        (
-            0x4BA30AB5E892B4E1649DD0928643,
-            0xADCD46F5882E3747DEF36E956E97
-        )
-    ),
-    706: (
-        # secp128r1
-        0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF,
-        0xFFFFFFFE0000000075A30D1B9038A115,
-        0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC,
-        0xE87579C11079F43DD824993C2CEE5ED3,
-        (
-            0x161FF7528B899B2D0C28607CA52C5B86,
-            0xCF5AC8395BAFEB13C02DA292DDED7A83
-        )
-    ),
-    707: (
-        # secp128r2
-        0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF,
-        0x3FFFFFFF7FFFFFFFBE0024720613B5A3,
-        0xD6031998D1B3BBFEBF59CC9BBFF9AEE1,
-        0x5EEEFCA380D02919DC2C6558BB6D8A5D,
-        (
-            0x7B6AA5D85E572983E6FB32A7CDEBC140,
-            0x27B6916A894D3AEE7106FE805FC34B44
-        )
-    ),
-    708: (
-        # secp160k1
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73,
-        0x0100000000000000000001B8FA16DFAB9ACA16B6B3,
-        0,
-        7,
-        (
-            0x3B4C382CE37AA192A4019E763036F4F5DD4D7EBB,
-            0x938CF935318FDCED6BC28286531733C3F03C4FEE
-        )
-    ),
-    709: (
-        # secp160r1
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF,
-        0x0100000000000000000001F4C8F927AED3CA752257,
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC,
-        0x001C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45,
-        (
-            0x4A96B5688EF573284664698968C38BB913CBFC82,
-            0x23A628553168947D59DCC912042351377AC5FB32
-        )
-    ),
-    710: (
-        # secp160r2
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73,
-        0x0100000000000000000000351EE786A818F3A1A16B,
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70,
-        0x00B4E134D3FB59EB8BAB57274904664D5AF50388BA,
-        (
-            0x52DCB034293A117E1F4FF11B30F7199D3144CE6D,
-            0xFEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E
-        )
-    ),
-    711: (
-        # secp192k1
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37,
-        0xFFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D,
-        0,
-        3,
-        (
-            0xDB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D,
-            0x9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D
-        )
-    ),
-    409: (
-        # prime192v1
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF,
-        0xFFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC,
-        0x64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1,
-        (
-            0x188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012,
-            0x07192B95FFC8DA78631011ED6B24CDD573F977A11E794811
-        )
-    ),
-    712: (
-        # secp224k1
-        0x00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D,
-        0x010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7,
-        0,
-        5,
-        (
-            0xA1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C,
-            0x7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5
-        )
-    ),
-    713: (
-        # secp224r1
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE,
-        0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4,
-        (
-            0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21,
-            0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34
-        )
-    ),
-    714: (
-        # secp256k1
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
-        0,
-        7,
-        (
-            0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
-            0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
-        )
-    ),
-    415: (
-        # prime256v1
-        0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF,
-        0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551,
-        0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC,
-        0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B,
-        (
-            0x6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296,
-            0x4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5
-        )
-    ),
-    715: (
-        # secp384r1
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973,
-        0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC,
-        0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF,
-        (
-            0xAA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7,
-            0x3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F
-        )
-    ),
-    716: (
-        # secp521r1
-        0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF,
-        0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409,
-        0x01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC,
-        0x0051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00,
-        (
-            0x00C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66,
-            0x011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650
-        )
-    )
-}
-# pylint: enable=line-too-long
-
-
 class EllipticCurveBackend:
-    def __init__(self, nid):
-        self.p, self.n, self.a, self.b, self.g = CURVES[nid]
-        self.jacobian = JacobianCurve(*CURVES[nid])
+    def __init__(self, p, n, a, b, g):
+        self.p, self.n, self.a, self.b, self.g = p, n, a, b, g
+        self.jacobian = JacobianCurve(p, n, a, b, g)
 
-        self.public_key_length = (len(bin(self.p).replace("0b", "")) + 7) // 8
-        self.order_bitlength = len(bin(self.n).replace("0b", ""))
+        self.public_key_length = (len(bin(p).replace("0b", "")) + 7) // 8
+        self.order_bitlength = len(bin(n).replace("0b", ""))
 
 
     def _int_to_bytes(self, raw, len=None):
diff --git a/src/lib/sslcrypto/openssl/ecc.py b/src/lib/sslcrypto/openssl/ecc.py
index 5b5f0bde..f9271e43 100644
--- a/src/lib/sslcrypto/openssl/ecc.py
+++ b/src/lib/sslcrypto/openssl/ecc.py
@@ -10,7 +10,7 @@ from .library import lib, openssl_backend
 lib.BN_new.restype = ctypes.POINTER(ctypes.c_char)
 lib.BN_bin2bn.restype = ctypes.POINTER(ctypes.c_char)
 lib.BN_CTX_new.restype = ctypes.POINTER(ctypes.c_char)
-lib.EC_GROUP_new_by_curve_name.restype = ctypes.POINTER(ctypes.c_char)
+lib.EC_GROUP_new_curve_GFp.restype = ctypes.POINTER(ctypes.c_char)
 lib.EC_KEY_new.restype = ctypes.POINTER(ctypes.c_char)
 lib.EC_POINT_new.restype = ctypes.POINTER(ctypes.c_char)
 lib.EC_KEY_get0_private_key.restype = ctypes.POINTER(ctypes.c_char)
@@ -28,12 +28,12 @@ thread_local = threading.local()
 # 1.1.0) use global objects so they aren't thread safe. Fortunately we can check
 # the code to find out which functions are thread safe.
 #
-# For example, EC_GROUP_new_by_curve_name checks global error code to initialize
+# For example, EC_GROUP_new_curve_GFp checks global error code to initialize
 # the group, so if two errors happen at once or two threads read the error code,
 # or the codes are read in the wrong order, the group is initialized in a wrong
 # way.
 #
-# EC_KEY_new_by_curve_name calls EC_GROUP_new_by_curve_name so it's not thread
+# EC_KEY_new_by_curve_name calls EC_GROUP_new_curve_GFp so it's not thread
 # safe. We can't use the lock because it would be too slow; instead, we use
 # EC_KEY_new and then EC_KEY_set_group which calls EC_GROUP_copy instead which
 # is thread safe.
@@ -68,14 +68,16 @@ class BN:
             if value is None:
                 self.bn = lib.BN_new()
                 self._free = True
-            elif isinstance(value, bytes):
-                self.bn = lib.BN_bin2bn(value, len(value), None)
-                self._free = True
-            else:
+            elif isinstance(value, int) and value < 256:
                 self.bn = lib.BN_new()
                 lib.BN_clear(self.bn)
                 lib.BN_add_word(self.bn, value)
                 self._free = True
+            else:
+                if isinstance(value, int):
+                    value = value.to_bytes(128, "big")
+                self.bn = lib.BN_bin2bn(value, len(value), None)
+                self._free = True
 
 
     def __del__(self):
@@ -201,21 +203,27 @@ class BN:
 
 
 class EllipticCurveBackend:
-    def __init__(self, nid):
+    def __init__(self, p, n, a, b, g):
+        bn_ctx = BN.Context.get()
+
         self.lib = lib  # For finalizer
-        self.nid = nid
+
+        self.p = BN(p)
+        self.order = BN(n)
+        self.a = BN(a)
+        self.b = BN(b)
+        self.h = BN((p + n // 2) // n)
+
         with lock:
             # Thread-safety
-            self.group = lib.EC_GROUP_new_by_curve_name(self.nid)
+            self.group = lib.EC_GROUP_new_curve_GFp(self.p.bn, self.a.bn, self.b.bn, bn_ctx)
+            if not self.group:
+                raise ValueError("Could not create group object")
+            generator = self._public_key_to_point(g)
+            lib.EC_GROUP_set_generator(self.group, generator, self.order.bn, self.h.bn)
         if not self.group:
             raise ValueError("The curve is not supported by OpenSSL")
 
-        self.order = BN()
-        self.p = BN()
-        bn_ctx = BN.Context.get()
-        lib.EC_GROUP_get_order(self.group, self.order.bn, bn_ctx)
-        lib.EC_GROUP_get_curve_GFp(self.group, self.p.bn, None, None, bn_ctx)
-
         self.public_key_length = (len(self.p) + 7) // 8
 
         self.is_supported_evp_pkey_ctx = hasattr(lib, "EVP_PKEY_CTX_new")