FM / PublicKey

/opt/imh-python/lib/python3.9/site-packages/Crypto/PublicKey/

/opt/imh-python/lib/python3.9/site-packages/Crypto/PublicKey

Name	Size	Mode	Actions
__pycache__/	-	0755	rm
DSA.py	22307	0644	edit dl rm
DSA.pyi	1353	0644	edit dl rm
ECC.py	41977	0644	edit dl rm
ECC.pyi	2354	0644	edit dl rm
ElGamal.py	8615	0644	edit dl rm
ElGamal.pyi	674	0644	edit dl rm
RSA.py	28754	0644	edit dl rm
RSA.pyi	1837	0644	edit dl rm
_ec_ws.cpython-39-x86_64-linux-gnu.so	716496	0755	edit dl rm
_openssh.py	5126	0644	edit dl rm
_openssh.pyi	324	0644	edit dl rm
__init__.py	3119	0644	edit dl rm
__init__.pyi	0	0644	edit dl rm

Edit: /opt/imh-python/lib/python3.9/site-packages/Crypto/PublicKey/ECC.py (41977B)

# ===================================================================
#
# Copyright (c) 2015, Legrandin <helderijs@gmail.com>
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
#    notice, this list of conditions and the following disclaimer.
# 2. Redistributions in binary form must reproduce the above copyright
#    notice, this list of conditions and the following disclaimer in
#    the documentation and/or other materials provided with the
#    distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
# ===================================================================

from __future__ import print_function

import re
import sys
import struct
import binascii
from collections import namedtuple

from Crypto.Util.py3compat import bord, tobytes, tostr, bchr, is_string
from Crypto.Util.number import bytes_to_long, long_to_bytes

from Crypto.Math.Numbers import Integer
from Crypto.Util.asn1 import (DerObjectId, DerOctetString, DerSequence,
                              DerBitString)

from Crypto.PublicKey import (_expand_subject_public_key_info,
                              _create_subject_public_key_info,
                              _extract_subject_public_key_info)

from Crypto.Util._raw_api import (load_pycryptodome_raw_lib, VoidPointer,
                                  SmartPointer, c_size_t, c_uint8_ptr,
                                  c_ulonglong)

from Crypto.Random import get_random_bytes
from Crypto.Random.random import getrandbits

_ec_lib = load_pycryptodome_raw_lib("Crypto.PublicKey._ec_ws", """
typedef void EcContext;
typedef void EcPoint;
int ec_ws_new_context(EcContext **pec_ctx,
                      const uint8_t *modulus,
                      const uint8_t *b,
                      const uint8_t *order,
                      size_t len,
                      uint64_t seed);
void ec_free_context(EcContext *ec_ctx);
int ec_ws_new_point(EcPoint **pecp,
                    const uint8_t *x,
                    const uint8_t *y,
                    size_t len,
                    const EcContext *ec_ctx);
void ec_free_point(EcPoint *ecp);
int ec_ws_get_xy(uint8_t *x,
                 uint8_t *y,
                 size_t len,
                 const EcPoint *ecp);
int ec_ws_double(EcPoint *p);
int ec_ws_add(EcPoint *ecpa, EcPoint *ecpb);
int ec_ws_scalar(EcPoint *ecp,
                 const uint8_t *k,
                 size_t len,
                 uint64_t seed);
int ec_ws_clone(EcPoint **pecp2, const EcPoint *ecp);
int ec_ws_copy(EcPoint *ecp1, const EcPoint *ecp2);
int ec_ws_cmp(const EcPoint *ecp1, const EcPoint *ecp2);
int ec_ws_neg(EcPoint *p);
int ec_ws_normalize(EcPoint *ecp);
int ec_ws_is_pai(EcPoint *ecp);
""")

_Curve = namedtuple("_Curve", "p b order Gx Gy G modulus_bits oid context desc openssh")
_curves = {}

p256_names = ["p256", "NIST P-256", "P-256", "prime256v1", "secp256r1",
              "nistp256"]

def init_p256():
    p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
    b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
    order = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
    Gx = 0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
    Gy = 0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5

p256_modulus = long_to_bytes(p, 32)
    p256_b = long_to_bytes(b, 32)
    p256_order = long_to_bytes(order, 32)

ec_p256_context = VoidPointer()
    result = _ec_lib.ec_ws_new_context(ec_p256_context.address_of(),
                                       c_uint8_ptr(p256_modulus),
                                       c_uint8_ptr(p256_b),
                                       c_uint8_ptr(p256_order),
                                       c_size_t(len(p256_modulus)),
                                       c_ulonglong(getrandbits(64))
                                       )
    if result:
        raise ImportError("Error %d initializing P-256 context" % result)

context = SmartPointer(ec_p256_context.get(), _ec_lib.ec_free_context)
    p256 = _Curve(Integer(p),
                  Integer(b),
                  Integer(order),
                  Integer(Gx),
                  Integer(Gy),
                  None,
                  256,
                  "1.2.840.10045.3.1.7",    # ANSI X9.62
                  context,
                  "NIST P-256",
                  "ecdsa-sha2-nistp256")
    global p256_names
    _curves.update(dict.fromkeys(p256_names, p256))

init_p256()
del init_p256

p384_names = ["p384", "NIST P-384", "P-384", "prime384v1", "secp384r1",
              "nistp384"]

def init_p384():
    p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff
    b = 0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef
    order = 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973
    Gx = 0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760aB7
    Gy = 0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5F

p384_modulus = long_to_bytes(p, 48)
    p384_b = long_to_bytes(b, 48)
    p384_order = long_to_bytes(order, 48)

ec_p384_context = VoidPointer()
    result = _ec_lib.ec_ws_new_context(ec_p384_context.address_of(),
                                       c_uint8_ptr(p384_modulus),
                                       c_uint8_ptr(p384_b),
                                       c_uint8_ptr(p384_order),
                                       c_size_t(len(p384_modulus)),
                                       c_ulonglong(getrandbits(64))
                                       )
    if result:
        raise ImportError("Error %d initializing P-384 context" % result)

context = SmartPointer(ec_p384_context.get(), _ec_lib.ec_free_context)
    p384 = _Curve(Integer(p),
                  Integer(b),
                  Integer(order),
                  Integer(Gx),
                  Integer(Gy),
                  None,
                  384,
                  "1.3.132.0.34",   # SEC 2
                  context,
                  "NIST P-384",
                  "ecdsa-sha2-nistp384")
    global p384_names
    _curves.update(dict.fromkeys(p384_names, p384))

init_p384()
del init_p384

p521_names = ["p521", "NIST P-521", "P-521", "prime521v1", "secp521r1",
              "nistp521"]

def init_p521():
    p = 0x000001ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
    b = 0x00000051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
    order = 0x000001fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409
    Gx = 0x000000c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
    Gy = 0x0000011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650

p521_modulus = long_to_bytes(p, 66)
    p521_b = long_to_bytes(b, 66)
    p521_order = long_to_bytes(order, 66)

ec_p521_context = VoidPointer()
    result = _ec_lib.ec_ws_new_context(ec_p521_context.address_of(),
                                       c_uint8_ptr(p521_modulus),
                                       c_uint8_ptr(p521_b),
                                       c_uint8_ptr(p521_order),
                                       c_size_t(len(p521_modulus)),
                                       c_ulonglong(getrandbits(64))
                                       )
    if result:
        raise ImportError("Error %d initializing P-521 context" % result)

context = SmartPointer(ec_p521_context.get(), _ec_lib.ec_free_context)
    p521 = _Curve(Integer(p),
                  Integer(b),
                  Integer(order),
                  Integer(Gx),
                  Integer(Gy),
                  None,
                  521,
                  "1.3.132.0.35",   # SEC 2
                  context,
                  "NIST P-521",
                  "ecdsa-sha2-nistp521")
    global p521_names
    _curves.update(dict.fromkeys(p521_names, p521))

init_p521()
del init_p521

class UnsupportedEccFeature(ValueError):
    pass

class EccPoint(object):
    """A class to abstract a point over an Elliptic Curve.

The class support special methods for:

* Adding two points: ``R = S + T``
    * In-place addition: ``S += T``
    * Negating a point: ``R = -T``
    * Comparing two points: ``if S == T: ...``
    * Multiplying a point by a scalar: ``R = S*k``
    * In-place multiplication by a scalar: ``T *= k``

:ivar x: The affine X-coordinate of the ECC point
    :vartype x: integer

:ivar y: The affine Y-coordinate of the ECC point
    :vartype y: integer

:ivar xy: The tuple with X- and Y- coordinates
    """

def __init__(self, x, y, curve="p256"):

try:
            self._curve = _curves[curve]
        except KeyError:
            raise ValueError("Unknown curve name %s" % str(curve))
        self._curve_name = curve

modulus_bytes = self.size_in_bytes()
        context = self._curve.context

xb = long_to_bytes(x, modulus_bytes)
        yb = long_to_bytes(y, modulus_bytes)
        if len(xb) != modulus_bytes or len(yb) != modulus_bytes:
            raise ValueError("Incorrect coordinate length")

self._point = VoidPointer()
        result = _ec_lib.ec_ws_new_point(self._point.address_of(),
                                         c_uint8_ptr(xb),
                                         c_uint8_ptr(yb),
                                         c_size_t(modulus_bytes),
                                         context.get())
        if result:
            if result == 15:
                raise ValueError("The EC point does not belong to the curve")
            raise ValueError("Error %d while instantiating an EC point" % result)

# Ensure that object disposal of this Python object will (eventually)
        # free the memory allocated by the raw library for the EC point
        self._point = SmartPointer(self._point.get(),
                                   _ec_lib.ec_free_point)

def set(self, point):
        self._point = VoidPointer()
        result = _ec_lib.ec_ws_clone(self._point.address_of(),
                                     point._point.get())
        if result:
            raise ValueError("Error %d while cloning an EC point" % result)

self._point = SmartPointer(self._point.get(),
                                   _ec_lib.ec_free_point)
        return self

def __eq__(self, point):
        return 0 == _ec_lib.ec_ws_cmp(self._point.get(), point._point.get())

def __neg__(self):
        np = self.copy()
        result = _ec_lib.ec_ws_neg(np._point.get())
        if result:
            raise ValueError("Error %d while inverting an EC point" % result)
        return np

def copy(self):
        """Return a copy of this point."""
        x, y = self.xy
        np = EccPoint(x, y, self._curve_name)
        return np

def is_point_at_infinity(self):
        """``True`` if this is the point-at-infinity."""
        return self.xy == (0, 0)

def point_at_infinity(self):
        """Return the point-at-infinity for the curve this point is on."""
        return EccPoint(0, 0, self._curve_name)

@property
    def x(self):
        return self.xy[0]

@property
    def y(self):
        return self.xy[1]

@property
    def xy(self):
        modulus_bytes = self.size_in_bytes()
        xb = bytearray(modulus_bytes)
        yb = bytearray(modulus_bytes)
        result = _ec_lib.ec_ws_get_xy(c_uint8_ptr(xb),
                                      c_uint8_ptr(yb),
                                      c_size_t(modulus_bytes),
                                      self._point.get())
        if result:
            raise ValueError("Error %d while encoding an EC point" % result)

return (Integer(bytes_to_long(xb)), Integer(bytes_to_long(yb)))

def size_in_bytes(self):
        """Size of each coordinate, in bytes."""
        return (self.size_in_bits() + 7) // 8

def size_in_bits(self):
        """Size of each coordinate, in bits."""
        return self._curve.modulus_bits

def double(self):
        """Double this point (in-place operation).

:Return:
            :class:`EccPoint` : this same object (to enable chaining)
        """

result = _ec_lib.ec_ws_double(self._point.get())
        if result:
            raise ValueError("Error %d while doubling an EC point" % result)
        return self

def __iadd__(self, point):
        """Add a second point to this one"""

result = _ec_lib.ec_ws_add(self._point.get(), point._point.get())
        if result:
            if result == 16:
                raise ValueError("EC points are not on the same curve")
            raise ValueError("Error %d while adding two EC points" % result)
        return self

def __add__(self, point):
        """Return a new point, the addition of this one and another"""

np = self.copy()
        np += point
        return np

def __imul__(self, scalar):
        """Multiply this point by a scalar"""

if scalar < 0:
            raise ValueError("Scalar multiplication is only defined for non-negative integers")
        sb = long_to_bytes(scalar)
        result = _ec_lib.ec_ws_scalar(self._point.get(),
                                      c_uint8_ptr(sb),
                                      c_size_t(len(sb)),
                                      c_ulonglong(getrandbits(64)))
        if result:
            raise ValueError("Error %d during scalar multiplication" % result)
        return self

def __mul__(self, scalar):
        """Return a new point, the scalar product of this one"""

np = self.copy()
        np *= scalar
        return np

def __rmul__(self, left_hand):
        return self.__mul__(left_hand)

# Last piece of initialization
p256_G = EccPoint(_curves['p256'].Gx, _curves['p256'].Gy, "p256")
p256 = _curves['p256']._replace(G=p256_G)
_curves.update(dict.fromkeys(p256_names, p256))
del p256_G, p256, p256_names

p384_G = EccPoint(_curves['p384'].Gx, _curves['p384'].Gy, "p384")
p384 = _curves['p384']._replace(G=p384_G)
_curves.update(dict.fromkeys(p384_names, p384))
del p384_G, p384, p384_names

p521_G = EccPoint(_curves['p521'].Gx, _curves['p521'].Gy, "p521")
p521 = _curves['p521']._replace(G=p521_G)
_curves.update(dict.fromkeys(p521_names, p521))
del p521_G, p521, p521_names

class EccKey(object):
    r"""Class defining an ECC key.
    Do not instantiate directly.
    Use :func:`generate`, :func:`construct` or :func:`import_key` instead.

:ivar curve: The name of the ECC as defined in :numref:`curve_names`.
    :vartype curve: string

:ivar pointQ: an ECC point representating the public component
    :vartype pointQ: :class:`EccPoint`

:ivar d: A scalar representating the private component
    :vartype d: integer
    """

def __init__(self, **kwargs):
        """Create a new ECC key

Keywords:
          curve : string
            It must be *"p256"*, *"P-256"*, *"prime256v1"* or *"secp256r1"*.
          d : integer
            Only for a private key. It must be in the range ``[1..order-1]``.
          point : EccPoint
            Mandatory for a public key. If provided for a private key,
            the implementation will NOT check whether it matches ``d``.
        """

kwargs_ = dict(kwargs)
        curve_name = kwargs_.pop("curve", None)
        self._d = kwargs_.pop("d", None)
        self._point = kwargs_.pop("point", None)
        if kwargs_:
            raise TypeError("Unknown parameters: " + str(kwargs_))

if curve_name not in _curves:
            raise ValueError("Unsupported curve (%s)", curve_name)
        self._curve = _curves[curve_name]

if self._d is None:
            if self._point is None:
                raise ValueError("Either private or public ECC component must be specified, not both")
        else:
            self._d = Integer(self._d)
            if not 1 <= self._d < self._curve.order:
                raise ValueError("Invalid ECC private component")

self.curve = self._curve.desc

def __eq__(self, other):
        if other.has_private() != self.has_private():
            return False

return other.pointQ == self.pointQ

def __repr__(self):
        if self.has_private():
            extra = ", d=%d" % int(self._d)
        else:
            extra = ""
        x, y = self.pointQ.xy
        return "EccKey(curve='%s', point_x=%d, point_y=%d%s)" % (self._curve.desc, x, y, extra)

def has_private(self):
        """``True`` if this key can be used for making signatures or decrypting data."""

return self._d is not None

def _sign(self, z, k):
        assert 0 < k < self._curve.order

order = self._curve.order
        blind = Integer.random_range(min_inclusive=1,
                                     max_exclusive=order)

blind_d = self._d * blind
        inv_blind_k = (blind * k).inverse(order)

r = (self._curve.G * k).x % order
        s = inv_blind_k * (blind * z + blind_d * r) % order
        return (r, s)

def _verify(self, z, rs):
        order = self._curve.order
        sinv = rs[1].inverse(order)
        point1 = self._curve.G * ((sinv * z) % order)
        point2 = self.pointQ * ((sinv * rs[0]) % order)
        return (point1 + point2).x == rs[0]

@property
    def d(self):
        if not self.has_private():
            raise ValueError("This is not a private ECC key")
        return self._d

@property
    def pointQ(self):
        if self._point is None:
            self._point = self._curve.G * self._d
        return self._point

def public_key(self):
        """A matching ECC public key.

Returns:
            a new :class:`EccKey` object
        """

return EccKey(curve=self._curve.desc, point=self.pointQ)

def _export_subjectPublicKeyInfo(self, compress):

# See 2.2 in RFC5480 and 2.3.3 in SEC1
        # The first byte is:
        # - 0x02:   compressed, only X-coordinate, Y-coordinate is even
        # - 0x03:   compressed, only X-coordinate, Y-coordinate is odd
        # - 0x04:   uncompressed, X-coordinate is followed by Y-coordinate
        #
        # PAI is in theory encoded as 0x00.

modulus_bytes = self.pointQ.size_in_bytes()

if compress:
            first_byte = 2 + self.pointQ.y.is_odd()
            public_key = (bchr(first_byte) +
                          self.pointQ.x.to_bytes(modulus_bytes))
        else:
            public_key = (b'\x04' +
                          self.pointQ.x.to_bytes(modulus_bytes) +
                          self.pointQ.y.to_bytes(modulus_bytes))

unrestricted_oid = "1.2.840.10045.2.1"
        return _create_subject_public_key_info(unrestricted_oid,
                                               public_key,
                                               DerObjectId(self._curve.oid))

def _export_private_der(self, include_ec_params=True):

assert self.has_private()

# ECPrivateKey ::= SEQUENCE {
        #           version        INTEGER { ecPrivkeyVer1(1) } (ecPrivkeyVer1),
        #           privateKey     OCTET STRING,
        #           parameters [0] ECParameters {{ NamedCurve }} OPTIONAL,
        #           publicKey  [1] BIT STRING OPTIONAL
        #    }

# Public key - uncompressed form
        modulus_bytes = self.pointQ.size_in_bytes()
        public_key = (b'\x04' +
                      self.pointQ.x.to_bytes(modulus_bytes) +
                      self.pointQ.y.to_bytes(modulus_bytes))

seq = [1,
               DerOctetString(self.d.to_bytes(modulus_bytes)),
               DerObjectId(self._curve.oid, explicit=0),
               DerBitString(public_key, explicit=1)]

if not include_ec_params:
            del seq[2]

return DerSequence(seq).encode()

def _export_pkcs8(self, **kwargs):
        from Crypto.IO import PKCS8

if kwargs.get('passphrase', None) is not None and 'protection' not in kwargs:
            raise ValueError("At least the 'protection' parameter should be present")

unrestricted_oid = "1.2.840.10045.2.1"
        private_key = self._export_private_der(include_ec_params=False)
        result = PKCS8.wrap(private_key,
                            unrestricted_oid,
                            key_params=DerObjectId(self._curve.oid),
                            **kwargs)
        return result

def _export_public_pem(self, compress):
        from Crypto.IO import PEM

encoded_der = self._export_subjectPublicKeyInfo(compress)
        return PEM.encode(encoded_der, "PUBLIC KEY")

def _export_private_pem(self, passphrase, **kwargs):
        from Crypto.IO import PEM

encoded_der = self._export_private_der()
        return PEM.encode(encoded_der, "EC PRIVATE KEY", passphrase, **kwargs)

def _export_private_clear_pkcs8_in_clear_pem(self):
        from Crypto.IO import PEM

encoded_der = self._export_pkcs8()
        return PEM.encode(encoded_der, "PRIVATE KEY")

def _export_private_encrypted_pkcs8_in_clear_pem(self, passphrase, **kwargs):
        from Crypto.IO import PEM

assert passphrase
        if 'protection' not in kwargs:
            raise ValueError("At least the 'protection' parameter should be present")
        encoded_der = self._export_pkcs8(passphrase=passphrase, **kwargs)
        return PEM.encode(encoded_der, "ENCRYPTED PRIVATE KEY")

def _export_openssh(self, compress):
        if self.has_private():
            raise ValueError("Cannot export OpenSSH private keys")

desc = self._curve.openssh
        modulus_bytes = self.pointQ.size_in_bytes()

middle = desc.split("-")[2]
        comps = (tobytes(desc), tobytes(middle), public_key)
        blob = b"".join([struct.pack(">I", len(x)) + x for x in comps])
        return desc + " " + tostr(binascii.b2a_base64(blob))

def export_key(self, **kwargs):
        """Export this ECC key.

Args:
          format (string):
            The format to use for encoding the key:

- ``'DER'``. The key will be encoded in ASN.1 DER format (binary).
              For a public key, the ASN.1 ``subjectPublicKeyInfo`` structure
              defined in `RFC5480`_ will be used.
              For a private key, the ASN.1 ``ECPrivateKey`` structure defined
              in `RFC5915`_ is used instead (possibly within a PKCS#8 envelope,
              see the ``use_pkcs8`` flag below).
            - ``'PEM'``. The key will be encoded in a PEM_ envelope (ASCII).
            - ``'OpenSSH'``. The key will be encoded in the OpenSSH_ format
              (ASCII, public keys only).

passphrase (byte string or string):
            The passphrase to use for protecting the private key.

use_pkcs8 (boolean):
            Only relevant for private keys.

If ``True`` (default and recommended), the `PKCS#8`_ representation
            will be used.

If ``False``, the much weaker `PEM encryption`_ mechanism will be used.

protection (string):
            When a private key is exported with password-protection
            and PKCS#8 (both ``DER`` and ``PEM`` formats), this parameter MUST be
            present and be a valid algorithm supported by :mod:`Crypto.IO.PKCS8`.
            It is recommended to use ``PBKDF2WithHMAC-SHA1AndAES128-CBC``.

compress (boolean):
            If ``True``, a more compact representation of the public key
            with the X-coordinate only is used.

If ``False`` (default), the full public key will be exported.

.. warning::
            If you don't provide a passphrase, the private key will be
            exported in the clear!

.. note::
            When exporting a private key with password-protection and `PKCS#8`_
            (both ``DER`` and ``PEM`` formats), any extra parameters
            to ``export_key()`` will be passed to :mod:`Crypto.IO.PKCS8`.

.. _PEM:        http://www.ietf.org/rfc/rfc1421.txt
        .. _`PEM encryption`: http://www.ietf.org/rfc/rfc1423.txt
        .. _`PKCS#8`:   http://www.ietf.org/rfc/rfc5208.txt
        .. _OpenSSH:    http://www.openssh.com/txt/rfc5656.txt
        .. _RFC5480:    https://tools.ietf.org/html/rfc5480
        .. _RFC5915:    http://www.ietf.org/rfc/rfc5915.txt

Returns:
            A multi-line string (for PEM and OpenSSH) or bytes (for DER) with the encoded key.
        """

args = kwargs.copy()
        ext_format = args.pop("format")
        if ext_format not in ("PEM", "DER", "OpenSSH"):
            raise ValueError("Unknown format '%s'" % ext_format)

compress = args.pop("compress", False)

if self.has_private():
            passphrase = args.pop("passphrase", None)
            if is_string(passphrase):
                passphrase = tobytes(passphrase)
                if not passphrase:
                    raise ValueError("Empty passphrase")
            use_pkcs8 = args.pop("use_pkcs8", True)
            if ext_format == "PEM":
                if use_pkcs8:
                    if passphrase:
                        return self._export_private_encrypted_pkcs8_in_clear_pem(passphrase, **args)
                    else:
                        return self._export_private_clear_pkcs8_in_clear_pem()
                else:
                    return self._export_private_pem(passphrase, **args)
            elif ext_format == "DER":
                # DER
                if passphrase and not use_pkcs8:
                    raise ValueError("Private keys can only be encrpyted with DER using PKCS#8")
                if use_pkcs8:
                    return self._export_pkcs8(passphrase=passphrase, **args)
                else:
                    return self._export_private_der()
            else:
                raise ValueError("Private keys cannot be exported in OpenSSH format")
        else:  # Public key
            if args:
                raise ValueError("Unexpected parameters: '%s'" % args)
            if ext_format == "PEM":
                return self._export_public_pem(compress)
            elif ext_format == "DER":
                return self._export_subjectPublicKeyInfo(compress)
            else:
                return self._export_openssh(compress)

def generate(**kwargs):
    """Generate a new private key on the given curve.

Args:

curve (string):
        Mandatory. It must be a curve name defined in :numref:`curve_names`.

randfunc (callable):
        Optional. The RNG to read randomness from.
        If ``None``, :func:`Crypto.Random.get_random_bytes` is used.
    """

curve_name = kwargs.pop("curve")
    curve = _curves[curve_name]
    randfunc = kwargs.pop("randfunc", get_random_bytes)
    if kwargs:
        raise TypeError("Unknown parameters: " + str(kwargs))

d = Integer.random_range(min_inclusive=1,
                             max_exclusive=curve.order,
                             randfunc=randfunc)

return EccKey(curve=curve_name, d=d)

def construct(**kwargs):
    """Build a new ECC key (private or public) starting
    from some base components.

Args:

curve (string):
        Mandatory. It must be a curve name defined in :numref:`curve_names`.

d (integer):
        Only for a private key. It must be in the range ``[1..order-1]``.

point_x (integer):
        Mandatory for a public key. X coordinate (affine) of the ECC point.

point_y (integer):
        Mandatory for a public key. Y coordinate (affine) of the ECC point.

Returns:
      :class:`EccKey` : a new ECC key object
    """

curve_name = kwargs["curve"]
    curve = _curves[curve_name]
    point_x = kwargs.pop("point_x", None)
    point_y = kwargs.pop("point_y", None)

if "point" in kwargs:
        raise TypeError("Unknown keyword: point")

if None not in (point_x, point_y):
        # ValueError is raised if the point is not on the curve
        kwargs["point"] = EccPoint(point_x, point_y, curve_name)

# Validate that the private key matches the public one
    d = kwargs.get("d", None)
    if d is not None and "point" in kwargs:
        pub_key = curve.G * d
        if pub_key.xy != (point_x, point_y):
            raise ValueError("Private and public ECC keys do not match")

return EccKey(**kwargs)

def _import_public_der(curve_oid, ec_point):
    """Convert an encoded EC point into an EccKey object

curve_name: string with the OID of the curve
    ec_point: byte string with the EC point (not DER encoded)

"""

for curve_name, curve in _curves.items():
        if curve.oid == curve_oid:
            break
    else:
        raise UnsupportedEccFeature("Unsupported ECC curve (OID: %s)" % curve_oid)

# See 2.2 in RFC5480 and 2.3.3 in SEC1
    # The first byte is:
    # - 0x02:   compressed, only X-coordinate, Y-coordinate is even
    # - 0x03:   compressed, only X-coordinate, Y-coordinate is odd
    # - 0x04:   uncompressed, X-coordinate is followed by Y-coordinate
    #
    # PAI is in theory encoded as 0x00.

modulus_bytes = curve.p.size_in_bytes()
    point_type = bord(ec_point[0])

# Uncompressed point
    if point_type == 0x04:
        if len(ec_point) != (1 + 2 * modulus_bytes):
            raise ValueError("Incorrect EC point length")
        x = Integer.from_bytes(ec_point[1:modulus_bytes+1])
        y = Integer.from_bytes(ec_point[modulus_bytes+1:])
    # Compressed point
    elif point_type in (0x02, 0x3):
        if len(ec_point) != (1 + modulus_bytes):
            raise ValueError("Incorrect EC point length")
        x = Integer.from_bytes(ec_point[1:])
        y = (x**3 - x*3 + curve.b).sqrt(curve.p)    # Short Weierstrass
        if point_type == 0x02 and y.is_odd():
            y = curve.p - y
        if point_type == 0x03 and y.is_even():
            y = curve.p - y
    else:
        raise ValueError("Incorrect EC point encoding")

return construct(curve=curve_name, point_x=x, point_y=y)

def _import_subjectPublicKeyInfo(encoded, *kwargs):
    """Convert a subjectPublicKeyInfo into an EccKey object"""

# See RFC5480

# Parse the generic subjectPublicKeyInfo structure
    oid, ec_point, params = _expand_subject_public_key_info(encoded)

# ec_point must be an encoded OCTET STRING
    # params is encoded ECParameters

# We accept id-ecPublicKey, id-ecDH, id-ecMQV without making any
    # distiction for now.

# Restrictions can be captured in the key usage certificate
    # extension
    unrestricted_oid = "1.2.840.10045.2.1"
    ecdh_oid = "1.3.132.1.12"
    ecmqv_oid = "1.3.132.1.13"

if oid not in (unrestricted_oid, ecdh_oid, ecmqv_oid):
        raise UnsupportedEccFeature("Unsupported ECC purpose (OID: %s)" % oid)

# Parameters are mandatory for all three types
    if not params:
        raise ValueError("Missing ECC parameters")

# ECParameters ::= CHOICE {
    #   namedCurve         OBJECT IDENTIFIER
    #   -- implicitCurve   NULL
    #   -- specifiedCurve  SpecifiedECDomain
    # }
    #
    # implicitCurve and specifiedCurve are not supported (as per RFC)
    curve_oid = DerObjectId().decode(params).value

return _import_public_der(curve_oid, ec_point)

def _import_private_der(encoded, passphrase, curve_oid=None):

# See RFC5915 https://tools.ietf.org/html/rfc5915
    #
    # ECPrivateKey ::= SEQUENCE {
    #           version        INTEGER { ecPrivkeyVer1(1) } (ecPrivkeyVer1),
    #           privateKey     OCTET STRING,
    #           parameters [0] ECParameters {{ NamedCurve }} OPTIONAL,
    #           publicKey  [1] BIT STRING OPTIONAL
    #    }

private_key = DerSequence().decode(encoded, nr_elements=(3, 4))
    if private_key[0] != 1:
        raise ValueError("Incorrect ECC private key version")

try:
        parameters = DerObjectId(explicit=0).decode(private_key[2]).value
        if curve_oid is not None and parameters != curve_oid:
            raise ValueError("Curve mismatch")
        curve_oid = parameters
    except ValueError:
        pass

if curve_oid is None:
        raise ValueError("No curve found")

for curve_name, curve in _curves.items():
        if curve.oid == curve_oid:
            break
    else:
        raise UnsupportedEccFeature("Unsupported ECC curve (OID: %s)" % curve_oid)

scalar_bytes = DerOctetString().decode(private_key[1]).payload
    modulus_bytes = curve.p.size_in_bytes()
    if len(scalar_bytes) != modulus_bytes:
        raise ValueError("Private key is too small")
    d = Integer.from_bytes(scalar_bytes)

# Decode public key (if any)
    if len(private_key) == 4:
        public_key_enc = DerBitString(explicit=1).decode(private_key[3]).value
        public_key = _import_public_der(curve_oid, public_key_enc)
        point_x = public_key.pointQ.x
        point_y = public_key.pointQ.y
    else:
        point_x = point_y = None

return construct(curve=curve_name, d=d, point_x=point_x, point_y=point_y)

def _import_pkcs8(encoded, passphrase):
    from Crypto.IO import PKCS8

# From RFC5915, Section 1:
    #
    # Distributing an EC private key with PKCS#8 [RFC5208] involves including:
    # a) id-ecPublicKey, id-ecDH, or id-ecMQV (from [RFC5480]) with the
    #    namedCurve as the parameters in the privateKeyAlgorithm field; and
    # b) ECPrivateKey in the PrivateKey field, which is an OCTET STRING.

algo_oid, private_key, params = PKCS8.unwrap(encoded, passphrase)

# We accept id-ecPublicKey, id-ecDH, id-ecMQV without making any
    # distiction for now.
    unrestricted_oid = "1.2.840.10045.2.1"
    ecdh_oid = "1.3.132.1.12"
    ecmqv_oid = "1.3.132.1.13"

if algo_oid not in (unrestricted_oid, ecdh_oid, ecmqv_oid):
        raise UnsupportedEccFeature("Unsupported ECC purpose (OID: %s)" % algo_oid)

curve_oid = DerObjectId().decode(params).value

return _import_private_der(private_key, passphrase, curve_oid)

def _import_x509_cert(encoded, *kwargs):

sp_info = _extract_subject_public_key_info(encoded)
    return _import_subjectPublicKeyInfo(sp_info)

def _import_der(encoded, passphrase):

try:
        return _import_subjectPublicKeyInfo(encoded, passphrase)
    except UnsupportedEccFeature as err:
        raise err
    except (ValueError, TypeError, IndexError):
        pass

try:
        return _import_x509_cert(encoded, passphrase)
    except UnsupportedEccFeature as err:
        raise err
    except (ValueError, TypeError, IndexError):
        pass

try:
        return _import_private_der(encoded, passphrase)
    except UnsupportedEccFeature as err:
        raise err
    except (ValueError, TypeError, IndexError):
        pass

try:
        return _import_pkcs8(encoded, passphrase)
    except UnsupportedEccFeature as err:
        raise err
    except (ValueError, TypeError, IndexError):
        pass

raise ValueError("Not an ECC DER key")

def _import_openssh_public(encoded):
    keystring = binascii.a2b_base64(encoded.split(b' ')[1])

keyparts = []
    while len(keystring) > 4:
        lk = struct.unpack(">I", keystring[:4])[0]
        keyparts.append(keystring[4:4 + lk])
        keystring = keystring[4 + lk:]

for curve_name, curve in _curves.items():
        middle = tobytes(curve.openssh.split("-")[2])
        if keyparts[1] == middle:
            break
    else:
        raise ValueError("Unsupported ECC curve")

return _import_public_der(curve.oid, keyparts[2])

def _import_openssh_private_ecc(data, password):

from ._openssh import (import_openssh_private_generic,
                           read_bytes, read_string, check_padding)

ssh_name, decrypted = import_openssh_private_generic(data, password)

name, decrypted = read_string(decrypted)
    if name not in _curves:
        raise UnsupportedEccFeature("Unsupported ECC curve %s" % name)
    curve = _curves[name]
    modulus_bytes = (curve.modulus_bits + 7) // 8

public_key, decrypted = read_bytes(decrypted)

if bord(public_key[0]) != 4:
        raise ValueError("Only uncompressed OpenSSH EC keys are supported")
    if len(public_key) != 2 * modulus_bytes + 1:
        raise ValueError("Incorrect public key length")

point_x = Integer.from_bytes(public_key[1:1+modulus_bytes])
    point_y = Integer.from_bytes(public_key[1+modulus_bytes:])
    point = EccPoint(point_x, point_y, curve=name)

private_key, decrypted = read_bytes(decrypted)
    d = Integer.from_bytes(private_key)

_, padded = read_string(decrypted)  # Comment
    check_padding(padded)

return EccKey(curve=name, d=d, point=point)

def import_key(encoded, passphrase=None):
    """Import an ECC key (public or private).

Args:
      encoded (bytes or multi-line string):
        The ECC key to import.

An ECC **public** key can be:

- An X.509 certificate, binary (DER) or ASCII (PEM)
        - An X.509 ``subjectPublicKeyInfo``, binary (DER) or ASCII (PEM)
        - An OpenSSH line (e.g. the content of ``~/.ssh/id_ecdsa``, ASCII)

An ECC **private** key can be:

- In binary format (DER, see section 3 of `RFC5915`_ or `PKCS#8`_)
        - In ASCII format (PEM or `OpenSSH 6.5+`_)

Private keys can be in the clear or password-protected.

For details about the PEM encoding, see `RFC1421`_/`RFC1423`_.

passphrase (byte string):
        The passphrase to use for decrypting a private key.
        Encryption may be applied protected at the PEM level or at the PKCS#8 level.
        This parameter is ignored if the key in input is not encrypted.

Returns:
      :class:`EccKey` : a new ECC key object

Raises:
      ValueError: when the given key cannot be parsed (possibly because
        the pass phrase is wrong).

.. _RFC1421: http://www.ietf.org/rfc/rfc1421.txt
    .. _RFC1423: http://www.ietf.org/rfc/rfc1423.txt
    .. _RFC5915: http://www.ietf.org/rfc/rfc5915.txt
    .. _`PKCS#8`: http://www.ietf.org/rfc/rfc5208.txt
    .. _`OpenSSH 6.5+`: https://flak.tedunangst.com/post/new-openssh-key-format-and-bcrypt-pbkdf
    """

from Crypto.IO import PEM

encoded = tobytes(encoded)
    if passphrase is not None:
        passphrase = tobytes(passphrase)

# PEM
    if encoded.startswith(b'-----BEGIN OPENSSH PRIVATE KEY'):
        text_encoded = tostr(encoded)
        openssh_encoded, marker, enc_flag = PEM.decode(text_encoded, passphrase)
        result = _import_openssh_private_ecc(openssh_encoded, passphrase)
        return result

elif encoded.startswith(b'-----'):

text_encoded = tostr(encoded)

# Remove any EC PARAMETERS section
        # Ignore its content because the curve type must be already given in the key
        if sys.version_info[:2] != (2, 6):
            ecparams_start = "-----BEGIN EC PARAMETERS-----"
            ecparams_end = "-----END EC PARAMETERS-----"
            text_encoded = re.sub(ecparams_start + ".*?" + ecparams_end, "",
                                  text_encoded,
                                  flags=re.DOTALL)

der_encoded, marker, enc_flag = PEM.decode(text_encoded, passphrase)
        if enc_flag:
            passphrase = None
        try:
            result = _import_der(der_encoded, passphrase)
        except UnsupportedEccFeature as uef:
            raise uef
        except ValueError:
            raise ValueError("Invalid DER encoding inside the PEM file")
        return result

# OpenSSH
    if encoded.startswith(b'ecdsa-sha2-'):
        return _import_openssh_public(encoded)

# DER
    if len(encoded) > 0 and bord(encoded[0]) == 0x30:
        return _import_der(encoded, passphrase)

raise ValueError("ECC key format is not supported")

if __name__ == "__main__":

import time

d = 0xc51e4753afdec1e6b6c6a5b992f43f8dd0c7a8933072708b6522468b2ffb06fd

point = _curves['p256'].G.copy()
    count = 3000

start = time.time()
    for x in range(count):
        pointX = point * d
    print("(P-256 G)", (time.time() - start) / count * 1000, "ms")

start = time.time()
    for x in range(count):
        pointX = pointX * d
    print("(P-256 arbitrary point)", (time.time() - start) / count * 1000, "ms")

cmd: