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# ===================================================================
#
# 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 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.Util._raw_api import (load_pycryptodome_raw_lib, VoidPointer,
SmartPointer, c_size_t, c_uint8_ptr,
c_ulonglong, null_pointer)
from Crypto.PublicKey import (_expand_subject_public_key_info,
_create_subject_public_key_info,
_extract_subject_public_key_info)
from Crypto.Hash import SHA512, SHAKE256
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_ws_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_cmp(const EcPoint *ecp1, const EcPoint *ecp2);
int ec_ws_neg(EcPoint *p);
""")
_ed25519_lib = load_pycryptodome_raw_lib("Crypto.PublicKey._ed25519", """
typedef void Point;
int ed25519_new_point(Point **out,
const uint8_t x[32],
const uint8_t y[32],
size_t modsize,
const void *context);
int ed25519_clone(Point **P, const Point *Q);
void ed25519_free_point(Point *p);
int ed25519_cmp(const Point *p1, const Point *p2);
int ed25519_neg(Point *p);
int ed25519_get_xy(uint8_t *xb, uint8_t *yb, size_t modsize, Point *p);
int ed25519_double(Point *p);
int ed25519_add(Point *P1, const Point *P2);
int ed25519_scalar(Point *P, const uint8_t *scalar, size_t scalar_len, uint64_t seed);
""")
_ed448_lib = load_pycryptodome_raw_lib("Crypto.PublicKey._ed448", """
typedef void EcContext;
typedef void PointEd448;
int ed448_new_context(EcContext **pec_ctx);
void ed448_context(EcContext *ec_ctx);
void ed448_free_context(EcContext *ec_ctx);
int ed448_new_point(PointEd448 **out,
const uint8_t x[56],
const uint8_t y[56],
size_t len,
const EcContext *context);
int ed448_clone(PointEd448 **P, const PointEd448 *Q);
void ed448_free_point(PointEd448 *p);
int ed448_cmp(const PointEd448 *p1, const PointEd448 *p2);
int ed448_neg(PointEd448 *p);
int ed448_get_xy(uint8_t *xb, uint8_t *yb, size_t len, const PointEd448 *p);
int ed448_double(PointEd448 *p);
int ed448_add(PointEd448 *P1, const PointEd448 *P2);
int ed448_scalar(PointEd448 *P, const uint8_t *scalar, size_t scalar_len, uint64_t seed);
""")
def lib_func(ecc_obj, func_name):
if ecc_obj._curve.desc == "Ed25519":
result = getattr(_ed25519_lib, "ed25519_" + func_name)
elif ecc_obj._curve.desc == "Ed448":
result = getattr(_ed448_lib, "ed448_" + func_name)
else:
result = getattr(_ec_lib, "ec_ws_" + func_name)
return result
#
# _curves is a database of curve parameters. Items are indexed by their
# human-friendly name, suchas "P-256". Each item has the following fields:
# - p: the prime number that defines the finite field for all modulo operations
# - b: the constant in the Short Weierstrass curve equation
# - order: the number of elements in the group with the generator below
# - Gx the affine coordinate X of the generator point
# - Gy the affine coordinate Y of the generator point
# - G the generator, as an EccPoint object
# - modulus_bits the minimum number of bits for encoding the modulus p
# - oid an ASCII string with the registered ASN.1 Object ID
# - context a raw pointer to memory holding a context for all curve operations (can be NULL)
# - desc an ASCII string describing the curve
# - openssh the ASCII string used in OpenSSH id files for public keys on this curve
# - name the ASCII string which is also a valid key in _curves
_Curve = namedtuple("_Curve", "p b order Gx Gy G modulus_bits oid context desc openssh name")
_curves = {}
p192_names = ["p192", "NIST P-192", "P-192", "prime192v1", "secp192r1",
"nistp192"]
def init_p192():
p = 0xfffffffffffffffffffffffffffffffeffffffffffffffff
b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
order = 0xffffffffffffffffffffffff99def836146bc9b1b4d22831
Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
p192_modulus = long_to_bytes(p, 24)
p192_b = long_to_bytes(b, 24)
p192_order = long_to_bytes(order, 24)
ec_p192_context = VoidPointer()
result = _ec_lib.ec_ws_new_context(ec_p192_context.address_of(),
c_uint8_ptr(p192_modulus),
c_uint8_ptr(p192_b),
c_uint8_ptr(p192_order),
c_size_t(len(p192_modulus)),
c_ulonglong(getrandbits(64))
)
if result:
raise ImportError("Error %d initializing P-192 context" % result)
context = SmartPointer(ec_p192_context.get(), _ec_lib.ec_free_context)
p192 = _Curve(Integer(p),
Integer(b),
Integer(order),
Integer(Gx),
Integer(Gy),
None,
192,
"1.2.840.10045.3.1.1", # ANSI X9.62 / SEC2
context,
"NIST P-192",
"ecdsa-sha2-nistp192",
"p192")
global p192_names
_curves.update(dict.fromkeys(p192_names, p192))
init_p192()
del init_p192
p224_names = ["p224", "NIST P-224", "P-224", "prime224v1", "secp224r1",
"nistp224"]
def init_p224():
p = 0xffffffffffffffffffffffffffffffff000000000000000000000001
b = 0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
order = 0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d
Gx = 0xb70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
Gy = 0xbd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
p224_modulus = long_to_bytes(p, 28)
p224_b = long_to_bytes(b, 28)
p224_order = long_to_bytes(order, 28)
ec_p224_context = VoidPointer()
result = _ec_lib.ec_ws_new_context(ec_p224_context.address_of(),
c_uint8_ptr(p224_modulus),
c_uint8_ptr(p224_b),
c_uint8_ptr(p224_order),
c_size_t(len(p224_modulus)),
c_ulonglong(getrandbits(64))
)
if result:
raise ImportError("Error %d initializing P-224 context" % result)
context = SmartPointer(ec_p224_context.get(), _ec_lib.ec_free_context)
p224 = _Curve(Integer(p),
Integer(b),
Integer(order),
Integer(Gx),
Integer(Gy),
None,
224,
"1.3.132.0.33", # SEC 2
context,
"NIST P-224",
"ecdsa-sha2-nistp224",
"p224")
global p224_names
_curves.update(dict.fromkeys(p224_names, p224))
init_p224()
del init_p224
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 / SEC2
context,
"NIST P-256",
"ecdsa-sha2-nistp256",
"p256")
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",
"p384")
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",
"p521")
global p521_names
_curves.update(dict.fromkeys(p521_names, p521))
init_p521()
del init_p521
ed25519_names = ["ed25519", "Ed25519"]
def init_ed25519():
p = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed # 2**255 - 19
order = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
Gx = 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a
Gy = 0x6666666666666666666666666666666666666666666666666666666666666658
ed25519 = _Curve(Integer(p),
None,
Integer(order),
Integer(Gx),
Integer(Gy),
None,
255,
"1.3.101.112", # RFC8410
None,
"Ed25519", # Used throughout; do not change
"ssh-ed25519",
"ed25519")
global ed25519_names
_curves.update(dict.fromkeys(ed25519_names, ed25519))
init_ed25519()
del init_ed25519
ed448_names = ["ed448", "Ed448"]
def init_ed448():
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff # 2**448 - 2**224 - 1
order = 0x3fffffffffffffffffffffffffffffffffffffffffffffffffffffff7cca23e9c44edb49aed63690216cc2728dc58f552378c292ab5844f3
Gx = 0x4f1970c66bed0ded221d15a622bf36da9e146570470f1767ea6de324a3d3a46412ae1af72ab66511433b80e18b00938e2626a82bc70cc05e
Gy = 0x693f46716eb6bc248876203756c9c7624bea73736ca3984087789c1e05a0c2d73ad3ff1ce67c39c4fdbd132c4ed7c8ad9808795bf230fa14
ed448_context = VoidPointer()
result = _ed448_lib.ed448_new_context(ed448_context.address_of())
if result:
raise ImportError("Error %d initializing Ed448 context" % result)
context = SmartPointer(ed448_context.get(), _ed448_lib.ed448_free_context)
ed448 = _Curve(Integer(p),
None,
Integer(order),
Integer(Gx),
Integer(Gy),
None,
448,
"1.3.101.113", # RFC8410
context,
"Ed448", # Used throughout; do not change
None,
"ed448")
global ed448_names
_curves.update(dict.fromkeys(ed448_names, ed448))
init_ed448()
del init_ed448
class UnsupportedEccFeature(ValueError):
pass
class EccPoint(object):
"""A class to model a point on an Elliptic Curve.
The class supports operators for:
* Adding two points: ``R = S + T``
* In-place addition: ``S += T``
* Negating a point: ``R = -T``
* Comparing two points: ``if S == T: ...`` or ``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 affine 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()
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")
new_point = lib_func(self, "new_point")
free_func = lib_func(self, "free_point")
self._point = VoidPointer()
try:
context = self._curve.context.get()
except AttributeError:
context = null_pointer
result = new_point(self._point.address_of(),
c_uint8_ptr(xb),
c_uint8_ptr(yb),
c_size_t(modulus_bytes),
context)
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(), free_func)
def set(self, point):
clone = lib_func(self, "clone")
free_func = lib_func(self, "free_point")
self._point = VoidPointer()
result = 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(), free_func)
return self
def __eq__(self, point):
if not isinstance(point, EccPoint):
return False
cmp_func = lib_func(self, "cmp")
return 0 == cmp_func(self._point.get(), point._point.get())
# Only needed for Python 2
def __ne__(self, point):
return not self == point
def __neg__(self):
neg_func = lib_func(self, "neg")
np = self.copy()
result = neg_func(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_eddsa(self):
return self._curve.name in ("ed25519", "ed448")
def is_point_at_infinity(self):
"""``True`` if this is the *point-at-infinity*."""
if self._is_eddsa():
return self.x == 0
else:
return self.xy == (0, 0)
def point_at_infinity(self):
"""Return the *point-at-infinity* for the curve."""
if self._is_eddsa():
return EccPoint(0, 1, self._curve_name)
else:
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)
get_xy = lib_func(self, "get_xy")
result = 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).
Returns:
This same object (to enable chaining).
"""
double_func = lib_func(self, "double")
result = double_func(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"""
add_func = lib_func(self, "add")
result = add_func(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"""
scalar_func = lib_func(self, "scalar")
if scalar < 0:
raise ValueError("Scalar multiplication is only defined for non-negative integers")
sb = long_to_bytes(scalar)
result = scalar_func(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
p192_G = EccPoint(_curves['p192'].Gx, _curves['p192'].Gy, "p192")
p192 = _curves['p192']._replace(G=p192_G)
_curves.update(dict.fromkeys(p192_names, p192))
del p192_G, p192, p192_names
p224_G = EccPoint(_curves['p224'].Gx, _curves['p224'].Gy, "p224")
p224 = _curves['p224']._replace(G=p224_G)
_curves.update(dict.fromkeys(p224_names, p224))
del p224_G, p224, p224_names
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
ed25519_G = EccPoint(_curves['Ed25519'].Gx, _curves['Ed25519'].Gy, "Ed25519")
ed25519 = _curves['Ed25519']._replace(G=ed25519_G)
_curves.update(dict.fromkeys(ed25519_names, ed25519))
del ed25519_G, ed25519, ed25519_names
ed448_G = EccPoint(_curves['Ed448'].Gx, _curves['Ed448'].Gy, "Ed448")
ed448 = _curves['Ed448']._replace(G=ed448_G)
_curves.update(dict.fromkeys(ed448_names, ed448))
del ed448_G, ed448, ed448_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 curve as defined in the `ECC table`_.
:vartype curve: string
:ivar pointQ: an ECC point representating the public component.
:vartype pointQ: :class:`EccPoint`
:ivar d: A scalar that represents the private component
in NIST P curves. It is smaller than the
order of the generator point.
:vartype d: integer
:ivar seed: A seed that representats the private component
in EdDSA curves
(Ed25519, 32 bytes; Ed448, 57 bytes).
:vartype seed: bytes
"""
def __init__(self, **kwargs):
"""Create a new ECC key
Keywords:
curve : string
The name of the curve.
d : integer
Mandatory for a private key one NIST P curves.
It must be in the range ``[1..order-1]``.
seed : bytes
Mandatory for a private key on the Ed25519 (32 bytes)
or Ed448 (57 bytes) curve.
point : EccPoint
Mandatory for a public key. If provided for a private key,
the implementation will NOT check whether it matches ``d``.
Only one parameter among ``d``, ``seed`` or ``point`` may be used.
"""
kwargs_ = dict(kwargs)
curve_name = kwargs_.pop("curve", None)
self._d = kwargs_.pop("d", None)
self._seed = kwargs_.pop("seed", None)
self._point = kwargs_.pop("point", None)
if curve_name is None and self._point:
curve_name = self._point._curve_name
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]
self.curve = self._curve.desc
count = int(self._d is not None) + int(self._seed is not None)
if count == 0:
if self._point is None:
raise ValueError("At lest one between parameters 'point', 'd' or 'seed' must be specified")
return
if count == 2:
raise ValueError("Parameters d and seed are mutually exclusive")
# NIST P curves work with d, EdDSA works with seed
if not self._is_eddsa():
if self._seed is not None:
raise ValueError("Parameter 'seed' can only be used with Ed25519 or Ed448")
self._d = Integer(self._d)
if not 1 <= self._d < self._curve.order:
raise ValueError("Parameter d must be an integer smaller than the curve order")
else:
if self._d is not None:
raise ValueError("Parameter d can only be used with NIST P curves")
# RFC 8032, 5.1.5
if self._curve.name == "ed25519":
if len(self._seed) != 32:
raise ValueError("Parameter seed must be 32 bytes long for Ed25519")
seed_hash = SHA512.new(self._seed).digest() # h
self._prefix = seed_hash[32:]
tmp = bytearray(seed_hash[:32])
tmp[0] &= 0xF8
tmp[31] = (tmp[31] & 0x7F) | 0x40
# RFC 8032, 5.2.5
elif self._curve.name == "ed448":
if len(self._seed) != 57:
raise ValueError("Parameter seed must be 57 bytes long for Ed448")
seed_hash = SHAKE256.new(self._seed).read(114) # h
self._prefix = seed_hash[57:]
tmp = bytearray(seed_hash[:57])
tmp[0] &= 0xFC
tmp[55] |= 0x80
tmp[56] = 0
self._d = Integer.from_bytes(tmp, byteorder='little')
def _is_eddsa(self):
return self._curve.desc in ("Ed25519", "Ed448")
def __eq__(self, other):
if not isinstance(other, EccKey):
return False
if other.has_private() != self.has_private():
return False
return other.pointQ == self.pointQ
def __repr__(self):
if self.has_private():
if self._is_eddsa():
extra = ", seed=%s" % tostr(binascii.hexlify(self._seed))
else:
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
# ECDSA
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)
# ECDSA
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 seed(self):
if not self.has_private():
raise ValueError("This is not a private ECC key")
return self._seed
@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_SEC1(self, compress):
if self._is_eddsa():
raise ValueError("SEC1 format is unsupported for EdDSA curves")
# 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:
if self.pointQ.y.is_odd():
first_byte = b'\x03'
else:
first_byte = b'\x02'
public_key = (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))
return public_key
def _export_eddsa(self):
x, y = self.pointQ.xy
if self._curve.name == "ed25519":
result = bytearray(y.to_bytes(32, byteorder='little'))
result[31] = ((x & 1) << 7) | result[31]
elif self._curve.name == "ed448":
result = bytearray(y.to_bytes(57, byteorder='little'))
result[56] = (x & 1) << 7
else:
raise ValueError("Not an EdDSA key to export")
return bytes(result)
def _export_subjectPublicKeyInfo(self, compress):
if self._is_eddsa():
oid = self._curve.oid
public_key = self._export_eddsa()
params = None
else:
oid = "1.2.840.10045.2.1" # unrestricted
public_key = self._export_SEC1(compress)
params = DerObjectId(self._curve.oid)
return _create_subject_public_key_info(oid,
public_key,
params)
def _export_rfc5915_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")
if self._is_eddsa():
oid = self._curve.oid
private_key = DerOctetString(self._seed).encode()
params = None
else:
oid = "1.2.840.10045.2.1" # unrestricted
private_key = self._export_rfc5915_private_der(include_ec_params=False)
params = DerObjectId(self._curve.oid)
result = PKCS8.wrap(private_key,
oid,
key_params=params,
**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_rfc5915_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
if desc is None:
raise ValueError("Cannot export %s keys as OpenSSH" % self._curve.name)
elif desc == "ssh-ed25519":
public_key = self._export_eddsa()
comps = (tobytes(desc), tobytes(public_key))
else:
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))
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).
- ``'SEC1'``. The public key (i.e., the EC point) will be encoded
into ``bytes`` according to Section 2.3.3 of `SEC1`_
(which is a subset of the older X9.62 ITU standard).
Only for NIST P-curves.
- ``'raw'``. The public key will be encoded as ``bytes``,
without any metadata.
* For NIST P-curves: equivalent to ``'SEC1'``.
* For EdDSA curves: ``bytes`` in the format defined in `RFC8032`_.
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. It must be ``True`` for EdDSA curves.
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``, the method returns a more compact representation
of the public key, with the X-coordinate only.
If ``False`` (default), the method returns the full public key.
This parameter is ignored for EdDSA curves, as compression is
mandatory.
.. 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
.. _OpenSSH: http://www.openssh.com/txt/rfc5656.txt
.. _RFC5480: https://tools.ietf.org/html/rfc5480
.. _SEC1: https://www.secg.org/sec1-v2.pdf
Returns:
A multi-line string (for ``'PEM'`` and ``'OpenSSH'``) or
``bytes`` (for ``'DER'``, ``'SEC1'``, and ``'raw'``) with the encoded key.
"""
args = kwargs.copy()
ext_format = args.pop("format")
if ext_format not in ("PEM", "DER", "OpenSSH", "SEC1", "raw"):
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 not use_pkcs8 and self._is_eddsa():
raise ValueError("'pkcs8' must be True for EdDSA curves")
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_rfc5915_private_der()
else:
raise ValueError("Private keys cannot be exported "
"in the '%s' format" % ext_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)
elif ext_format == "SEC1":
return self._export_SEC1(compress)
elif ext_format == "raw":
if self._curve.name in ('ed25519', 'ed448'):
return self._export_eddsa()
else:
return self._export_SEC1(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 the `ECC table`_.
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))
if _curves[curve_name].name == "ed25519":
seed = randfunc(32)
new_key = EccKey(curve=curve_name, seed=seed)
elif _curves[curve_name].name == "ed448":
seed = randfunc(57)
new_key = EccKey(curve=curve_name, seed=seed)
else:
d = Integer.random_range(min_inclusive=1,
max_exclusive=curve.order,
randfunc=randfunc)
new_key = EccKey(curve=curve_name, d=d)
return new_key
def construct(**kwargs):
"""Build a new ECC key (private or public) starting
from some base components.
In most cases, you will already have an existing key
which you can read in with :func:`import_key` instead
of this function.
Args:
curve (string):
Mandatory. The name of the elliptic curve, as defined in the `ECC table`_.
d (integer):
Mandatory for a private key and a NIST P-curve (e.g., P-256):
the integer in the range ``[1..order-1]`` that represents the key.
seed (bytes):
Mandatory for a private key and an EdDSA curve.
It must be 32 bytes for Ed25519, and 57 bytes for Ed448.
point_x (integer):
Mandatory for a public key: the X coordinate (affine) of the ECC point.
point_y (integer):
Mandatory for a public key: the 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)
new_key = EccKey(**kwargs)
# Validate that the private key matches the public one
# because EccKey will not do that automatically
if new_key.has_private() and 'point' in kwargs:
pub_key = curve.G * new_key.d
if pub_key.xy != (point_x, point_y):
raise ValueError("Private and public ECC keys do not match")
return new_key
def _import_public_der(ec_point, curve_oid=None, curve_name=None):
"""Convert an encoded EC point into an EccKey object
ec_point: byte string with the EC point (SEC1-encoded)
curve_oid: string with the name the curve
curve_name: string with the OID of the curve
Either curve_id or curve_name must be specified
"""
for _curve_name, curve in _curves.items():
if curve_oid and curve.oid == curve_oid:
break
if curve_name == _curve_name:
break
else:
if curve_oid:
raise UnsupportedEccFeature("Unsupported ECC curve (OID: %s)" % curve_oid)
else:
raise UnsupportedEccFeature("Unsupported ECC curve (%s)" % curve_name)
# 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, 0x03):
if len(ec_point) != (1 + modulus_bytes):
raise ValueError("Incorrect EC point length")
x = Integer.from_bytes(ec_point[1:])
# Right now, we only support Short Weierstrass curves
y = (x**3 - x*3 + curve.b).sqrt(curve.p)
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)
nist_p_oids = (
"1.2.840.10045.2.1", # id-ecPublicKey (unrestricted)
"1.3.132.1.12", # id-ecDH
"1.3.132.1.13" # id-ecMQV
)
eddsa_oids = {
"1.3.101.112": ("Ed25519", _import_ed25519_public_key), # id-Ed25519
"1.3.101.113": ("Ed448", _import_ed448_public_key) # id-Ed448
}
if oid in nist_p_oids:
# See RFC5480
# Parameters are mandatory and encoded as ECParameters
# ECParameters ::= CHOICE {
# namedCurve OBJECT IDENTIFIER
# -- implicitCurve NULL
# -- specifiedCurve SpecifiedECDomain
# }
# implicitCurve and specifiedCurve are not supported (as per RFC)
if not params:
raise ValueError("Missing ECC parameters for ECC OID %s" % oid)
try:
curve_oid = DerObjectId().decode(params).value
except ValueError:
raise ValueError("Error decoding namedCurve")
# ECPoint ::= OCTET STRING
return _import_public_der(ec_point, curve_oid=curve_oid)
elif oid in eddsa_oids:
# See RFC8410
curve_name, import_eddsa_public_key = eddsa_oids[oid]
# Parameters must be absent
if params:
raise ValueError("Unexpected ECC parameters for ECC OID %s" % oid)
x, y = import_eddsa_public_key(ec_point)
return construct(point_x=x, point_y=y, curve=curve_name)
else:
raise UnsupportedEccFeature("Unsupported ECC OID: %s" % oid)
def _import_rfc5915_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) > 2:
public_key_enc = DerBitString(explicit=1).decode(private_key[-1]).value
public_key = _import_public_der(public_key_enc, curve_oid=curve_oid)
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
algo_oid, private_key, params = PKCS8.unwrap(encoded, passphrase)
nist_p_oids = (
"1.2.840.10045.2.1", # id-ecPublicKey (unrestricted)
"1.3.132.1.12", # id-ecDH
"1.3.132.1.13" # id-ecMQV
)
eddsa_oids = {
"1.3.101.112": "Ed25519", # id-Ed25519
"1.3.101.113": "Ed448", # id-Ed448
}
if algo_oid in nist_p_oids:
curve_oid = DerObjectId().decode(params).value
return _import_rfc5915_der(private_key, passphrase, curve_oid)
elif algo_oid in eddsa_oids:
if params is not None:
raise ValueError("EdDSA ECC private key must not have parameters")
curve_oid = None
seed = DerOctetString().decode(private_key).payload
return construct(curve=eddsa_oids[algo_oid], seed=seed)
else:
raise UnsupportedEccFeature("Unsupported ECC purpose (OID: %s)" % algo_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_rfc5915_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):
parts = encoded.split(b' ')
if len(parts) not in (2, 3):
raise ValueError("Not an openssh public key")
try:
keystring = binascii.a2b_base64(parts[1])
keyparts = []
while len(keystring) > 4:
lk = struct.unpack(">I", keystring[:4])[0]
keyparts.append(keystring[4:4 + lk])
keystring = keystring[4 + lk:]
if parts[0] != keyparts[0]:
raise ValueError("Mismatch in openssh public key")
# NIST P curves
if parts[0].startswith(b"ecdsa-sha2-"):
for curve_name, curve in _curves.items():
if curve.openssh is None:
continue
if not curve.openssh.startswith("ecdsa-sha2"):
continue
middle = tobytes(curve.openssh.split("-")[2])
if keyparts[1] == middle:
break
else:
raise ValueError("Unsupported ECC curve: " + middle)
ecc_key = _import_public_der(keyparts[2], curve_oid=curve.oid)
# EdDSA
elif parts[0] == b"ssh-ed25519":
x, y = _import_ed25519_public_key(keyparts[1])
ecc_key = construct(curve="Ed25519", point_x=x, point_y=y)
else:
raise ValueError("Unsupported SSH key type: " + parts[0])
except (IndexError, TypeError, binascii.Error):
raise ValueError("Error parsing SSH key type: " + parts[0])
return ecc_key
def _import_openssh_private_ecc(data, password):
from ._openssh import (import_openssh_private_generic,
read_bytes, read_string, check_padding)
key_type, decrypted = import_openssh_private_generic(data, password)
eddsa_keys = {
"ssh-ed25519": ("Ed25519", _import_ed25519_public_key, 32),
}
# https://datatracker.ietf.org/doc/html/draft-miller-ssh-agent-04
if key_type.startswith("ecdsa-sha2"):
ecdsa_curve_name, decrypted = read_string(decrypted)
if ecdsa_curve_name not in _curves:
raise UnsupportedEccFeature("Unsupported ECC curve %s" % ecdsa_curve_name)
curve = _curves[ecdsa_curve_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:])
private_key, decrypted = read_bytes(decrypted)
d = Integer.from_bytes(private_key)
params = {'d': d, 'curve': ecdsa_curve_name}
elif key_type in eddsa_keys:
curve_name, import_eddsa_public_key, seed_len = eddsa_keys[key_type]
public_key, decrypted = read_bytes(decrypted)
point_x, point_y = import_eddsa_public_key(public_key)
private_public_key, decrypted = read_bytes(decrypted)
seed = private_public_key[:seed_len]
params = {'seed': seed, 'curve': curve_name}
else:
raise ValueError("Unsupport SSH agent key type:" + key_type)
_, padded = read_string(decrypted) # Comment
check_padding(padded)
return construct(point_x=point_x, point_y=point_y, **params)
def _import_ed25519_public_key(encoded):
"""Import an Ed25519 ECC public key, encoded as raw bytes as described
in RFC8032_.
Args:
encoded (bytes):
The Ed25519 public key to import. It must be 32 bytes long.
Returns:
:class:`EccKey` : a new ECC key object
Raises:
ValueError: when the given key cannot be parsed.
.. _RFC8032: https://datatracker.ietf.org/doc/html/rfc8032
"""
if len(encoded) != 32:
raise ValueError("Incorrect length. Only Ed25519 public keys are supported.")
p = Integer(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed) # 2**255 - 19
d = 37095705934669439343138083508754565189542113879843219016388785533085940283555
y = bytearray(encoded)
x_lsb = y[31] >> 7
y[31] &= 0x7F
point_y = Integer.from_bytes(y, byteorder='little')
if point_y >= p:
raise ValueError("Invalid Ed25519 key (y)")
if point_y == 1:
return 0, 1
u = (point_y**2 - 1) % p
v = ((point_y**2 % p) * d + 1) % p
try:
v_inv = v.inverse(p)
x2 = (u * v_inv) % p
point_x = Integer._tonelli_shanks(x2, p)
if (point_x & 1) != x_lsb:
point_x = p - point_x
except ValueError:
raise ValueError("Invalid Ed25519 public key")
return point_x, point_y
def _import_ed448_public_key(encoded):
"""Import an Ed448 ECC public key, encoded as raw bytes as described
in RFC8032_.
Args:
encoded (bytes):
The Ed448 public key to import. It must be 57 bytes long.
Returns:
:class:`EccKey` : a new ECC key object
Raises:
ValueError: when the given key cannot be parsed.
.. _RFC8032: https://datatracker.ietf.org/doc/html/rfc8032
"""
if len(encoded) != 57:
raise ValueError("Incorrect length. Only Ed448 public keys are supported.")
p = Integer(0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff) # 2**448 - 2**224 - 1
d = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffff6756
y = encoded[:56]
x_lsb = bord(encoded[56]) >> 7
point_y = Integer.from_bytes(y, byteorder='little')
if point_y >= p:
raise ValueError("Invalid Ed448 key (y)")
if point_y == 1:
return 0, 1
u = (point_y**2 - 1) % p
v = ((point_y**2 % p) * d - 1) % p
try:
v_inv = v.inverse(p)
x2 = (u * v_inv) % p
point_x = Integer._tonelli_shanks(x2, p)
if (point_x & 1) != x_lsb:
point_x = p - point_x
except ValueError:
raise ValueError("Invalid Ed448 public key")
return point_x, point_y
def import_key(encoded, passphrase=None, curve_name=None):
"""Import an ECC key (public or private).
Args:
encoded (bytes or multi-line string):
The ECC key to import.
The function will try to automatically detect the right format.
Supported formats for an ECC **public** key:
* X.509 certificate: binary (DER) or ASCII (PEM).
* X.509 ``subjectPublicKeyInfo``: binary (DER) or ASCII (PEM).
* SEC1_ (or X9.62), as ``bytes``. NIST P curves only.
You must also provide the ``curve_name`` (with a value from the `ECC table`_)
* OpenSSH line, defined in RFC5656_ and RFC8709_ (ASCII).
This is normally the content of files like ``~/.ssh/id_ecdsa.pub``.
Supported formats for an ECC **private** key:
* A binary ``ECPrivateKey`` structure, as defined in `RFC5915`_ (DER).
NIST P curves only.
* A `PKCS#8`_ structure (or the more recent Asymmetric Key Package, RFC5958_): binary (DER) or ASCII (PEM).
* `OpenSSH 6.5`_ and newer versions (ASCII).
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 (not recommended)
or at the PKCS#8 level (recommended).
This parameter is ignored if the key in input is not encrypted.
curve_name (string):
For a SEC1 encoding only. This is the name of the curve,
as defined in the `ECC table`_.
.. note::
To import EdDSA private and public keys, when encoded as raw ``bytes``, use:
* :func:`Crypto.Signature.eddsa.import_public_key`, or
* :func:`Crypto.Signature.eddsa.import_private_key`.
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: https://datatracker.ietf.org/doc/html/rfc1421
.. _RFC1423: https://datatracker.ietf.org/doc/html/rfc1423
.. _RFC5915: https://datatracker.ietf.org/doc/html/rfc5915
.. _RFC5656: https://datatracker.ietf.org/doc/html/rfc5656
.. _RFC8709: https://datatracker.ietf.org/doc/html/rfc8709
.. _RFC5958: https://datatracker.ietf.org/doc/html/rfc5958
.. _`PKCS#8`: https://datatracker.ietf.org/doc/html/rfc5208
.. _`OpenSSH 6.5`: https://flak.tedunangst.com/post/new-openssh-key-format-and-bcrypt-pbkdf
.. _SEC1: https://www.secg.org/sec1-v2.pdf
"""
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
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-', b'ssh-ed25519')):
return _import_openssh_public(encoded)
# DER
if len(encoded) > 0 and bord(encoded[0]) == 0x30:
return _import_der(encoded, passphrase)
# SEC1
if len(encoded) > 0 and bord(encoded[0]) in b'\x02\x03\x04':
if curve_name is None:
raise ValueError("No curve name was provided")
return _import_public_der(encoded, curve_name=curve_name)
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")