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# This file is licensed under the BSD 2-Clause License.
# See https://opensource.org/licenses/BSD-2-Clause for details.
import threading
from Crypto.Util.number import bytes_to_long, long_to_bytes
from Crypto.Util._raw_api import (VoidPointer, null_pointer,
SmartPointer, c_size_t, c_uint8_ptr,
c_ulonglong)
from Crypto.Math.Numbers import Integer
from Crypto.Random.random import getrandbits
class CurveID(object):
P192 = 1
P224 = 2
P256 = 3
P384 = 4
P521 = 5
ED25519 = 6
ED448 = 7
CURVE25519 = 8
CURVE448 = 9
class _Curves(object):
curves = {}
curves_lock = threading.RLock()
p192_names = ["p192", "NIST P-192", "P-192", "prime192v1", "secp192r1",
"nistp192"]
p224_names = ["p224", "NIST P-224", "P-224", "prime224v1", "secp224r1",
"nistp224"]
p256_names = ["p256", "NIST P-256", "P-256", "prime256v1", "secp256r1",
"nistp256"]
p384_names = ["p384", "NIST P-384", "P-384", "prime384v1", "secp384r1",
"nistp384"]
p521_names = ["p521", "NIST P-521", "P-521", "prime521v1", "secp521r1",
"nistp521"]
ed25519_names = ["ed25519", "Ed25519"]
ed448_names = ["ed448", "Ed448"]
curve25519_names = ["curve25519", "Curve25519", "X25519"]
curve448_names = ["curve448", "Curve448", "X448"]
all_names = p192_names + p224_names + p256_names + p384_names + p521_names + \
ed25519_names + ed448_names + curve25519_names + curve448_names
def __contains__(self, item):
return item in self.all_names
def __dir__(self):
return self.all_names
def load(self, name):
if name in self.p192_names:
from . import _nist_ecc
p192 = _nist_ecc.p192_curve()
p192.id = CurveID.P192
self.curves.update(dict.fromkeys(self.p192_names, p192))
elif name in self.p224_names:
from . import _nist_ecc
p224 = _nist_ecc.p224_curve()
p224.id = CurveID.P224
self.curves.update(dict.fromkeys(self.p224_names, p224))
elif name in self.p256_names:
from . import _nist_ecc
p256 = _nist_ecc.p256_curve()
p256.id = CurveID.P256
self.curves.update(dict.fromkeys(self.p256_names, p256))
elif name in self.p384_names:
from . import _nist_ecc
p384 = _nist_ecc.p384_curve()
p384.id = CurveID.P384
self.curves.update(dict.fromkeys(self.p384_names, p384))
elif name in self.p521_names:
from . import _nist_ecc
p521 = _nist_ecc.p521_curve()
p521.id = CurveID.P521
self.curves.update(dict.fromkeys(self.p521_names, p521))
elif name in self.ed25519_names:
from . import _edwards
ed25519 = _edwards.ed25519_curve()
ed25519.id = CurveID.ED25519
self.curves.update(dict.fromkeys(self.ed25519_names, ed25519))
elif name in self.ed448_names:
from . import _edwards
ed448 = _edwards.ed448_curve()
ed448.id = CurveID.ED448
self.curves.update(dict.fromkeys(self.ed448_names, ed448))
elif name in self.curve25519_names:
from . import _montgomery
curve25519 = _montgomery.curve25519_curve()
curve25519.id = CurveID.CURVE25519
self.curves.update(dict.fromkeys(self.curve25519_names, curve25519))
elif name in self.curve448_names:
from . import _montgomery
curve448 = _montgomery.curve448_curve()
curve448.id = CurveID.CURVE448
self.curves.update(dict.fromkeys(self.curve448_names, curve448))
else:
raise ValueError("Unsupported curve '%s'" % name)
return self.curves[name]
def __getitem__(self, name):
with self.curves_lock:
curve = self.curves.get(name)
if curve is None:
curve = self.load(name)
if name in self.curve25519_names or name in self.curve448_names:
curve.G = EccXPoint(curve.Gx, name)
else:
curve.G = EccPoint(curve.Gx, curve.Gy, name)
curve.is_edwards = curve.id in (CurveID.ED25519, CurveID.ED448)
curve.is_montgomery = curve.id in (CurveID.CURVE25519,
CurveID.CURVE448)
curve.is_weierstrass = not (curve.is_edwards or
curve.is_montgomery)
return curve
def items(self):
# Load all curves
for name in self.all_names:
_ = self[name]
return self.curves.items()
_curves = _Curves()
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 curve: The **canonical** name of the curve as defined in the `ECC table`_.
:vartype curve: string
: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 = self._curve.canonical
if self._curve.id == CurveID.CURVE25519:
raise ValueError("EccPoint cannot be created for Curve25519")
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 = self._curve.rawlib.new_point
free_func = self._curve.rawlib.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 = self._curve.rawlib.clone
free_func = self._curve.rawlib.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 = self._curve.rawlib.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 = self._curve.rawlib.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)
return np
def is_point_at_infinity(self):
"""``True`` if this is the *point-at-infinity*."""
if self._curve.is_edwards:
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._curve.is_edwards:
return EccPoint(0, 1, self.curve)
else:
return EccPoint(0, 0, self.curve)
@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 = self._curve.rawlib.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 = self._curve.rawlib.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 = self._curve.rawlib.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 = self._curve.rawlib.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)
class EccXPoint(object):
"""A class to model a point on an Elliptic Curve,
where only the X-coordinate is exposed.
The class supports operators for:
* Multiplying a point by a scalar: ``R = S*k``
* In-place multiplication by a scalar: ``T *= k``
:ivar curve: The **canonical** name of the curve as defined in the `ECC table`_.
:vartype curve: string
:ivar x: The affine X-coordinate of the ECC point
:vartype x: integer
"""
def __init__(self, x, curve):
# Once encoded, x must not exceed the length of the modulus,
# but its value may match or exceed the modulus itself
# (i.e., non-canonical value)
try:
self._curve = _curves[curve]
except KeyError:
raise ValueError("Unknown curve name %s" % str(curve))
self.curve = self._curve.canonical
if self._curve.id not in (CurveID.CURVE25519, CurveID.CURVE448):
raise ValueError("EccXPoint can only be created for Curve25519/Curve448")
new_point = self._curve.rawlib.new_point
free_func = self._curve.rawlib.free_point
self._point = VoidPointer()
try:
context = self._curve.context.get()
except AttributeError:
context = null_pointer
modulus_bytes = self.size_in_bytes()
if x is None:
xb = null_pointer
else:
xb = c_uint8_ptr(long_to_bytes(x, modulus_bytes))
if len(xb) != modulus_bytes:
raise ValueError("Incorrect coordinate length")
self._point = VoidPointer()
result = new_point(self._point.address_of(),
xb,
c_size_t(modulus_bytes),
context)
if result == 15:
raise ValueError("The EC point does not belong to the curve")
if result:
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 = self._curve.rawlib.clone
free_func = self._curve.rawlib.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, EccXPoint):
return False
cmp_func = self._curve.rawlib.cmp
p1 = self._point.get()
p2 = point._point.get()
res = cmp_func(p1, p2)
return 0 == res
def copy(self):
"""Return a copy of this point."""
try:
x = self.x
except ValueError:
return self.point_at_infinity()
return EccXPoint(x, self.curve)
def is_point_at_infinity(self):
"""``True`` if this is the *point-at-infinity*."""
try:
_ = self.x
except ValueError:
return True
return False
def point_at_infinity(self):
"""Return the *point-at-infinity* for the curve."""
return EccXPoint(None, self.curve)
@property
def x(self):
modulus_bytes = self.size_in_bytes()
xb = bytearray(modulus_bytes)
get_x = self._curve.rawlib.get_x
result = get_x(c_uint8_ptr(xb),
c_size_t(modulus_bytes),
self._point.get())
if result == 19: # ERR_ECC_PAI
raise ValueError("No X coordinate for the point at infinity")
if result:
raise ValueError("Error %d while getting X of an EC point" % result)
return Integer(bytes_to_long(xb))
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 __imul__(self, scalar):
"""Multiply this point by a scalar"""
scalar_func = self._curve.rawlib.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)
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