"""Implementation of Edwards Digital Signature Algorithm."""
import hashlib
from ._sha3 import shake_256
from . import ellipticcurve
from ._compat import (
remove_whitespace,
bit_length,
bytes_to_int,
int_to_bytes,
compat26_str,
)
# edwards25519, defined in RFC7748
_p = 2**255 - 19
_a = -1
_d = int(
remove_whitespace(
"370957059346694393431380835087545651895421138798432190163887855330"
"85940283555"
)
)
_h = 8
_Gx = int(
remove_whitespace(
"151122213495354007725011514095885315114540126930418572060461132"
"83949847762202"
)
)
_Gy = int(
remove_whitespace(
"463168356949264781694283940034751631413079938662562256157830336"
"03165251855960"
)
)
_r = 2**252 + 0x14DEF9DEA2F79CD65812631A5CF5D3ED
def _sha512(data):
return hashlib.new("sha512", compat26_str(data)).digest()
curve_ed25519 = ellipticcurve.CurveEdTw(_p, _a, _d, _h, _sha512)
generator_ed25519 = ellipticcurve.PointEdwards(
curve_ed25519, _Gx, _Gy, 1, _Gx * _Gy % _p, _r, generator=True
)
# edwards448, defined in RFC7748
_p = 2**448 - 2**224 - 1
_a = 1
_d = -39081 % _p
_h = 4
_Gx = int(
remove_whitespace(
"224580040295924300187604334099896036246789641632564134246125461"
"686950415467406032909029192869357953282578032075146446173674602635"
"247710"
)
)
_Gy = int(
remove_whitespace(
"298819210078481492676017930443930673437544040154080242095928241"
"372331506189835876003536878655418784733982303233503462500531545062"
"832660"
)
)
_r = 2**446 - 0x8335DC163BB124B65129C96FDE933D8D723A70AADC873D6D54A7BB0D
def _shake256(data):
return shake_256(data, 114)
curve_ed448 = ellipticcurve.CurveEdTw(_p, _a, _d, _h, _shake256)
generator_ed448 = ellipticcurve.PointEdwards(
curve_ed448, _Gx, _Gy, 1, _Gx * _Gy % _p, _r, generator=True
)
[docs]
class PublicKey(object):
"""Public key for the Edwards Digital Signature Algorithm."""
def __init__(self, generator, public_key, public_point=None):
self.generator = generator
self.curve = generator.curve()
self.__encoded = public_key
# plus one for the sign bit and round up
self.baselen = (bit_length(self.curve.p()) + 1 + 7) // 8
if len(public_key) != self.baselen:
raise ValueError(
"Incorrect size of the public key, expected: {0} bytes".format(
self.baselen
)
)
if public_point:
self.__point = public_point
else:
self.__point = ellipticcurve.PointEdwards.from_bytes(
self.curve, public_key
)
def __eq__(self, other):
if isinstance(other, PublicKey):
return (
self.curve == other.curve and self.__encoded == other.__encoded
)
return NotImplemented
def __ne__(self, other):
return not self == other
@property
def point(self):
return self.__point
@point.setter
def point(self, other):
if self.__point != other:
raise ValueError("Can't change the coordinates of the point")
self.__point = other
[docs]
def public_point(self):
return self.__point
[docs]
def public_key(self):
return self.__encoded
[docs]
def verify(self, data, signature):
"""Verify a Pure EdDSA signature over data."""
data = compat26_str(data)
if len(signature) != 2 * self.baselen:
raise ValueError(
"Invalid signature length, expected: {0} bytes".format(
2 * self.baselen
)
)
R = ellipticcurve.PointEdwards.from_bytes(
self.curve, signature[: self.baselen]
)
S = bytes_to_int(signature[self.baselen :], "little")
if S >= self.generator.order():
raise ValueError("Invalid signature")
dom = bytearray()
if self.curve == curve_ed448:
dom = bytearray(b"SigEd448" + b"\x00\x00")
k = bytes_to_int(
self.curve.hash_func(dom + R.to_bytes() + self.__encoded + data),
"little",
)
if self.generator * S != self.__point * k + R:
raise ValueError("Invalid signature")
return True
[docs]
class PrivateKey(object):
"""Private key for the Edwards Digital Signature Algorithm."""
def __init__(self, generator, private_key):
self.generator = generator
self.curve = generator.curve()
# plus one for the sign bit and round up
self.baselen = (bit_length(self.curve.p()) + 1 + 7) // 8
if len(private_key) != self.baselen:
raise ValueError(
"Incorrect size of private key, expected: {0} bytes".format(
self.baselen
)
)
self.__private_key = bytes(private_key)
self.__h = bytearray(self.curve.hash_func(private_key))
self.__public_key = None
a = self.__h[: self.baselen]
a = self._key_prune(a)
scalar = bytes_to_int(a, "little")
self.__s = scalar
@property
def private_key(self):
return self.__private_key
def __eq__(self, other):
if isinstance(other, PrivateKey):
return (
self.curve == other.curve
and self.__private_key == other.__private_key
)
return NotImplemented
def __ne__(self, other):
return not self == other
def _key_prune(self, key):
# make sure the key is not in a small subgroup
h = self.curve.cofactor()
if h == 4:
h_log = 2
elif h == 8:
h_log = 3
else:
raise ValueError("Only cofactor 4 and 8 curves supported")
key[0] &= ~((1 << h_log) - 1)
# ensure the highest bit is set but no higher
l = bit_length(self.curve.p())
if l % 8 == 0:
key[-1] = 0
key[-2] |= 0x80
else:
key[-1] = key[-1] & (1 << (l % 8)) - 1 | 1 << (l % 8) - 1
return key
[docs]
def public_key(self):
"""Generate the public key based on the included private key"""
if self.__public_key:
return self.__public_key
public_point = self.generator * self.__s
self.__public_key = PublicKey(
self.generator, public_point.to_bytes(), public_point
)
return self.__public_key
[docs]
def sign(self, data):
"""Perform a Pure EdDSA signature over data."""
data = compat26_str(data)
A = self.public_key().public_key()
prefix = self.__h[self.baselen :]
dom = bytearray()
if self.curve == curve_ed448:
dom = bytearray(b"SigEd448" + b"\x00\x00")
r = bytes_to_int(self.curve.hash_func(dom + prefix + data), "little")
R = (self.generator * r).to_bytes()
k = bytes_to_int(self.curve.hash_func(dom + R + A + data), "little")
k %= self.generator.order()
S = (r + k * self.__s) % self.generator.order()
return R + int_to_bytes(S, self.baselen, "little")