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curve25519 ec-kcdsa python impl
# a pedagogical implementation of curve25519 with ec-kcdsa
# coded by doctorevil to validate nxt's port of Matthijs van Duin's implementation
# warning: this implementation is not timing attack resistant
# ec arithmetic equations from http://hyperelliptic.org/EFD/g1p/auto-montgom.html
from hashlib import sha256
from ecdsa.numbertheory import square_root_mod_prime, SquareRootError, inverse_mod
CURVE_P = 2**255 - 19
CURVE_A = 486662
CURVE_ORDER = 7237005577332262213973186563042994240857116359379907606001950938285454250989L
CURVE_G_X = 9
CURVE_G_Y = 14781619447589544791020593568409986887264606134616475288964881837755586237401
def le32(n): # to little endian
return ('%064x' % n).decode('hex')[::-1]
def from_le32(s):
return int(s[::-1].encode('hex'), 16)
def curve25519_x_to_y(x):
t = (x ** 3 + CURVE_A * x ** 2 + x) % CURVE_P
try:
return square_root_mod_prime(t, CURVE_P)
except SquareRootError:
return None
def curve25519_affine_add(x1, y1, x2, y2):
if (x1, y1) == (1, 0):
return x2, y2
if (x2, y2) == (1, 0):
return x1, y1
if x1 == x2 and y1 != y2:
return (1, 0)
if x1 == x2 and y1 == y2:
return curve25519_affine_double(x1, y1)
t1 = (y2 - y1) ** 2 % CURVE_P
t2 = (x2 - x1) ** 2 % CURVE_P
x3 = (t1 * inverse_mod(t2, CURVE_P) - 486662 - x1 - x2) % CURVE_P
t1 = (2 * x1 + x2 + 486662) % CURVE_P
t2 = (y2 - y1) % CURVE_P
t3 = (x2 - x1) % CURVE_P
y3 = t1 * (y2 - y1) * inverse_mod((x2 - x1) % CURVE_P, CURVE_P) - \
t2 ** 3 * inverse_mod(t3 ** 3 % CURVE_P, CURVE_P) - y1
y3 = y3 % CURVE_P
return x3, y3
def curve25519_affine_double(x1, y1):
if (x1, y1) == (1, 0):
return (1, 0)
x2 = (3 * x1 ** 2 + 2 * CURVE_A * x1 + 1) ** 2 * inverse_mod((2 * y1) ** 2, CURVE_P) - CURVE_A - x1 - x1
y2 = (2 * x1 + x1 + CURVE_A) * (3 * x1 ** 2 + 2 * CURVE_A * x1 + 1) * inverse_mod(2 * y1, CURVE_P) - \
(3 * x1 ** 2 + 2 * CURVE_A * x1 + 1) ** 3 * inverse_mod((2 * y1) ** 3, CURVE_P) - y1
return x2 % CURVE_P, y2 % CURVE_P
def curve25519_affine_mult(n, x1, y1):
tx, ty = 1, 0
for bit in map(int, bin(n)[2:]):
tx, ty = curve25519_affine_double(tx, ty)
if bit:
tx, ty = curve25519_affine_add(tx, ty, x1, y1)
return tx, ty
def clamp(secret):
a = ord(secret[0])
a &= 248
b = ord(secret[31])
b &= 127
b |= 64
return chr(a) + secret[1:-1] + chr(b)
def is_negative(x):
return x & 1
def curve25519_eckcdsa_keygen(secret):
s = from_le32(clamp(secret))
x, y = curve25519_affine_mult(s, CURVE_G_X, CURVE_G_Y)
signing_key = inverse_mod(s if is_negative(y) else -s, CURVE_ORDER)
return le32(x), le32(signing_key), le32(s)
def kcdsa_sign(message, secret):
verification_key, signing_key, ignored = curve25519_eckcdsa_keygen(secret)
m = sha256(message).digest()
k = sha256(m + signing_key).digest()
k_Gx, ignored, k_clamped = curve25519_eckcdsa_keygen(k)
r = sha256(m + k_Gx).digest()
s = (from_le32(k_clamped) - from_le32(r)) * from_le32(signing_key) % CURVE_ORDER
return le32(s) + r
def kcdsa_verify(signature, message, public_key):
if len(signature) != 64:
return False
s = from_le32(signature[:32])
r = from_le32(signature[32:64])
px = from_le32(public_key)
py = curve25519_x_to_y(px)
if py is None: # pubkey is bogus; bail
return False
tx1, ty1 = curve25519_affine_mult(s, px, py)
tx2, ty2 = curve25519_affine_mult(r, CURVE_G_X, CURVE_G_Y)
if not is_negative(py):
ty2 = -ty2
k_Gx, k_Gy = curve25519_affine_add(tx1, ty1, tx2, ty2)
m = sha256(message).digest()
return le32(r) == sha256(m + le32(k_Gx)).digest()
if __name__ == "__main__":
import sys
passphrase = sys.argv[1].encode('utf-8')
secret = sha256(passphrase).digest()
message = sys.argv[2].encode('utf-8')
verification_key, signing_key, secret_clamped = curve25519_eckcdsa_keygen(secret)
print 'pubkey', verification_key.encode('hex')
print 'signing key', signing_key.encode('hex')
signature = kcdsa_sign(message, secret)
print 'signature', signature.encode('hex')
assert kcdsa_verify(signature, message, verification_key)
assert not kcdsa_verify(signature[::-1], signature, verification_key)
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