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# Copyright (c) 2022, Legrandin <helderijs@gmail.com>
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import unittest
from binascii import unhexlify
from Crypto.SelfTest.st_common import list_test_cases
from Crypto.SelfTest.loader import load_test_vectors
from Crypto.PublicKey import ECC
from Crypto.PublicKey.ECC import EccPoint, _curves, EccKey
from Crypto.Math.Numbers import Integer
from Crypto.Hash import SHAKE128
class TestEccPoint_Ed448(unittest.TestCase):
Gxy = {"x": 0x4f1970c66bed0ded221d15a622bf36da9e146570470f1767ea6de324a3d3a46412ae1af72ab66511433b80e18b00938e2626a82bc70cc05e,
"y": 0x693f46716eb6bc248876203756c9c7624bea73736ca3984087789c1e05a0c2d73ad3ff1ce67c39c4fdbd132c4ed7c8ad9808795bf230fa14}
G2xy = {"x": 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa955555555555555555555555555555555555555555555555555555555,
"y": 0xae05e9634ad7048db359d6205086c2b0036ed7a035884dd7b7e36d728ad8c4b80d6565833a2a3098bbbcb2bed1cda06bdaeafbcdea9386ed}
G3xy = {"x": 0x865886b9108af6455bd64316cb6943332241b8b8cda82c7e2ba077a4a3fcfe8daa9cbf7f6271fd6e862b769465da8575728173286ff2f8f,
"y": 0xe005a8dbd5125cf706cbda7ad43aa6449a4a8d952356c3b9fce43c82ec4e1d58bb3a331bdb6767f0bffa9a68fed02dafb822ac13588ed6fc}
pointG = EccPoint(Gxy['x'], Gxy['y'], curve="Ed448")
pointG2 = EccPoint(G2xy['x'], G2xy['y'], curve="Ed448")
pointG3 = EccPoint(G3xy['x'], G3xy['y'], curve="Ed448")
def test_init_xy(self):
EccPoint(self.Gxy['x'], self.Gxy['y'], curve="Ed448")
# Neutral point
pai = EccPoint(0, 1, curve="Ed448")
self.assertEqual(pai.x, 0)
self.assertEqual(pai.y, 1)
self.assertEqual(pai.xy, (0, 1))
# G
bp = self.pointG.copy()
self.assertEqual(bp.x, 0x4f1970c66bed0ded221d15a622bf36da9e146570470f1767ea6de324a3d3a46412ae1af72ab66511433b80e18b00938e2626a82bc70cc05e)
self.assertEqual(bp.y, 0x693f46716eb6bc248876203756c9c7624bea73736ca3984087789c1e05a0c2d73ad3ff1ce67c39c4fdbd132c4ed7c8ad9808795bf230fa14)
self.assertEqual(bp.xy, (bp.x, bp.y))
# 2G
bp2 = self.pointG2.copy()
self.assertEqual(bp2.x, 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa955555555555555555555555555555555555555555555555555555555)
self.assertEqual(bp2.y, 0xae05e9634ad7048db359d6205086c2b0036ed7a035884dd7b7e36d728ad8c4b80d6565833a2a3098bbbcb2bed1cda06bdaeafbcdea9386ed)
self.assertEqual(bp2.xy, (bp2.x, bp2.y))
# 5G
EccPoint(x=0x7a9f9335a48dcb0e2ba7601eedb50def80cbcf728562ada756d761e8958812808bc0d57a920c3c96f07b2d8cefc6f950d0a99d1092030034,
y=0xadfd751a2517edd3b9109ce4fd580ade260ca1823ab18fced86551f7b698017127d7a4ee59d2b33c58405512881f225443b4731472f435eb,
curve="Ed448")
# Catch if point is not on the curve
self.assertRaises(ValueError, EccPoint, 34, 35, curve="Ed448")
def test_set(self):
pointW = EccPoint(0, 1, curve="Ed448")
pointW.set(self.pointG)
self.assertEqual(pointW.x, self.pointG.x)
self.assertEqual(pointW.y, self.pointG.y)
def test_copy(self):
pointW = self.pointG.copy()
self.assertEqual(pointW.x, self.pointG.x)
self.assertEqual(pointW.y, self.pointG.y)
def test_equal(self):
pointH = self.pointG.copy()
pointI = self.pointG2.copy()
self.assertEqual(self.pointG, pointH)
self.assertNotEqual(self.pointG, pointI)
def test_pai(self):
pai = EccPoint(0, 1, curve="Ed448")
self.assertTrue(pai.is_point_at_infinity())
self.assertEqual(pai, pai.point_at_infinity())
def test_negate(self):
negG = -self.pointG
sum = self.pointG + negG
self.assertTrue(sum.is_point_at_infinity())
def test_addition(self):
self.assertEqual(self.pointG + self.pointG2, self.pointG3)
self.assertEqual(self.pointG2 + self.pointG, self.pointG3)
self.assertEqual(self.pointG2 + self.pointG.point_at_infinity(), self.pointG2)
self.assertEqual(self.pointG.point_at_infinity() + self.pointG2, self.pointG2)
G5 = self.pointG2 + self.pointG3
self.assertEqual(G5.x, 0x7a9f9335a48dcb0e2ba7601eedb50def80cbcf728562ada756d761e8958812808bc0d57a920c3c96f07b2d8cefc6f950d0a99d1092030034)
self.assertEqual(G5.y, 0xadfd751a2517edd3b9109ce4fd580ade260ca1823ab18fced86551f7b698017127d7a4ee59d2b33c58405512881f225443b4731472f435eb)
def test_inplace_addition(self):
pointH = self.pointG.copy()
pointH += self.pointG
self.assertEqual(pointH, self.pointG2)
pointH += self.pointG
self.assertEqual(pointH, self.pointG3)
pointH += self.pointG.point_at_infinity()
self.assertEqual(pointH, self.pointG3)
def test_doubling(self):
pointH = self.pointG.copy()
pointH.double()
self.assertEqual(pointH.x, self.pointG2.x)
self.assertEqual(pointH.y, self.pointG2.y)
# 2*0
pai = self.pointG.point_at_infinity()
pointR = pai.copy()
pointR.double()
self.assertEqual(pointR, pai)
def test_scalar_multiply(self):
d = 0
pointH = d * self.pointG
self.assertEqual(pointH.x, 0)
self.assertEqual(pointH.y, 1)
d = 1
pointH = d * self.pointG
self.assertEqual(pointH.x, self.pointG.x)
self.assertEqual(pointH.y, self.pointG.y)
d = 2
pointH = d * self.pointG
self.assertEqual(pointH.x, self.pointG2.x)
self.assertEqual(pointH.y, self.pointG2.y)
d = 3
pointH = d * self.pointG
self.assertEqual(pointH.x, self.pointG3.x)
self.assertEqual(pointH.y, self.pointG3.y)
d = 4
pointH = d * self.pointG
self.assertEqual(pointH.x, 0x49dcbc5c6c0cce2c1419a17226f929ea255a09cf4e0891c693fda4be70c74cc301b7bdf1515dd8ba21aee1798949e120e2ce42ac48ba7f30)
self.assertEqual(pointH.y, 0xd49077e4accde527164b33a5de021b979cb7c02f0457d845c90dc3227b8a5bc1c0d8f97ea1ca9472b5d444285d0d4f5b32e236f86de51839)
d = 5
pointH = d * self.pointG
self.assertEqual(pointH.x, 0x7a9f9335a48dcb0e2ba7601eedb50def80cbcf728562ada756d761e8958812808bc0d57a920c3c96f07b2d8cefc6f950d0a99d1092030034)
self.assertEqual(pointH.y, 0xadfd751a2517edd3b9109ce4fd580ade260ca1823ab18fced86551f7b698017127d7a4ee59d2b33c58405512881f225443b4731472f435eb)
d = 10
pointH = d * self.pointG
self.assertEqual(pointH.x, 0x77486f9d19f6411cdd35d30d1c3235f71936452c787e5c034134d3e8172278aca61622bc805761ce3dab65118a0122d73b403165d0ed303d)
self.assertEqual(pointH.y, 0x4d2fea0b026be11024f1f0fe7e94e618e8ac17381ada1d1bf7ee293a68ff5d0bf93c1997dc1aabdc0c7e6381428d85b6b1954a89e4cddf67)
d = 20
pointH = d * self.pointG
self.assertEqual(pointH.x, 0x3c236422354600fe6763defcc1503737e4ed89e262d0de3ec1e552020f2a56fe3b9e1e012d021072598c3c2821e18268bb8fb8339c0d1216)
self.assertEqual(pointH.y, 0xb555b9721f630ccb05fc466de4c74d3d2781e69eca88e1b040844f04cab39fd946f91c688fa42402bb38fb9c3e61231017020b219b4396e1)
d = 255
pointH = d * self.pointG
self.assertEqual(pointH.x, 0xbeb7f8388b05cd9c1aa2e3c0dcf31e2b563659361826225390e7748654f627d5c36cbe627e9019936b56d15d4dad7c337c09bac64ff4197f)
self.assertEqual(pointH.y, 0x1e37312b2dd4e9440c43c6e7725fc4fa3d11e582d4863f1d018e28f50c0efdb1f53f9b01ada7c87fa162b1f0d72401015d57613d25f1ad53)
d = 256
pointH = d * self.pointG
self.assertEqual(pointH.x, 0xf19c34feb56730e3e2be761ac0a2a2b24853b281dda019fc35a5ab58e3696beb39609ae756b0d20fb7ccf0d79aaf5f3bca2e4fdb25bfac1c)
self.assertEqual(pointH.y, 0x3beb69cc9111bffcaddc61d363ce6fe5dd44da4aadce78f52e92e985d5442344ced72c4611ed0daac9f4f5661eab73d7a12d25ce8a30241e)
def test_sizes(self):
self.assertEqual(self.pointG.size_in_bits(), 448)
self.assertEqual(self.pointG.size_in_bytes(), 56)
class TestEccKey_Ed448(unittest.TestCase):
def test_private_key(self):
seed = unhexlify("4adf5d37ac6785e83e99a924f92676d366a78690af59c92b6bdf14f9cdbcf26fdad478109607583d633b60078d61d51d81b7509c5433b0d4c9")
Px = 0x72a01eea003a35f9ac44231dc4aae2a382f351d80bf32508175b0855edcf389aa2bbf308dd961ce361a6e7c2091bc78957f6ebcf3002a617
Py = 0x9e0d08d84586e9aeefecacb41d049b831f1a3ee0c3eada63e34557b30702b50ab59fb372feff7c30b8cbb7dd51afbe88444ec56238722ec1
key = EccKey(curve="Ed448", seed=seed)
self.assertEqual(key.seed, seed)
self.assertEqual(key.d, 0xb07cf179604f83433186e5178760c759c15125ee54ff6f8dcde46e872b709ac82ed0bd0a4e036d774034dcb18a9fb11894657a1485895f80)
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ.x, Px)
self.assertEqual(key.pointQ.y, Py)
point = EccPoint(Px, Py, "ed448")
key = EccKey(curve="Ed448", seed=seed, point=point)
self.assertEqual(key.d, 0xb07cf179604f83433186e5178760c759c15125ee54ff6f8dcde46e872b709ac82ed0bd0a4e036d774034dcb18a9fb11894657a1485895f80)
self.assertTrue(key.has_private())
self.assertEqual(key.pointQ, point)
# Other names
key = EccKey(curve="ed448", seed=seed)
# Must not accept d parameter
self.assertRaises(ValueError, EccKey, curve="ed448", d=1)
def test_public_key(self):
point = EccPoint(_curves['ed448'].Gx, _curves['ed448'].Gy, curve='ed448')
key = EccKey(curve="ed448", point=point)
self.assertFalse(key.has_private())
self.assertEqual(key.pointQ, point)
def test_public_key_derived(self):
priv_key = EccKey(curve="ed448", seed=b'H'*57)
pub_key = priv_key.public_key()
self.assertFalse(pub_key.has_private())
self.assertEqual(priv_key.pointQ, pub_key.pointQ)
def test_invalid_seed(self):
self.assertRaises(ValueError, lambda: EccKey(curve="ed448", seed=b'H' * 56))
def test_equality(self):
private_key = ECC.construct(seed=b'H'*57, curve="Ed448")
private_key2 = ECC.construct(seed=b'H'*57, curve="ed448")
private_key3 = ECC.construct(seed=b'C'*57, curve="Ed448")
public_key = private_key.public_key()
public_key2 = private_key2.public_key()
public_key3 = private_key3.public_key()
self.assertEqual(private_key, private_key2)
self.assertNotEqual(private_key, private_key3)
self.assertEqual(public_key, public_key2)
self.assertNotEqual(public_key, public_key3)
self.assertNotEqual(public_key, private_key)
def test_name_consistency(self):
key = ECC.generate(curve='ed448')
self.assertIn("curve='Ed448'", repr(key))
self.assertEqual(key.curve, 'Ed448')
self.assertEqual(key.public_key().curve, 'Ed448')
class TestEccModule_Ed448(unittest.TestCase):
def test_generate(self):
key = ECC.generate(curve="Ed448")
self.assertTrue(key.has_private())
point = EccPoint(_curves['Ed448'].Gx, _curves['Ed448'].Gy, curve="Ed448") * key.d
self.assertEqual(key.pointQ, point)
# Always random
key2 = ECC.generate(curve="Ed448")
self.assertNotEqual(key, key2)
# Other names
ECC.generate(curve="Ed448")
# Random source
key1 = ECC.generate(curve="Ed448", randfunc=SHAKE128.new().read)
key2 = ECC.generate(curve="Ed448", randfunc=SHAKE128.new().read)
self.assertEqual(key1, key2)
def test_construct(self):
seed = unhexlify("4adf5d37ac6785e83e99a924f92676d366a78690af59c92b6bdf14f9cdbcf26fdad478109607583d633b60078d61d51d81b7509c5433b0d4c9")
Px = 0x72a01eea003a35f9ac44231dc4aae2a382f351d80bf32508175b0855edcf389aa2bbf308dd961ce361a6e7c2091bc78957f6ebcf3002a617
Py = 0x9e0d08d84586e9aeefecacb41d049b831f1a3ee0c3eada63e34557b30702b50ab59fb372feff7c30b8cbb7dd51afbe88444ec56238722ec1
d = 0xb07cf179604f83433186e5178760c759c15125ee54ff6f8dcde46e872b709ac82ed0bd0a4e036d774034dcb18a9fb11894657a1485895f80
point = EccPoint(Px, Py, curve="Ed448")
# Private key only
key = ECC.construct(curve="Ed448", seed=seed)
self.assertEqual(key.pointQ, point)
self.assertTrue(key.has_private())
# Public key only
key = ECC.construct(curve="Ed448", point_x=Px, point_y=Py)
self.assertEqual(key.pointQ, point)
self.assertFalse(key.has_private())
# Private and public key
key = ECC.construct(curve="Ed448", seed=seed, point_x=Px, point_y=Py)
self.assertEqual(key.pointQ, point)
self.assertTrue(key.has_private())
# Other names
key = ECC.construct(curve="ed448", seed=seed)
def test_negative_construct(self):
coord = dict(point_x=10, point_y=4)
coordG = dict(point_x=_curves['ed448'].Gx, point_y=_curves['ed448'].Gy)
self.assertRaises(ValueError, ECC.construct, curve="Ed448", **coord)
self.assertRaises(ValueError, ECC.construct, curve="Ed448", d=2, **coordG)
self.assertRaises(ValueError, ECC.construct, curve="Ed448", seed=b'H'*58)
def get_tests(config={}):
tests = []
tests += list_test_cases(TestEccPoint_Ed448)
tests += list_test_cases(TestEccKey_Ed448)
tests += list_test_cases(TestEccModule_Ed448)
return tests
if __name__ == '__main__':
def suite():
return unittest.TestSuite(get_tests())
unittest.main(defaultTest='suite')
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