def test_genkey(self):
for _ in range(1024):
while True:
private = urandom(32)
(v, public, representative) = elligator.scalarbasemult(private)
if v:
break
def test_public(self):
while True:
private = urandom(32)
(v, public, representative) = elligator.scalarbasemult(private)
if v:
break
public2 = elligator.representativetopublic(representative)
self.assertEqual(public, public2)
def test_nacl_scalarmult_curve25519_base(self):
try:
import nacl
while True:
private = urandom(32)
(v, public, representative) = elligator.scalarbasemult(private)
if v:
break
public2 = nacl.crypto_scalarmult_curve25519_base(private)
self.assertEqual(public, public2)
except ImportError:
raise ImportError('Can\'t import TweetNaCl')
def test_kat(self):
kat_vectors = [
(
True,
bytearray((0x4b, 0x97, 0x97, 0xd0, 0x98, 0x5a, 0xf7, 0x42, 0x9b, 0xc3, 0x55, 0xd9, 0x4, 0x81, 0xcf,
0xc7, 0xcc, 0x14, 0x54, 0x5c, 0xa5, 0xe6, 0x7c, 0x84, 0xcb, 0x1b, 0x4a, 0x4c, 0x4d, 0xa1, 0xda, 0x33,)),
bytearray((0xbc, 0x13, 0x1a, 0x67, 0xb, 0x92, 0x2, 0x65, 0x8f, 0x2f, 0x79, 0xa, 0x7e, 0x4, 0x71,
0xd0, 0xe, 0x67, 0x90, 0xdb, 0x4d, 0x59, 0x8, 0xd2, 0x54, 0x4e, 0x5f, 0xbb, 0x8d, 0xa, 0x89, 0x78,)),
bytearray((0x10, 0x3d, 0xba, 0xb8, 0x6f, 0x99, 0xee, 0xdb, 0xec, 0xa, 0xd6, 0x8f, 0xa9, 0x20, 0x3d,
0x5f, 0xd4, 0xf5, 0xe0, 0xdc, 0x48, 0xbc, 0xaf, 0x6c, 0x98, 0x50, 0xd0, 0x1a, 0x12, 0x9f, 0x28, 0x5c,))
),
(
True,
bytearray((0xf1, 0x8, 0x6d, 0x75, 0xb3, 0x59, 0x5c, 0xe7, 0x3c, 0x41, 0xa8, 0x11, 0xbf, 0x1a, 0x10,
0xb1, 0xba, 0x1a, 0x75, 0xe4, 0xff, 0xd4, 0x98, 0x6c, 0x37, 0x98, 0xe3, 0x54, 0xf3, 0x24, 0x6b, 0x50,)),
bytearray((0x6, 0x13, 0x6a, 0x4f, 0x20, 0x93, 0x37, 0x12, 0x4f, 0x4d, 0x92, 0x31, 0xc8, 0x34, 0xe9,
0xa0, 0x94, 0x8f, 0x89, 0x6d, 0xc9, 0x1c, 0x85, 0x5b, 0x32, 0x80, 0xd3, 0xd1, 0x4f, 0x42, 0xe8, 0x4e,)),
bytearray((0x68, 0x4f, 0x96, 0xdf, 0xde, 0xa0, 0x57, 0xf5, 0xb2, 0x3f, 0xf6, 0x29, 0x52, 0xb3, 0x34,
0x95, 0xb0, 0x7b, 0xa3, 0xd5, 0x4, 0xac, 0x79, 0x1d, 0xf, 0x3c, 0x87, 0x52, 0x3a, 0xa7, 0x3f, 0x6d,))
),
(
True,
bytearray((0x49, 0x76, 0xe, 0x1, 0x60, 0x24, 0x44, 0x48, 0x48, 0xc7, 0x9d, 0xc1, 0x81, 0x4, 0x6d, 0xc,
0x3a, 0x48, 0x8e, 0xf8, 0x67, 0xbd, 0xf9, 0xd1, 0x6f, 0x8c, 0x8f, 0xe4, 0x9b, 0x7b, 0x7f, 0x66,)),
bytearray((0xb7, 0xdd, 0x0, 0x28, 0x3, 0xe0, 0x9f, 0x93, 0x52, 0x5d, 0xf6, 0x49, 0xa3, 0x9, 0xbf, 0x29,
0x16, 0x71, 0xfd, 0x82, 0x52, 0x23, 0xf2, 0x96, 0x2, 0xee, 0x97, 0x20, 0xc1, 0xd7, 0xa6, 0x3b,)),
bytearray((0x8, 0x69, 0x14, 0xc7, 0xc7, 0xe8, 0x33, 0x79, 0x27, 0xf4, 0xa7, 0x1c, 0xda, 0x21, 0x25,
0x41, 0x9a, 0xe7, 0xe1, 0x83, 0x90, 0x52, 0x1f, 0xaf, 0x14, 0x3d, 0x5a, 0x2, 0xbc, 0x2e, 0x9c, 0x55,))
),
(
False,
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x78, 0x51, 0x2b, 0xcf, 0xe1, 0x62, 0x1d, 0x53, 0xed, 0xfc, 0xd5, 0xc0, 0x96, 0xc8, 0xb9,
0x96, 0x8e, 0x3, 0x7, 0x5e, 0xc3, 0x3a, 0x2e, 0xea, 0xaa, 0x44, 0x96, 0x64, 0x71, 0xfc, 0x98, 0x65,))
),
(
False,
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x38, 0xa9, 0xb4, 0x8a, 0xe8, 0x8b, 0xad, 0xbe, 0x15, 0xd9, 0xbe, 0x6b, 0x1d, 0xf8, 0x82,
0xa1, 0x89, 0x60, 0xd1, 0x14, 0xb6, 0x74, 0xba, 0xe8, 0x3f, 0xb6, 0xac, 0xd4, 0x5d, 0x94, 0x1, 0x68,))
),
(
True,
bytearray((0x1e, 0x92, 0x62, 0xd, 0xc3, 0x9f, 0xf1, 0x28, 0x86, 0x40, 0x80, 0xb1, 0xfd, 0x37, 0xb9,
0x91, 0xac, 0xcc, 0xbf, 0x3d, 0x2e, 0x48, 0x67, 0xd2, 0xed, 0xf1, 0x75, 0xa6, 0x58, 0x10, 0x6d, 0x55,)),
bytearray((0x5a, 0x25, 0x9d, 0x71, 0x1f, 0xec, 0xb2, 0x6d, 0xe7, 0x8, 0x4f, 0x8d, 0x80, 0x15, 0x4e,
0xec, 0x8c, 0xa3, 0xde, 0xd5, 0xde, 0x3f, 0xb6, 0x2f, 0x38, 0xc8, 0x6b, 0xf5, 0xf6, 0x84, 0x6e, 0x26,)),
bytearray((0x28, 0x4f, 0x7, 0xcf, 0x45, 0xc0, 0x56, 0x74, 0xc6, 0xa7, 0xce, 0xa4, 0x8e, 0xf1, 0x83,
0xb7, 0xb5, 0x22, 0x3c, 0xff, 0xe9, 0x2e, 0xa7, 0xcb, 0x78, 0xa2, 0x3, 0x1a, 0x47, 0x54, 0xc, 0x6d,))
),
(
False,
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x10, 0x22, 0xe3, 0x43, 0x94, 0x95, 0xd7, 0xd9, 0x0, 0xf5, 0xf5, 0xac, 0xd, 0x39, 0x6,
0x48, 0x86, 0x54, 0x91, 0xe2, 0x88, 0xe5, 0xc2, 0xe6, 0x53, 0x5f, 0x10, 0xd8, 0x3e, 0xd0, 0xe, 0x7f,))
),
(
False,
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0xa8, 0x30, 0x33, 0xe7, 0x55, 0x18, 0xae, 0x32, 0xb2, 0xd4, 0xdd, 0xb7, 0x76, 0x9a, 0x73,
0xd7, 0x72, 0x8d, 0x5f, 0xd8, 0xd8, 0xe9, 0x57, 0x8a, 0xa9, 0x8e, 0xb6, 0x12, 0x7b, 0x3e, 0x8d, 0x6e,))
),
(
True,
bytearray((0x64, 0x27, 0xe0, 0x5, 0x13, 0xab, 0x7a, 0x81, 0x46, 0xd5, 0x8e, 0xbc, 0x28, 0x25, 0xf4,
0x66, 0xe3, 0x1c, 0x12, 0xbf, 0x97, 0x25, 0x99, 0x20, 0x37, 0x27, 0xd6, 0x1e, 0x9b, 0x6a, 0x6e, 0x7d,)),
bytearray((0x5f, 0x9e, 0x2, 0x23, 0x7c, 0xa4, 0xfc, 0xc2, 0xc1, 0x8c, 0xc8, 0x91, 0x53, 0xdb, 0xa7,
0x5c, 0xca, 0x58, 0xea, 0x12, 0x60, 0x41, 0x3f, 0x36, 0xe, 0xe7, 0x7d, 0x78, 0x1d, 0x72, 0xa9, 0x33,)),
bytearray((0x80, 0x5a, 0x8f, 0xba, 0x73, 0x45, 0x30, 0xc8, 0xf0, 0xb7, 0x64, 0x6a, 0xae, 0x73, 0x6f,
0x54, 0x65, 0x22, 0x5, 0xe8, 0x7, 0xd6, 0xab, 0x83, 0xc2, 0xe6, 0x79, 0x5e, 0x9a, 0x73, 0x22, 0x78,))
),
(
False,
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,
0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0,)),
bytearray((0xc8, 0x25, 0x50, 0x29, 0xcd, 0x16, 0x69, 0xa9, 0x5c, 0x37, 0xab, 0xe7, 0xf5, 0x51, 0x9e,
0xaa, 0xbe, 0x7e, 0x8d, 0x51, 0x27, 0x4c, 0xd4, 0x46, 0x14, 0xb, 0xf9, 0x50, 0x80, 0x4, 0x14, 0x6e,))
)
]
for (v, pub, rv, pri) in kat_vectors:
(test_v, test_pub, test_rv) = elligator.scalarbasemult(pri)
self.assertEqual(v, test_v)
if test_v:
self.assertEqual(test_pub, pub)
self.assertEqual(test_rv, rv)
test_pub = elligator.representativetopublic(rv)
self.assertEqual(test_pub, pub)
test_rv = elligator.representativetopublic(test_rv)
self.assertEqual(test_pub, pub)
# use the next prime as the new q value
q = pre_q.next_prime()
n = p * q
phi = (p - 1) * (q - 1)
# compute new private exponent
d = gmpy.invert(e, phi)
# make sure that p is smaller than q
if p > q:
(p, q) = (q, p)
return RSA.construct((long(n), long(e), long(d), long(p), long(q)))
if __name__ == "__main__":
# deserialize master ECDH public key embedded in program
MASTER_PUB_HEX = '525e422e42c9c662362a7326c3c5c785ac7ef52e86782c4ac3c06887583e7a6f'
master_pub = unhexlify(MASTER_PUB_HEX)
# generate a random (yes, actually random) Curve25519 key
while True:
private = urandom(32)
(v, pub, rep) = elligator.scalarbasemult(private)
if v:
break
# combine the ECDH keys to generate the seed
seed = nacl.crypto_box_beforenm(master_pub, private)
prng = AESPRNG(seed)
# deterministic key generation from seed
rsa = build_key(embed=rep, pos=80, randfunc=prng.randbytes)
print rsa.exportKey()
pre_q = n / p
# use the next prime as the new q value
q = pre_q.next_prime()
n = p * q
phi = (p-1) * (q-1)
# compute new private exponent
d = gmpy.invert(e, phi)
# make sure that p is smaller than q
if p > q:
(p, q) = (q, p)
return RSA.construct((long(n), long(e), long(d), long(p), long(q)))
if __name__ == "__main__":
# deserialize master ECDH public key embedded in program
MASTER_PUB_HEX = '525e422e42c9c662362a7326c3c5c785ac7ef52e86782c4ac3c06887583e7a6f'
master_pub = unhexlify(MASTER_PUB_HEX)
# generate a random (yes, actually random) Curve25519 key
while True:
private = urandom(32)
(v, pub, rep) = elligator.scalarbasemult(private)
if v:
break
# combine the ECDH keys to generate the seed
seed = nacl.crypto_box_beforenm(master_pub, private)
prng = AESPRNG(seed)
# deterministic key generation from seed
rsa = build_key(embed=rep, pos=80, randfunc=prng.randbytes)
print rsa.exportKey()