def cints(n):
i = 0
j = 0
while j < n:
i += 1
print i
factors = pr.primefactors(i, u=True)
if len(factors) == n:
j += 1
if j == 1:
first = i
else:
j = 0
return first
from prime import primefactors
def numbers():
c = 1
i = 1
while True:
yield i
c += 1
i += c
for n in numbers():
pf = primefactors(n)
d = {-1: 1}
for i in pf:
if i in d.keys():
d[i] += 1
else:
d[i] = 2
if reduce(lambda x, y: x * y, d.values()) > 500:
print(n)
break
def create_auth_key(self):
nonce = os.urandom(16)
print("Requesting pq")
ResPQ = self.method_call('req_pq', nonce=nonce)
server_nonce = ResPQ['server_nonce']
# TODO: selecting RSA public key based on this fingerprint
public_key_fingerprint = ResPQ['server_public_key_fingerprints'][0]
pq_bytes = ResPQ['pq']
pq = bytes_to_long(pq_bytes)
[p, q] = prime.primefactors(pq)
if p > q: (p, q) = (q, p)
assert p*q == pq and p < q
print("Factorization %d = %d * %d" % (pq, p, q))
p_bytes = long_to_bytes(p)
q_bytes = long_to_bytes(q)
f = open(os.path.join(os.path.dirname(__file__), "rsa.pub"))
key = RSA.importKey(f.read())
new_nonce = os.urandom(32)
data = TL.serialize_obj('p_q_inner_data',
pq=pq_bytes,
p=p_bytes,
q=q_bytes,
nonce=nonce,
server_nonce=server_nonce,
new_nonce=new_nonce)
sha_digest = SHA.new(data).digest()
random_bytes = os.urandom(255-len(data)-len(sha_digest))
to_encrypt = sha_digest + data + random_bytes
encrypted_data = key.encrypt(to_encrypt, 0)[0]
print("Starting Diffie Hellman key exchange")
server_dh_params = self.method_call('req_DH_params',
nonce=nonce,
server_nonce=server_nonce,
p=p_bytes,
q=q_bytes,
public_key_fingerprint=public_key_fingerprint,
encrypted_data=encrypted_data)
assert nonce == server_dh_params['nonce']
assert server_nonce == server_dh_params['server_nonce']
encrypted_answer = server_dh_params['encrypted_answer']
tmp_aes_key = SHA.new(new_nonce + server_nonce).digest() + SHA.new(server_nonce + new_nonce).digest()[0:12]
tmp_aes_iv = SHA.new(server_nonce + new_nonce).digest()[12:20] + SHA.new(new_nonce + new_nonce).digest() + new_nonce[0:4]
answer_with_hash = crypt.ige_decrypt(encrypted_answer, tmp_aes_key, tmp_aes_iv)
answer_hash = answer_with_hash[:20]
answer = answer_with_hash[20:]
# TODO: SHA hash assertion here
server_DH_inner_data = TL.deserialize(io.BytesIO(answer))
assert nonce == server_DH_inner_data['nonce']
assert server_nonce == server_DH_inner_data['server_nonce']
dh_prime_str = server_DH_inner_data['dh_prime']
g = server_DH_inner_data['g']
g_a_str = server_DH_inner_data['g_a']
server_time = server_DH_inner_data['server_time']
self.timedelta = server_time - time()
print("Server-client time delta = %.1f s" % self.timedelta)
dh_prime = bytes_to_long(dh_prime_str)
g_a = bytes_to_long(g_a_str)
assert prime.isprime(dh_prime)
retry_id = 0
b_str = os.urandom(256)
b = bytes_to_long(b_str)
g_b = pow(g, b, dh_prime)
g_b_str = long_to_bytes(g_b)
data = TL.serialize_obj('client_DH_inner_data',
nonce=nonce,
server_nonce=server_nonce,
retry_id=retry_id,
g_b=g_b_str)
data_with_sha = SHA.new(data).digest()+data
data_with_sha_padded = data_with_sha + os.urandom(-len(data_with_sha) % 16)
encrypted_data = crypt.ige_encrypt(data_with_sha_padded, tmp_aes_key, tmp_aes_iv)
for i in range(1, self.AUTH_MAX_RETRY): # retry when dh_gen_retry or dh_gen_fail
Set_client_DH_params_answer = self.method_call('set_client_DH_params',
nonce=nonce,
server_nonce=server_nonce,
encrypted_data=encrypted_data)
# print Set_client_DH_params_answer
auth_key = pow(g_a, b, dh_prime)
auth_key_str = long_to_bytes(auth_key)
auth_key_sha = SHA.new(auth_key_str).digest()
auth_key_aux_hash = auth_key_sha[:8]
new_nonce_hash1 = SHA.new(new_nonce+b'\x01'+auth_key_aux_hash).digest()[-16:]
new_nonce_hash2 = SHA.new(new_nonce+b'\x02'+auth_key_aux_hash).digest()[-16:]
new_nonce_hash3 = SHA.new(new_nonce+b'\x03'+auth_key_aux_hash).digest()[-16:]
assert Set_client_DH_params_answer['nonce'] == nonce
assert Set_client_DH_params_answer['server_nonce'] == server_nonce
if Set_client_DH_params_answer.name == 'dh_gen_ok':
assert Set_client_DH_params_answer['new_nonce_hash1'] == new_nonce_hash1
print("Diffie Hellman key exchange processed successfully")
self.server_salt = strxor(new_nonce[0:8], server_nonce[0:8])
self.auth_key = auth_key_str
self.auth_key_id = auth_key_sha[-8:]
print("Auth key generated")
return "Auth Ok"
elif Set_client_DH_params_answer.name == 'dh_gen_retry':
assert Set_client_DH_params_answer['new_nonce_hash2'] == new_nonce_hash2
print ("Retry Auth")
elif Set_client_DH_params_answer.name == 'dh_gen_fail':
assert Set_client_DH_params_answer['new_nonce_hash3'] == new_nonce_hash3
print("Auth Failed")
raise Exception("Auth Failed")
else: raise Exception("Response Error")
def create_auth_key(self):
nonce = os.urandom(16)
print("Requesting pq")
ResPQ = self.method_call('req_pq', nonce=nonce)
server_nonce = ResPQ['server_nonce']
# TODO: selecting RSA public key based on this fingerprint
public_key_fingerprint = ResPQ['server_public_key_fingerprints'][0]
pq_bytes = ResPQ['pq']
pq = bytes_to_long(pq_bytes)
[p, q] = prime.primefactors(pq)
if p > q: (p, q) = (q, p)
assert p * q == pq and p < q
print("Factorization %d = %d * %d" % (pq, p, q))
p_bytes = long_to_bytes(p)
q_bytes = long_to_bytes(q)
f = open(os.path.join(os.path.dirname(__file__), "rsa.pub"))
key = RSA.importKey(f.read())
new_nonce = os.urandom(32)
data = TL.serialize_obj('p_q_inner_data',
pq=pq_bytes,
p=p_bytes,
q=q_bytes,
nonce=nonce,
server_nonce=server_nonce,
new_nonce=new_nonce)
sha_digest = SHA.new(data).digest()
random_bytes = os.urandom(255 - len(data) - len(sha_digest))
to_encrypt = sha_digest + data + random_bytes
encrypted_data = key.encrypt(to_encrypt, 0)[0]
print("Starting Diffie Hellman key exchange")
server_dh_params = self.method_call(
'req_DH_params',
nonce=nonce,
server_nonce=server_nonce,
p=p_bytes,
q=q_bytes,
public_key_fingerprint=public_key_fingerprint,
encrypted_data=encrypted_data)
assert nonce == server_dh_params['nonce']
assert server_nonce == server_dh_params['server_nonce']
encrypted_answer = server_dh_params['encrypted_answer']
tmp_aes_key = SHA.new(new_nonce + server_nonce).digest() + SHA.new(
server_nonce + new_nonce).digest()[0:12]
tmp_aes_iv = SHA.new(server_nonce + new_nonce).digest(
)[12:20] + SHA.new(new_nonce + new_nonce).digest() + new_nonce[0:4]
answer_with_hash = crypt.ige_decrypt(encrypted_answer, tmp_aes_key,
tmp_aes_iv)
answer_hash = answer_with_hash[:20]
answer = answer_with_hash[20:]
# TODO: SHA hash assertion here
server_DH_inner_data = TL.deserialize(io.BytesIO(answer))
assert nonce == server_DH_inner_data['nonce']
assert server_nonce == server_DH_inner_data['server_nonce']
dh_prime_str = server_DH_inner_data['dh_prime']
g = server_DH_inner_data['g']
g_a_str = server_DH_inner_data['g_a']
server_time = server_DH_inner_data['server_time']
self.timedelta = server_time - time()
print("Server-client time delta = %.1f s" % self.timedelta)
dh_prime = bytes_to_long(dh_prime_str)
g_a = bytes_to_long(g_a_str)
assert prime.isprime(dh_prime)
retry_id = 0
b_str = os.urandom(256)
b = bytes_to_long(b_str)
g_b = pow(g, b, dh_prime)
g_b_str = long_to_bytes(g_b)
data = TL.serialize_obj('client_DH_inner_data',
nonce=nonce,
server_nonce=server_nonce,
retry_id=retry_id,
g_b=g_b_str)
data_with_sha = SHA.new(data).digest() + data
data_with_sha_padded = data_with_sha + os.urandom(
-len(data_with_sha) % 16)
encrypted_data = crypt.ige_encrypt(data_with_sha_padded, tmp_aes_key,
tmp_aes_iv)
Set_client_DH_params_answer = self.method_call(
'set_client_DH_params',
nonce=nonce,
server_nonce=server_nonce,
encrypted_data=encrypted_data)
auth_key = pow(g_a, b, dh_prime)
auth_key_str = long_to_bytes(auth_key)
auth_key_sha = SHA.new(auth_key_str).digest()
auth_key_aux_hash = auth_key_sha[:8]
new_nonce_hash1 = SHA.new(new_nonce + b'\x01' +
auth_key_aux_hash).digest()[-16:]
new_nonce_hash2 = SHA.new(new_nonce + b'\x02' +
auth_key_aux_hash).digest()[-16:]
new_nonce_hash3 = SHA.new(new_nonce + b'\x03' +
auth_key_aux_hash).digest()[-16:]
assert Set_client_DH_params_answer['nonce'] == nonce
assert Set_client_DH_params_answer['server_nonce'] == server_nonce
assert Set_client_DH_params_answer[
'new_nonce_hash1'] == new_nonce_hash1
print("Diffie Hellman key exchange processed successfully")
self.server_salt = strxor(new_nonce[0:8], server_nonce[0:8])
self.auth_key = auth_key_str
self.auth_key_id = auth_key_sha[-8:]
print("Auth key generated")
#!/usr/bin/env python
from __future__ import print_function
import prime
import sys
import json
def eprint(*args, **kwargs):
print(*args, file=sys.stderr, **kwargs)
pq = prime.primefactors(long(sys.argv[1]))
sys.stdout.write(json.dumps(pq))
sys.stdout.flush()