1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
|
import hashlib
import os
from .crypto import factorization
from .tl import types
def check_prime_and_good_check(prime: int, g: int):
good_prime_bits_count = 2048
if prime < 0 or prime.bit_length() != good_prime_bits_count:
raise ValueError('bad prime count {}, expected {}'
.format(prime.bit_length(), good_prime_bits_count))
# TODO This is awfully slow
if factorization.Factorization.factorize(prime)[0] != 1:
raise ValueError('given "prime" is not prime')
if g == 2:
if prime % 8 != 7:
raise ValueError('bad g {}, mod8 {}'.format(g, prime % 8))
elif g == 3:
if prime % 3 != 2:
raise ValueError('bad g {}, mod3 {}'.format(g, prime % 3))
elif g == 4:
pass
elif g == 5:
if prime % 5 not in (1, 4):
raise ValueError('bad g {}, mod5 {}'.format(g, prime % 5))
elif g == 6:
if prime % 24 not in (19, 23):
raise ValueError('bad g {}, mod24 {}'.format(g, prime % 24))
elif g == 7:
if prime % 7 not in (3, 5, 6):
raise ValueError('bad g {}, mod7 {}'.format(g, prime % 7))
else:
raise ValueError('bad g {}'.format(g))
prime_sub1_div2 = (prime - 1) // 2
if factorization.Factorization.factorize(prime_sub1_div2)[0] != 1:
raise ValueError('(prime - 1) // 2 is not prime')
# Else it's good
def check_prime_and_good(prime_bytes: bytes, g: int):
good_prime = bytes((
0xC7, 0x1C, 0xAE, 0xB9, 0xC6, 0xB1, 0xC9, 0x04, 0x8E, 0x6C, 0x52, 0x2F, 0x70, 0xF1, 0x3F, 0x73,
0x98, 0x0D, 0x40, 0x23, 0x8E, 0x3E, 0x21, 0xC1, 0x49, 0x34, 0xD0, 0x37, 0x56, 0x3D, 0x93, 0x0F,
0x48, 0x19, 0x8A, 0x0A, 0xA7, 0xC1, 0x40, 0x58, 0x22, 0x94, 0x93, 0xD2, 0x25, 0x30, 0xF4, 0xDB,
0xFA, 0x33, 0x6F, 0x6E, 0x0A, 0xC9, 0x25, 0x13, 0x95, 0x43, 0xAE, 0xD4, 0x4C, 0xCE, 0x7C, 0x37,
0x20, 0xFD, 0x51, 0xF6, 0x94, 0x58, 0x70, 0x5A, 0xC6, 0x8C, 0xD4, 0xFE, 0x6B, 0x6B, 0x13, 0xAB,
0xDC, 0x97, 0x46, 0x51, 0x29, 0x69, 0x32, 0x84, 0x54, 0xF1, 0x8F, 0xAF, 0x8C, 0x59, 0x5F, 0x64,
0x24, 0x77, 0xFE, 0x96, 0xBB, 0x2A, 0x94, 0x1D, 0x5B, 0xCD, 0x1D, 0x4A, 0xC8, 0xCC, 0x49, 0x88,
0x07, 0x08, 0xFA, 0x9B, 0x37, 0x8E, 0x3C, 0x4F, 0x3A, 0x90, 0x60, 0xBE, 0xE6, 0x7C, 0xF9, 0xA4,
0xA4, 0xA6, 0x95, 0x81, 0x10, 0x51, 0x90, 0x7E, 0x16, 0x27, 0x53, 0xB5, 0x6B, 0x0F, 0x6B, 0x41,
0x0D, 0xBA, 0x74, 0xD8, 0xA8, 0x4B, 0x2A, 0x14, 0xB3, 0x14, 0x4E, 0x0E, 0xF1, 0x28, 0x47, 0x54,
0xFD, 0x17, 0xED, 0x95, 0x0D, 0x59, 0x65, 0xB4, 0xB9, 0xDD, 0x46, 0x58, 0x2D, 0xB1, 0x17, 0x8D,
0x16, 0x9C, 0x6B, 0xC4, 0x65, 0xB0, 0xD6, 0xFF, 0x9C, 0xA3, 0x92, 0x8F, 0xEF, 0x5B, 0x9A, 0xE4,
0xE4, 0x18, 0xFC, 0x15, 0xE8, 0x3E, 0xBE, 0xA0, 0xF8, 0x7F, 0xA9, 0xFF, 0x5E, 0xED, 0x70, 0x05,
0x0D, 0xED, 0x28, 0x49, 0xF4, 0x7B, 0xF9, 0x59, 0xD9, 0x56, 0x85, 0x0C, 0xE9, 0x29, 0x85, 0x1F,
0x0D, 0x81, 0x15, 0xF6, 0x35, 0xB1, 0x05, 0xEE, 0x2E, 0x4E, 0x15, 0xD0, 0x4B, 0x24, 0x54, 0xBF,
0x6F, 0x4F, 0xAD, 0xF0, 0x34, 0xB1, 0x04, 0x03, 0x11, 0x9C, 0xD8, 0xE3, 0xB9, 0x2F, 0xCC, 0x5B))
if good_prime == prime_bytes:
if g in (3, 4, 5, 7):
return # It's good
check_prime_and_good_check(int.from_bytes(prime_bytes, 'big'), g)
def is_good_large(number: int, p: int) -> bool:
return number > 0 and p - number > 0
SIZE_FOR_HASH = 256
def num_bytes_for_hash(number: bytes) -> bytes:
return bytes(SIZE_FOR_HASH - len(number)) + number
def big_num_for_hash(g: int) -> bytes:
return g.to_bytes(SIZE_FOR_HASH, 'big')
def sha256(*p: bytes) -> bytes:
hash = hashlib.sha256()
for q in p:
hash.update(q)
return hash.digest()
def is_good_mod_exp_first(modexp, prime) -> bool:
diff = prime - modexp
min_diff_bits_count = 2048 - 64
max_mod_exp_size = 256
if diff < 0 or \
diff.bit_length() < min_diff_bits_count or \
modexp.bit_length() < min_diff_bits_count or \
(modexp.bit_length() + 7) // 8 > max_mod_exp_size:
return False
return True
def xor(a: bytes, b: bytes) -> bytes:
return bytes(x ^ y for x, y in zip(a, b))
def pbkdf2sha512(password: bytes, salt: bytes, iterations: int):
return hashlib.pbkdf2_hmac('sha512', password, salt, iterations)
def compute_hash(algo: types.PasswordKdfAlgoSHA256SHA256PBKDF2HMACSHA512iter100000SHA256ModPow,
password: str):
hash1 = sha256(algo.salt1, password.encode('utf-8'), algo.salt1)
hash2 = sha256(algo.salt2, hash1, algo.salt2)
hash3 = pbkdf2sha512(hash2, algo.salt1, 100000)
return sha256(algo.salt2, hash3, algo.salt2)
def compute_digest(algo: types.PasswordKdfAlgoSHA256SHA256PBKDF2HMACSHA512iter100000SHA256ModPow,
password: str):
try:
check_prime_and_good(algo.p, algo.g)
except ValueError:
raise ValueError('bad p/g in password')
value = pow(algo.g,
int.from_bytes(compute_hash(algo, password), 'big'),
int.from_bytes(algo.p, 'big'))
return big_num_for_hash(value)
# https://github.com/telegramdesktop/tdesktop/blob/18b74b90451a7db2379a9d753c9cbaf8734b4d5d/Telegram/SourceFiles/core/core_cloud_password.cpp
def compute_check(request: types.account.Password, password: str):
algo = request.current_algo
if not isinstance(algo, types.PasswordKdfAlgoSHA256SHA256PBKDF2HMACSHA512iter100000SHA256ModPow):
raise ValueError('unsupported password algorithm {}'
.format(algo.__class__.__name__))
pw_hash = compute_hash(algo, password)
p = int.from_bytes(algo.p, 'big')
g = algo.g
B = int.from_bytes(request.srp_B, 'big')
try:
check_prime_and_good(algo.p, g)
except ValueError:
raise ValueError('bad p/g in password')
if not is_good_large(B, p):
raise ValueError('bad b in check')
x = int.from_bytes(pw_hash, 'big')
p_for_hash = num_bytes_for_hash(algo.p)
g_for_hash = big_num_for_hash(g)
b_for_hash = num_bytes_for_hash(request.srp_B)
g_x = pow(g, x, p)
k = int.from_bytes(sha256(p_for_hash, g_for_hash), 'big')
kg_x = (k * g_x) % p
def generate_and_check_random():
random_size = 256
while True:
random = os.urandom(random_size)
a = int.from_bytes(random, 'big')
A = pow(g, a, p)
if is_good_mod_exp_first(A, p):
a_for_hash = big_num_for_hash(A)
u = int.from_bytes(sha256(a_for_hash, b_for_hash), 'big')
if u > 0:
return (a, a_for_hash, u)
a, a_for_hash, u = generate_and_check_random()
g_b = (B - kg_x) % p
if not is_good_mod_exp_first(g_b, p):
raise ValueError('bad g_b')
ux = u * x
a_ux = a + ux
S = pow(g_b, a_ux, p)
K = sha256(big_num_for_hash(S))
M1 = sha256(
xor(sha256(p_for_hash), sha256(g_for_hash)),
sha256(algo.salt1),
sha256(algo.salt2),
a_for_hash,
b_for_hash,
K
)
return types.InputCheckPasswordSRP(
request.srp_id, bytes(a_for_hash), bytes(M1))
|
