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
|
from sage.all import *
from random import getrandbits, randint
from secrets import randbelow
from Crypto.Util.number import getPrime,isPrime,inverse
from Crypto.Util.Padding import pad
from Crypto.Cipher import AES
from secret import priKey, flag
from hashlib import sha1
import os
q = getPrime(160)
while True:
t0 = q*getrandbits(864)
if isPrime(t0+1):
p = t0 + 1
break
x = priKey
assert p % q == 1
h = randint(1,p-1)
g = pow(h,(p-1)//q,p)
y = pow(g,x,p)
def sign(z, k):
r = pow(g,k,p) % q
s = (inverse(k,q)*(z+r*priKey)) % q
return (r,s)
def verify(m,s,r):
z = int.from_bytes(sha1(m).digest(), 'big')
u1 = (inverse(s,q)*z) % q
u2 = (inverse(s,q)*r) % q
r0 = ((pow(g,u1,p)*pow(y,u2,p)) % p) % q
return r0 == r
def lcg(a, b, q, x):
while True:
x = (a * x + b) % q
yield x
msg = [os.urandom(16) for i in range(5)]
a, b, x = [randbelow(q) for _ in range(3)]
prng = lcg(a, b, q, x)
sigs = []
for m, k in zip(msg,prng):
z = int.from_bytes(sha1(m).digest(), "big") % q
r, s = sign(z, k)
assert verify(m, s, r)
sigs.append((r,s))
print(f"{g = }")
print(f"{h = }")
print(f"{q = }")
print(f"{p = }")
print(f"{msg = }")
print(f"{sigs = }")
key = sha1(str(priKey).encode()).digest()[:16]
iv = os.urandom(16)
cipher = AES.new(key, AES.MODE_CBC,iv)
ct = cipher.encrypt(pad(flag,16))
print(f"{iv = }")
print(f"{ct = }")
'''
g = 81569684196645348869992756399797937971436996812346070571468655785762437078898141875334855024163673443340626854915520114728947696423441493858938345078236621180324085934092037313264170158390556505922997447268262289413542862021771393535087410035145796654466502374252061871227164352744675750669230756678480403551
h = 13360659280755238232904342818943446234394025788199830559222919690197648501739683227053179022521444870802363019867146013415532648906174842607370958566866152133141600828695657346665923432059572078189013989803088047702130843109809724983853650634669946823993666248096402349533564966478014376877154404963309438891
q = 1303803697251710037027345981217373884089065173721
p = 135386571420682237420633670579115261427110680959831458510661651985522155814624783887385220768310381778722922186771694358185961218902544998325115481951071052630790578356532158887162956411742570802131927372034113509208643043526086803989709252621829703679985669846412125110620244866047891680775125948940542426381
msg = [b'I\xf0\xccy\xd5~\xed\xf8A\xe4\xdf\x91+\xd4_$', b'~\xa0\x9bCB\xef\xc3SY4W\xf9Aa\rO', b'\xe6\x96\xf4\xac\n9\xa7\xc4\xef\x82S\xe9 XpJ', b'3,\xbb\xe2-\xcc\xa1o\xe6\x93+\xe8\xea=\x17\xd1', b'\x8c\x19PHN\xa8\xbc\xfc\xa20r\xe5\x0bMwJ']
sigs = [(913082810060387697659458045074628688804323008021, 601727298768376770098471394299356176250915124698), (406607720394287512952923256499351875907319590223, 946312910102100744958283218486828279657252761118), (1053968308548067185640057861411672512429603583019, 1284314986796793233060997182105901455285337520635), (878633001726272206179866067197006713383715110096, 1117986485818472813081237963762660460310066865326), (144589405182012718667990046652227725217611617110, 1028458755419859011294952635587376476938670485840)]
iv = b'M\xdf\x0e\x7f\xeaj\x17PE\x97\x8e\xee\xaf:\xa0\xc7'
ct = b"\xa8a\xff\xf1[(\x7f\xf9\x93\xeb0J\xc43\x99\xb25:\xf5>\x1c?\xbd\x8a\xcd)i)\xdd\x87l1\xf5L\xc5\xc5'N\x18\x8d\xa5\x9e\x84\xfe\x80\x9dm\xcc"
'''
from sage.all import *
from random import getrandbits, randint
from secrets import randbelow
from Crypto.Util.number import getPrime,isPrime,inverse
from Crypto.Util.Padding import pad
from Crypto.Cipher import AES
from secret import priKey, flag
from hashlib import sha1
import os
q = getPrime(160)
while True:
t0 = q*getrandbits(864)
if isPrime(t0+1):
p = t0 + 1
break
x = priKey
assert p % q == 1
h = randint(1,p-1)
g = pow(h,(p-1)//q,p)
y = pow(g,x,p)
def sign(z, k):
r = pow(g,k,p) % q
s = (inverse(k,q)*(z+r*priKey)) % q
return (r,s)
def verify(m,s,r):
z = int.from_bytes(sha1(m).digest(), 'big')
u1 = (inverse(s,q)*z) % q
u2 = (inverse(s,q)*r) % q
r0 = ((pow(g,u1,p)*pow(y,u2,p)) % p) % q
return r0 == r
def lcg(a, b, q, x):
while True:
x = (a * x + b) % q
yield x
msg = [os.urandom(16) for i in range(5)]
a, b, x = [randbelow(q) for _ in range(3)]
prng = lcg(a, b, q, x)
sigs = []
for m, k in zip(msg,prng):
z = int.from_bytes(sha1(m).digest(), "big") % q
r, s = sign(z, k)
assert verify(m, s, r)
sigs.append((r,s))
print(f"{g = }")
print(f"{h = }")
print(f"{q = }")
print(f"{p = }")
print(f"{msg = }")
print(f"{sigs = }")
key = sha1(str(priKey).encode()).digest()[:16]
iv = os.urandom(16)
cipher = AES.new(key, AES.MODE_CBC,iv)
ct = cipher.encrypt(pad(flag,16))
print(f"{iv = }")
print(f"{ct = }")
'''
g = 81569684196645348869992756399797937971436996812346070571468655785762437078898141875334855024163673443340626854915520114728947696423441493858938345078236621180324085934092037313264170158390556505922997447268262289413542862021771393535087410035145796654466502374252061871227164352744675750669230756678480403551
h = 13360659280755238232904342818943446234394025788199830559222919690197648501739683227053179022521444870802363019867146013415532648906174842607370958566866152133141600828695657346665923432059572078189013989803088047702130843109809724983853650634669946823993666248096402349533564966478014376877154404963309438891
q = 1303803697251710037027345981217373884089065173721
p = 135386571420682237420633670579115261427110680959831458510661651985522155814624783887385220768310381778722922186771694358185961218902544998325115481951071052630790578356532158887162956411742570802131927372034113509208643043526086803989709252621829703679985669846412125110620244866047891680775125948940542426381
msg = [b'I\xf0\xccy\xd5~\xed\xf8A\xe4\xdf\x91+\xd4_$', b'~\xa0\x9bCB\xef\xc3SY4W\xf9Aa\rO', b'\xe6\x96\xf4\xac\n9\xa7\xc4\xef\x82S\xe9 XpJ', b'3,\xbb\xe2-\xcc\xa1o\xe6\x93+\xe8\xea=\x17\xd1', b'\x8c\x19PHN\xa8\xbc\xfc\xa20r\xe5\x0bMwJ']
sigs = [(913082810060387697659458045074628688804323008021, 601727298768376770098471394299356176250915124698), (406607720394287512952923256499351875907319590223, 946312910102100744958283218486828279657252761118), (1053968308548067185640057861411672512429603583019, 1284314986796793233060997182105901455285337520635), (878633001726272206179866067197006713383715110096, 1117986485818472813081237963762660460310066865326), (144589405182012718667990046652227725217611617110, 1028458755419859011294952635587376476938670485840)]
iv = b'M\xdf\x0e\x7f\xeaj\x17PE\x97\x8e\xee\xaf:\xa0\xc7'
ct = b"\xa8a\xff\xf1[(\x7f\xf9\x93\xeb0J\xc43\x99\xb25:\xf5>\x1c?\xbd\x8a\xcd)i)\xdd\x87l1\xf5L\xc5\xc5'N\x18\x8d\xa5\x9e\x84\xfe\x80\x9dm\xcc"
'''
|
