上线看了一下题，就做了三个，还是太菜了（T~T）
r0system
题目出的很抽象，就是代码长，没有啥别的考点，先创建一个账号，登录进入后修改Alice账号密码，再使用Alice登录拿到私钥就好了。
from hashlib import md5
from Crypto.Cipher import AES
from Crypto.Util.number import *
import gmpy2
from pwn import *
AliceUsername = b'AliceIsSomeBody'
BobUsername = b'BobCanBeAnyBody'
context.log_level = 'DEBUG'
sh = remote('ctf2024-entry.r3kapig.com',31781)
sh.recvuntil(b'Now input your option: ')
sh.sendline(b'3')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(b'try1'.hex().encode())
sh.recvuntil(b'Password[HEX]: ')
sh.sendline(b'try2key'.hex().encode())
sh.recvuntil(b"Register successfully, try1 's token is ")
try1token = int(sh.recvuntil(b'.\n')[:-2],16)
# print(try1token)
sh.recvuntil(b"Now input your option: ")
sh.sendline(b'1')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(b'try1'.hex().encode())
sh.recvuntil(b'Password[HEX]: ')
sh.sendline(b'try2key'.hex().encode())
sh.recvuntil(b'Login successfully!\n')
sh.recvuntil(b'Hello try1,do you need any services? ')
sh.sendline(b'1')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(BobUsername.hex().encode())
sh.recvuntil(b"New Password[HEX]: ")
sh.sendline(b'Bob11'.hex().encode())
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'1')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(AliceUsername.hex().encode())
sh.recvuntil(b"New Password[HEX]: ")
sh.sendline(b'Alice11'.hex().encode())
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'5')
sh.recvuntil(b"Now input your option: ")
sh.sendline(b'1')
sh.recvuntil(b"Username[HEX]: ")
sh.sendline(AliceUsername.hex().encode())
sh.recvuntil(b"Password[HEX]: ")
sh.sendline(b'Alice11'.hex().encode())
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'3')
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'4')
sh.recv()
拿到后，离线处理一下（DH算法拿到key，AES解密即可）
from Crypto.Util.number import *
Alice_pub = '632d947f774d6f4c0f462233682bab1e2305976b35b89fef050aa7dfb516885b4d5c6e46c1c0c9427a5c82539aaa18a99cc4ba1adafbacdc860f0d88eedd2713'
Bob_pub = '364d168180a928286d448bceb0b06ca186da0968469b5e4ffa88fcd91929e3345dcf724620318dc3f45b84c9849c43874cb02a53afea98db59b6c8a09070f0f3'
c = 'e3a583dfd51a1278c4e49ddce9fcf606af78a2d02a0a804c6b8b2a3deae301a9df7ff8fdfa0b115378f771eec6f54dade6730ea6d3ab460973f2345aa8fc2ae53e1f47e9cfa9f32ab1e11e1863f65b40e5b01831c0c0ab092b9af9ebaaa3035f'
Alice_pri = int('cd2a4b358441c00c43d966b28612c2233c649b6f648b35c97422f985e5c2dffa',16)
print(len(Bob_pub))
def b2i(b):
return int.from_bytes(b,byteorder='big')
def pad(msg):
return msg + bytes([i for i in range(16 - int(len(msg) % 16))])
class Curve:
def __init__(self):
# Nist p-256
self.p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
self.a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
self.b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
self.G = (0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296,
0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
self.n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
def add(self,P, Q):
if (P == (0, 0)):
return Q
elif (Q == (0, 0)):
return P
else:
x1, y1 = P
x2, y2 = Q
if ((x1 == x2) & (y1 == -y2)):
return ((0, 0))
else:
if (P != Q):
l = (y2 - y1) * pow(x2 - x1, -1, self.p)
else:
l = (3 * (x1**2) + self.a) * pow(2 * y1, -1, self.p)
x3 = ((l**2) - x1 - x2) % self.p
y3 = (l * (x1 - x3) - y1) % self.p
return x3, y3
def mul(self, n , P):
Q = P
R = (0, 0)
while (n > 0):
if (n % 2 == 1):
R = self.add(R, Q)
Q = self.add(Q, Q)
n = n // 2
return R
class ECDH:
def __init__(self):
self.curve = Curve()
self.private_key = Alice_pri
self.public_key = self.curve.mul(self.private_key, self.curve.G)
def exchange_key(self,publickey):
return md5(str(self.curve.mul(self.private_key,publickey)).encode()).digest()
def enc(msg,key):
aes = AES.new(key,AES.MODE_ECB)
return aes.decrypt(msg)
pub = (int(Bob_pub[:64],16),int(Bob_pub[64:],16))
K = ECDH()
key = K.exchange_key(pub)
m = enc(long_to_bytes(int(c,16)),key)
print(m)
r1system
emmmm，更抽象了。。。，不就是我们没法修改密码了吗，但是Bob账号没有创建，我们直接创建Bob账号，用Bob账号登录拿到私钥。
当时有点晕，python交互不知道那里写错了，也不需要交互太多。直接手动了：
离线DH处理一下：
from Crypto.Util.number import *
from hashlib import md5
from Crypto.Cipher import AES
from Crypto.Util.number import *
import gmpy2
Alice_pub = '4a215c357541eeb3e55bd2ec965a4d8482f737c875eb0b3cbaa8c7d3f242f43ed107e6be779aa9beca0e7a7730edacd258af9a42668f66689dc64f93b7c253ad'
Bob_pub = '0dd29bca4ad78a4c3db149ad2a2eceab7915e7edcacabb904518256d7d16fa4ca6014a0adc7933444ccd43d0ef53135bd298c64bfa4ac45ee3ce26924fffd07b'
c = 'ffec0914ffeacda46c41d64c5bcf80f8d70fa0d48fa3f2f0cdbad88524fc6f47bc31ebceae0a441f3d56d6be438f39897ffbb68308b60ce2f32e6d3186375b1d'
Bob_pri = int('01a0ed4997b932229e13475a876758114ce1c737f22125fe053c802a74503a7f',16)
# print(len(Bob_pub))
def b2i(b):
return int.from_bytes(b,byteorder='big')
def pad(msg):
return msg + bytes([i for i in range(16 - int(len(msg) % 16))])
class Curve:
def __init__(self):
# Nist p-256
self.p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
self.a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
self.b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
self.G = (0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296,
0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
self.n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
def add(self,P, Q):
if (P == (0, 0)):
return Q
elif (Q == (0, 0)):
return P
else:
x1, y1 = P
x2, y2 = Q
if ((x1 == x2) & (y1 == -y2)):
return ((0, 0))
else:
if (P != Q):
l = (y2 - y1) * pow(x2 - x1, -1, self.p)
else:
l = (3 * (x1**2) + self.a) * pow(2 * y1, -1, self.p)
x3 = ((l**2) - x1 - x2) % self.p
y3 = (l * (x1 - x3) - y1) % self.p
return x3, y3
def mul(self, n , P):
Q = P
R = (0, 0)
while (n > 0):
if (n % 2 == 1):
R = self.add(R, Q)
Q = self.add(Q, Q)
n = n // 2
return R
class ECDH:
def __init__(self):
self.curve = Curve()
self.private_key = Bob_pri
self.public_key = self.curve.mul(self.private_key, self.curve.G)
def exchange_key(self,publickey):
return md5(str(self.curve.mul(self.private_key,publickey)).encode()).digest()
def enc(msg,key):
aes = AES.new(key,AES.MODE_ECB)
return aes.decrypt(msg)
pub = (int(Alice_pub[:64],16),int(Alice_pub[64:],16))
K = ECDH()
key = K.exchange_key(pub)
m = enc(long_to_bytes(int(c,16)),key)
print(m)
r2system
这题目修改之后我们没法直接登录了，于是考虑一直没用到的token，如何进行伪造token
https://7rocky.github.io/en/ctf/other/corctf/qcg-k/
上述ecdsa中的等式本题等式变换一下类似，都给求解x的代码了，我们直接用可以求导等式中的x值，求得x值后，我们需要求解题目伪随机数生成器中的8个生成数。
https://eprint.iacr.org/2023/305.pdf
查看论文，最后可以看到，over
# https://eprint.iacr.org/2023/305.pdf
# https://7rocky.github.io/en/ctf/other/corctf/qcg-k/
from hashlib import md5
from Crypto.Cipher import AES
from Crypto.Util.number import *
import gmpy2
from pwn import *
AliceUsername = b'AliceIsSomeBody'
BobUsername = b'BobCanBeAnyBody'
MOD = 0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000283
context.log_level = 'DEBUG'
while 1:
sh = remote('ctf2024-entry.r3kapig.com','31886')
token = []
def b2i(b):
return int.from_bytes(b,byteorder='big')
for i in range(10):
sh.recvuntil(b'Now input your option: ')
sh.sendline(b'3')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(f'try{i}'.encode().hex().encode())
sh.recvuntil(b'Password[HEX]: ')
sh.sendline(b'trykey'.hex().encode())
sh.recvuntil(f"Register successfully, try{i} 's token is ".encode())
token.append(int(sh.recvuntil(b".\n")[:-2],16))
# print(token)
# print(f'try{i}'.encode().hex())
# print(b'trykey'.hex())
# print('-'*60)
from functools import cache
from sage.all import GF, PolynomialRing
from Crypto.Util.number import *
def k_ij(i, j):
return x * (pow(token[i],-1,q) - pow(token[j],-1,q)) + (-u[i]) - (-u[j])
def dpoly(n, i, j):
if i == 0:
return k_ij(j + 1, j + 2) ** 2 - k_ij(j + 2, j + 3) * k_ij(j, j + 1)
left = dpoly(n, i - 1, j)
for m in range(1, i + 2):
left *= k_ij(j + m, j + i + 2)
right = dpoly(n, i - 1, j + 1)
for m in range(1, i + 2):
right *= k_ij(j, j + m)
return left - right
q = 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859
Fq = GF(q)
x = PolynomialRing(Fq, 'x').gens()[0]
u = []
for i in range(10):
token[i] = Fq(token[i])
u.append(int(f'try{i}'.encode().hex(),16))
N = 10
pol = dpoly(N - 4, N - 4, 0)
secret = pol.roots()
print(len(secret))
if len(secret) == 2:
print('-'*60)
print(token)
print(secret[1][0])
print(pol.roots())
q = 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137859
# token = [106059497226230078458408573548321522716731725799788329078185586313815926198786283229056460822188793913821381666495251726267106621314658816426114026202874264301311981366174550459244596265305815754933877853234119479492566891678520638945193574839652838841897044204741673519677458754474366826547057897515026724848, 47779134463461938926784751047825979292269094946568692939404713492011230117629761155779851181457396929641936224158552994587078896758215173995601320993839406108967926874172990659955225199974449650174420457407282282200571423658580354611757483081890798193660712063358386112539821026744968444515622130726900239736, 6019943175433302947934690873635058162287681100248021727464564163519392818412390410331290937835893162877644138873871237079538825688146346220557440276548235811524529326955065109956245587384883118646717417832321909917952062203568707642969977550858219727897942030447721296260910991378960446932119401177088481101, 87366091011617621011994203682638757774549496014511565786019048885633795608534406810797304904842442962750474688522542125102222205045224867671241373679622534023429816640889029782226330278878222739729367046959641320415162583370782941515441049046525274560503163657767716097889995000902550291930655118630272187236, 162253270840664463417218196571085196871091797499865805208031509772425458817614063479197094963500577594095925971402551698239212052148910616858817156373954657472523576731428256448818335996409727698745257604493772170217937612767064335133206868791051299144418047833021240318645816550420294524729988468480435887497, 16316159479225612300545615409718990694205381146382791061875851500122541211303872430537288252492644632122096208526557818206957172949606411140810284034078506052569405921204754742275767216885404857318557969754723282586567318942107713278795011776474047765849328695928938150210465524196392099313042988854140728571, 110684449328943736291261911386113967696573864578481873880367217362009886560991405747198017836213552234301282996693430383750292263465467888387505858193619361586819843726572232285738123704133886101707221931680558660384074855076241699302349982605324147403540584525624326285095590160394006554279025380946081520300, 7356599452619556773251194532777561267773145160514835573833588213879013017196468709171138802612399590197923948339027347406993627143242196724078569150122270247338513256791925724480915374824804344499044323246127533120391390418146580877249943216801651260909727234265972977871490098310852917404374165851771600054, 79378643533773177910480239060210987694532674099080062811324829674731184600353273644681398671779081023781611203106498867926311834788227689646072834319606886671941281030178549230498622518109279323029421140996969495153113038798152281011121979052267716458401937806197678273055467808912219079291805483775278618402, 110179524962782493054573311837314282098980987859591882395423393533138851596355452556474077550143760118285004986723362769018067819061818008647687561164809569238857587591201709593890657073827773089305542908925988851353176471460589495509823945721749989059560328268409542559444192460370913632249416427930608028847, 35384376988896111495552489453762246315478997052680054073836682930332914874238114867688834674464731577039550267819156800221016033350889962187366758327534596906583466852055407646306410231870664867147693493193476597590756070907821288287575690452983279436282212713311407594154490312755517436369884174770742549861]
se = int(secret[1][0])
Fq = GF(q)
x = PolynomialRing(Fq, 'x').gens()[0]
u = []
for i in range(10):
token[i] = Fq(token[i])
u.append(int(f'try{i}'.encode().hex(), 16))
k = []
for i in range(10):
# print(i)
k.append((-u[i]) + se*pow(token[i],-1,q) % q)
a = matrix(Fq,8,8)
for i in range(8):
for j in range(8):
a[i,j] = k[i]^(7-j) % q
inverse_matrix0 = a^(-1)
k_solve0 = vector(k[1:9])
result_matrix0 = inverse_matrix0 * k_solve0
AA = result_matrix0[::-1]
print(AA)
if AA[-2] == 0 and AA[-1] == 0:
continue
print(k[1],k[2])
sum = 0
for i in range(8):
sum += AA[i]*(k[1]^i) % q
print(sum)
s = 0
for i in range(8):
s += AA[i]*(k[-1]^i) % q
Bob_token = se*pow(s+bytes_to_long(BobUsername),-1,q) % q
sh.recvuntil(b'Now input your option: ')
sh.sendline(b'1')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(f'try0'.encode().hex().encode())
sh.recvuntil(b'Password[HEX]: ')
sh.sendline(b'trykey'.hex().encode())
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'5')
sh.recvuntil(b'Now input your option: ')
sh.sendline(b'2')
sh.recvuntil(b'Username[HEX]: ')
sh.sendline(BobUsername.hex().encode())
sh.recvuntil(b"Token[HEX]: ")
sh.sendline(hex(Bob_token)[2:].encode())
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'4')
sh.recvuntil(b",do you need any services? ")
sh.sendline(b'3')
sh.recv()
break
sh.close()
from Crypto.Util.number import *
from hashlib import md5
from Crypto.Cipher import AES
from Crypto.Util.number import *
import gmpy2
Alice_pub = '2f964b3572232b1b6059c8994cb99287134e6545693320ff676d09d9b304686d8d8ac7e2ebefa2edcd5df186efdcd45ea755edab77593f64e25fdbf6e79d754b'
Bob_pub = 'aa8b8272443ec7e941197729996a86a121d4f635e584858f0152de2bb983bf295a6ff58354cb89d23318b3490f3c76cd633686a00f6c82e9eb54fbe621bc44cf'
c = 'f7eb15c02d440c835677e0d884ff559b93e1bb96a1821f1221545affaa6ba5eec39982110f1971b8d2e75a3b35ce585fb5f75ed360bd2eeb23a9dbaedfa27fc171b5ba3ac923ab6b835ac0be0e6c7b2c'
Bob_pri = int('97947336c7e877ed359f4268074bf9cbd4788bcd5a160cbea1e95b5d2516d7dc',16)
# print(len(Bob_pub))
def b2i(b):
return int.from_bytes(b,byteorder='big')
def pad(msg):
return msg + bytes([i for i in range(16 - int(len(msg) % 16))])
class Curve:
def __init__(self):
# Nist p-256
self.p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff
self.a = 0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc
self.b = 0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
self.G = (0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296,
0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
self.n = 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551
def add(self,P, Q):
if (P == (0, 0)):
return Q
elif (Q == (0, 0)):
return P
else:
x1, y1 = P
x2, y2 = Q
if ((x1 == x2) & (y1 == -y2)):
return ((0, 0))
else:
if (P != Q):
l = (y2 - y1) * pow(x2 - x1, -1, self.p)
else:
l = (3 * (x1**2) + self.a) * pow(2 * y1, -1, self.p)
x3 = ((l**2) - x1 - x2) % self.p
y3 = (l * (x1 - x3) - y1) % self.p
return x3, y3
def mul(self, n , P):
Q = P
R = (0, 0)
while (n > 0):
if (n % 2 == 1):
R = self.add(R, Q)
Q = self.add(Q, Q)
n = n // 2
return R
class ECDH:
def __init__(self):
self.curve = Curve()
self.private_key = Bob_pri
self.public_key = self.curve.mul(self.private_key, self.curve.G)
def exchange_key(self,publickey):
return md5(str(self.curve.mul(self.private_key,publickey)).encode()).digest()
def enc(msg,key):
aes = AES.new(key,AES.MODE_ECB)
return aes.decrypt(msg)
pub = (int(Alice_pub[:64],16),int(Alice_pub[64:],16))
K = ECDH()
key = K.exchange_key(pub)
m = enc(long_to_bytes(int(c,16)),key)
print(m)