题目并不是很难,不过挺有意思
# WriteUps on crypto problems in 东华杯 2021
# The_RSA
# 「Description」
我的加密系统有可能有点点问题。
# 「SourceCode」
from Crypto.Util.number import* | |
from hashlib import sha256 | |
import socketserver | |
import signal | |
import string | |
import random | |
from secret import flag | |
table = string.ascii_letters+string.digits | |
flag = bytes_to_long(flag) | |
MENU = br'''[+] 1.Get Encrypt: | |
[+] 2.Exit: | |
''' | |
class Task(socketserver.BaseRequestHandler): | |
def _recvall(self): | |
BUFF_SIZE = 2048 | |
data = b'' | |
while True: | |
part = self.request.recv(BUFF_SIZE) | |
data += part | |
if len(part) < BUFF_SIZE: | |
break | |
return data.strip() | |
def send(self, msg, newline=True): | |
try: | |
if newline: | |
msg += b'\n' | |
self.request.sendall(msg) | |
except: | |
pass | |
def recv(self, prompt=b'[-] '): | |
self.send(prompt, newline=False) | |
return self._recvall() | |
def proof_of_work(self): | |
proof = (''.join([random.choice(table)for _ in range(20)])).encode() | |
sha = sha256( proof ).hexdigest().encode() | |
self.send(b"[+] sha256(XXXX+" + proof[4:] + b") == " + sha ) | |
XXXX = self.recv(prompt = b'[+] Plz Tell Me XXXX :') | |
if len(XXXX) != 4 or sha256(XXXX + proof[4:]).hexdigest().encode() != sha: | |
return False | |
return True | |
def EncRy(self): | |
p,q = getPrime(512),getPrime(512) | |
n = p * q | |
phi = (p - 1) * (q - 1) | |
e = inverse(self.d, phi) | |
c = pow(flag, e, n) | |
return(e,n,c) | |
def handle(self): | |
signal.alarm(60) | |
if not self.proof_of_work(): | |
return | |
self.send(b"Welcome to my RSA!") | |
self.d = getPrime(random.randint(435, 436)) | |
while 1: | |
self.send(MENU) | |
self.send(b"Now!What do you want to do?") | |
option = self.recv() | |
if option == b'1': | |
self.send(str(self.EncRy()).encode()) | |
else: | |
break | |
self.request.close() | |
class ThreadedServer(socketserver.ThreadingMixIn, socketserver.TCPServer): | |
pass | |
class ForkedServer(socketserver.ForkingMixIn, socketserver.TCPServer): | |
pass | |
if __name__ == "__main__": | |
HOST, PORT = '0.0.0.0', 10004 | |
print("HOST:POST " + HOST+":" + str(PORT)) | |
server = ForkedServer((HOST, PORT), Task) | |
server.allow_reuse_address = True | |
server.serve_forever() |
# 「Analyze」
题目给出 [task.py]
,在 handle
部分即定义一个 435 位的素数 并把它用作 RSA
的私钥,由此去生成 RSA
之中的所有参数,并对 flag
进行加密,给出每组加密使用的公钥 以及对应的密文
可以发现所有的密文都是通过 去产生实现的,于是可以通过以下式子 (1) 去构造格 (2) , LLL
之后就能够拿到目标向量 (3)
\left[ \matrix{M&e_0&e_1&...&e_i\\ 0&-n_0&0&...&0\\ 0&0&-n_1&...&0\\ ...&...&...&...&...\\ 0&0&0&...&-n_i} \right]
接着根据闵科夫斯基定理去计算大概需要几条拿到 SVP
,即想要得到的私钥 ,发现需要 10 组数据即可。
# 「Exp」
from Crypto.Util.number import* | |
import gmpy2 | |
from pwn import * | |
from hashlib import sha256 | |
import string | |
from pwnlib.util.iters import mbruteforce | |
table = string.ascii_letters+string.digits | |
def pow(): | |
io.recvuntil("XXXX+") | |
suffix = io.recv(16).decode("utf8") | |
io.recvuntil("== ") | |
cipher = io.recvline().strip().decode("utf8") | |
proof = mbruteforce(lambda x: sha256((x + suffix).encode()).hexdigest() == | |
cipher, table, length=4, method='fixed') | |
io.sendlineafter("XXXX :", proof) | |
io = remote("0.0.0.0",10004) | |
pow() | |
io.interactive() | |
e0,n0,c0 = | |
e1,n1,c1 = | |
e2,n2,c2 = | |
e3,n3,c3 = | |
e4,n4,c4 = | |
e5,n5,c5 = | |
e6,n6,c6 = | |
e7,n7,c7 = | |
e8,n8,c8 = | |
e9,n9,c9 = | |
maxN = max(n0,n1,n2,n3,n4,n5,n6,n7,n8,n9) | |
M = gmpy2.iroot(maxN,2)[0] | |
from sage.all import* | |
L = Matrix(ZZ,[[M,e0,e1,e2,e3,e4,e5,e6,e7,e8,e9], | |
[0,-n0,0,0,0,0,0,0,0,0,0], | |
[0,0,-n1,0,0,0,0,0,0,0,0], | |
[0,0,0,-n2,0,0,0,0,0,0,0], | |
[0,0,0,0,-n3,0,0,0,0,0,0], | |
[0,0,0,0,0,-n4,0,0,0,0,0], | |
[0,0,0,0,0,0,-n5,0,0,0,0], | |
[0,0,0,0,0,0,0,-n6,0,0,0], | |
[0,0,0,0,0,0,0,0,-n7,0,0], | |
[0,0,0,0,0,0,0,0,0,-n8,0], | |
[0,0,0,0,0,0,0,0,0,0,-n9]]) | |
v = L.LLL()[0] | |
d = v[0]//M | |
m = long_to_bytes(pow(c0,d,n0)) | |
print(m) |
# BlockEncrypt
# 「Description」
你能猜猜看我的 flag 是什么吗
# 「SourceCode」
[task.py]
from Crypto.Util.number import* | |
from Crypto.Cipher import AES | |
from secret import flag | |
from my_encrypt import block_encrypt | |
from hashlib import sha256 | |
import socketserver | |
import signal | |
import string | |
import random | |
import os | |
table = string.ascii_letters+string.digits | |
MENU = br'''[+] 1.Encrypt the Flag: | |
[+] 2.Encrypt your Plaintext: | |
[+] 3.Exit: | |
''' | |
def pad(m): | |
padlen = 16 - len(m) % 16 | |
return m + padlen * bytes([padlen]) | |
def xor(msg1,msg2): | |
assert len(msg1)==len(msg2) | |
return long_to_bytes(bytes_to_long(msg1)^bytes_to_long(msg2)) | |
class Task(socketserver.BaseRequestHandler): | |
def _recvall(self): | |
BUFF_SIZE = 2048 | |
data = b'' | |
while True: | |
part = self.request.recv(BUFF_SIZE) | |
data += part | |
if len(part) < BUFF_SIZE: | |
break | |
return data.strip() | |
def send(self, msg, newline=True): | |
try: | |
if newline: | |
msg += b'\n' | |
self.request.sendall(msg) | |
except: | |
pass | |
def recv(self, prompt=b'[-] '): | |
self.send(prompt, newline=False) | |
return self._recvall() | |
def proof_of_work(self): | |
proof = (''.join([random.choice(table)for _ in range(20)])).encode() | |
sha = sha256( proof ).hexdigest().encode() | |
self.send(b"[+] sha256(XXXX+" + proof[4:] + b") == " + sha ) | |
XXXX = self.recv(prompt = b'[+] Plz Tell Me XXXX :') | |
if len(XXXX) != 4 or sha256(XXXX + proof[4:]).hexdigest().encode() != sha: | |
return False | |
return True | |
def enc_msg(self,msg): | |
return block_encrypt(pad(msg),self.key,self.ivv) | |
def handle(self): | |
signal.alarm(50) | |
if not self.proof_of_work(): | |
return | |
self.ivv = os.urandom(16) | |
self.key = os.urandom(16) | |
while 1: | |
self.send(MENU,newline = False) | |
option = self.recv() | |
if (option == b'1'): | |
self.send(b"My Encrypted flag is:") | |
self.send(self.enc_msg(flag)) | |
elif option == b'2': | |
self.send(b"Give me Your Plain & I'll give you the Cipher.") | |
plaintext = self.recv() | |
self.send(b'PlainText:' + plaintext + b'\nCipherText:' + self.enc_msg(plaintext)) | |
else: | |
break | |
self.send(b"\n[.]Down the Connection.") | |
self.request.close() | |
class ThreadedServer(socketserver.ThreadingMixIn, socketserver.TCPServer): | |
pass | |
class ForkedServer(socketserver.ForkingMixIn, socketserver.TCPServer): | |
pass | |
if __name__ == "__main__": | |
HOST, PORT = '0.0.0.0', 10004 | |
print("HOST:POST " + HOST+":" + str(PORT)) | |
server = ForkedServer((HOST, PORT), Task) | |
server.allow_reuse_address = True | |
server.serve_forever() |
[my_encrypt.py]
from Crypto.Util.number import * | |
Sbox = ( | |
0x63, 0x7C, 0x77, 0x7B, 0xF2, 0x6B, 0x6F, 0xC5, 0x30, 0x01, 0x67, 0x2B, 0xFE, 0xD7, 0xAB, 0x76, | |
0xCA, 0x82, 0xC9, 0x7D, 0xFA, 0x59, 0x47, 0xF0, 0xAD, 0xD4, 0xA2, 0xAF, 0x9C, 0xA4, 0x72, 0xC0, | |
0xB7, 0xFD, 0x93, 0x26, 0x36, 0x3F, 0xF7, 0xCC, 0x34, 0xA5, 0xE5, 0xF1, 0x71, 0xD8, 0x31, 0x15, | |
0x04, 0xC7, 0x23, 0xC3, 0x18, 0x96, 0x05, 0x9A, 0x07, 0x12, 0x80, 0xE2, 0xEB, 0x27, 0xB2, 0x75, | |
0x09, 0x83, 0x2C, 0x1A, 0x1B, 0x6E, 0x5A, 0xA0, 0x52, 0x3B, 0xD6, 0xB3, 0x29, 0xE3, 0x2F, 0x84, | |
0x53, 0xD1, 0x00, 0xED, 0x20, 0xFC, 0xB1, 0x5B, 0x6A, 0xCB, 0xBE, 0x39, 0x4A, 0x4C, 0x58, 0xCF, | |
0xD0, 0xEF, 0xAA, 0xFB, 0x43, 0x4D, 0x33, 0x85, 0x45, 0xF9, 0x02, 0x7F, 0x50, 0x3C, 0x9F, 0xA8, | |
0x51, 0xA3, 0x40, 0x8F, 0x92, 0x9D, 0x38, 0xF5, 0xBC, 0xB6, 0xDA, 0x21, 0x10, 0xFF, 0xF3, 0xD2, | |
0xCD, 0x0C, 0x13, 0xEC, 0x5F, 0x97, 0x44, 0x17, 0xC4, 0xA7, 0x7E, 0x3D, 0x64, 0x5D, 0x19, 0x73, | |
0x60, 0x81, 0x4F, 0xDC, 0x22, 0x2A, 0x90, 0x88, 0x46, 0xEE, 0xB8, 0x14, 0xDE, 0x5E, 0x0B, 0xDB, | |
0xE0, 0x32, 0x3A, 0x0A, 0x49, 0x06, 0x24, 0x5C, 0xC2, 0xD3, 0xAC, 0x62, 0x91, 0x95, 0xE4, 0x79, | |
0xE7, 0xC8, 0x37, 0x6D, 0x8D, 0xD5, 0x4E, 0xA9, 0x6C, 0x56, 0xF4, 0xEA, 0x65, 0x7A, 0xAE, 0x08, | |
0xBA, 0x78, 0x25, 0x2E, 0x1C, 0xA6, 0xB4, 0xC6, 0xE8, 0xDD, 0x74, 0x1F, 0x4B, 0xBD, 0x8B, 0x8A, | |
0x70, 0x3E, 0xB5, 0x66, 0x48, 0x03, 0xF6, 0x0E, 0x61, 0x35, 0x57, 0xB9, 0x86, 0xC1, 0x1D, 0x9E, | |
0xE1, 0xF8, 0x98, 0x11, 0x69, 0xD9, 0x8E, 0x94, 0x9B, 0x1E, 0x87, 0xE9, 0xCE, 0x55, 0x28, 0xDF, | |
0x8C, 0xA1, 0x89, 0x0D, 0xBF, 0xE6, 0x42, 0x68, 0x41, 0x99, 0x2D, 0x0F, 0xB0, 0x54, 0xBB, 0x16, | |
) | |
InvSbox = ( | |
0x52, 0x09, 0x6A, 0xD5, 0x30, 0x36, 0xA5, 0x38, 0xBF, 0x40, 0xA3, 0x9E, 0x81, 0xF3, 0xD7, 0xFB, | |
0x7C, 0xE3, 0x39, 0x82, 0x9B, 0x2F, 0xFF, 0x87, 0x34, 0x8E, 0x43, 0x44, 0xC4, 0xDE, 0xE9, 0xCB, | |
0x54, 0x7B, 0x94, 0x32, 0xA6, 0xC2, 0x23, 0x3D, 0xEE, 0x4C, 0x95, 0x0B, 0x42, 0xFA, 0xC3, 0x4E, | |
0x08, 0x2E, 0xA1, 0x66, 0x28, 0xD9, 0x24, 0xB2, 0x76, 0x5B, 0xA2, 0x49, 0x6D, 0x8B, 0xD1, 0x25, | |
0x72, 0xF8, 0xF6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xD4, 0xA4, 0x5C, 0xCC, 0x5D, 0x65, 0xB6, 0x92, | |
0x6C, 0x70, 0x48, 0x50, 0xFD, 0xED, 0xB9, 0xDA, 0x5E, 0x15, 0x46, 0x57, 0xA7, 0x8D, 0x9D, 0x84, | |
0x90, 0xD8, 0xAB, 0x00, 0x8C, 0xBC, 0xD3, 0x0A, 0xF7, 0xE4, 0x58, 0x05, 0xB8, 0xB3, 0x45, 0x06, | |
0xD0, 0x2C, 0x1E, 0x8F, 0xCA, 0x3F, 0x0F, 0x02, 0xC1, 0xAF, 0xBD, 0x03, 0x01, 0x13, 0x8A, 0x6B, | |
0x3A, 0x91, 0x11, 0x41, 0x4F, 0x67, 0xDC, 0xEA, 0x97, 0xF2, 0xCF, 0xCE, 0xF0, 0xB4, 0xE6, 0x73, | |
0x96, 0xAC, 0x74, 0x22, 0xE7, 0xAD, 0x35, 0x85, 0xE2, 0xF9, 0x37, 0xE8, 0x1C, 0x75, 0xDF, 0x6E, | |
0x47, 0xF1, 0x1A, 0x71, 0x1D, 0x29, 0xC5, 0x89, 0x6F, 0xB7, 0x62, 0x0E, 0xAA, 0x18, 0xBE, 0x1B, | |
0xFC, 0x56, 0x3E, 0x4B, 0xC6, 0xD2, 0x79, 0x20, 0x9A, 0xDB, 0xC0, 0xFE, 0x78, 0xCD, 0x5A, 0xF4, | |
0x1F, 0xDD, 0xA8, 0x33, 0x88, 0x07, 0xC7, 0x31, 0xB1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xEC, 0x5F, | |
0x60, 0x51, 0x7F, 0xA9, 0x19, 0xB5, 0x4A, 0x0D, 0x2D, 0xE5, 0x7A, 0x9F, 0x93, 0xC9, 0x9C, 0xEF, | |
0xA0, 0xE0, 0x3B, 0x4D, 0xAE, 0x2A, 0xF5, 0xB0, 0xC8, 0xEB, 0xBB, 0x3C, 0x83, 0x53, 0x99, 0x61, | |
0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D, | |
) | |
xc = lambda a: (((a << 1) ^ 0x1B) & 0xFF) if (a & 0x80) else (a << 1) | |
R = ( | |
0x00, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, | |
0x80, 0x1B, 0x36, 0x6C, 0xD8, 0xAB, 0x4D, 0x9A, | |
0x2F, 0x5E, 0xBC, 0x63, 0xC6, 0x97, 0x35, 0x6A, | |
0xD4, 0xB3, 0x7D, 0xFA, 0xEF, 0xC5, 0x91, 0x39, | |
) | |
def t2m(text): | |
text = bytes_to_long(text) | |
matrix = [] | |
for i in range(16): | |
byte = (text >> (8 * (15 - i))) & 0xFF | |
if i % 4 == 0: | |
matrix.append([byte]) | |
else: | |
matrix[i // 4].append(byte) | |
return matrix | |
def m2t(matrix): | |
text = 0 | |
for i in range(4): | |
for j in range(4): | |
text |= (matrix[i][j] << (120 - 8 * (4 * i + j))) | |
return long_to_bytes(text) | |
class myAES: | |
def __init__(self, MasterKey): | |
self.ChangeKey(MasterKey) | |
def ChangeKey(self, MasterKey): | |
self.RoundKeys = t2m(MasterKey) | |
# print self.RoundKeys | |
for i in range(4, 4 * 11): | |
self.RoundKeys.append([]) | |
if i % 4 == 0: | |
byte = self.RoundKeys[i - 4][0] \ | |
^ Sbox[self.RoundKeys[i - 1][1]] \ | |
^ R[i // 4] | |
self.RoundKeys[i].append(byte) | |
for j in range(1, 4): | |
byte = self.RoundKeys[i - 4][j] \ | |
^ Sbox[self.RoundKeys[i - 1][(j + 1) % 4]] | |
self.RoundKeys[i].append(byte) | |
else: | |
for j in range(4): | |
byte = self.RoundKeys[i - 4][j] \ | |
^ self.RoundKeys[i - 1][j] | |
self.RoundKeys[i].append(byte) | |
# print self.RoundKeys | |
def encrypt(self, plaintext): | |
self.plain_state = t2m(plaintext) | |
self.__add_round_key(self.plain_state, self.RoundKeys[:4]) | |
for i in range(1, 10): | |
self.__round_encrypt(self.plain_state, self.RoundKeys[4 * i : 4 * (i + 1)]) | |
self.__sub_bytes(self.plain_state) | |
self.__shift_rows(self.plain_state) | |
self.__sub_bytes(self.plain_state) | |
self.__add_round_key(self.plain_state, self.RoundKeys[40:]) | |
return m2t(self.plain_state) | |
def __add_round_key(self, s, k): | |
for i in range(4): | |
for j in range(4): | |
s[i][j] ^= k[i][j] | |
def __round_encrypt(self, state_matrix, key_matrix): | |
self.__sub_bytes(state_matrix) | |
self.__shift_rows(state_matrix) | |
self.__mix_columns(state_matrix) | |
self.__add_round_key(state_matrix, key_matrix) | |
def __sub_bytes(self, s): | |
for i in range(4): | |
for j in range(4): | |
s[i][j] = Sbox[s[i][j]] | |
def __shift_rows(self, s): | |
s[0][1], s[1][1], s[2][1], s[3][1] = s[1][1], s[2][1], s[3][1], s[0][1] | |
s[0][2], s[1][2], s[2][2], s[3][2] = s[2][2], s[3][2], s[0][2], s[1][2] | |
s[0][3], s[1][3], s[2][3], s[3][3] = s[3][3], s[0][3], s[1][3], s[2][3] | |
def __mix_single_column(self, a): | |
# please see Sec 4.1.2 in The Design of Rijndael | |
t = a[0] ^ a[1] ^ a[2] ^ a[3] | |
u = a[0] | |
a[0] ^= t ^ xc(a[0] ^ a[1]) | |
a[1] ^= t ^ xc(a[1] ^ a[2]) | |
a[2] ^= t ^ xc(a[2] ^ a[3]) | |
a[3] ^= t ^ xc(a[3] ^ u) | |
def __mix_columns(self, s): | |
for i in range(4): | |
self.__mix_single_column(s[i]) | |
def xor(a,b): | |
assert len(a) == len(b) | |
tmp = [] | |
for i in range(len(a)): | |
tmp.append(a[i]^b[i]) | |
return bytes(tmp) | |
def exchange_plain(plaintext): | |
new_plain = [] | |
for i in plaintext: | |
new_plain.append(i<<1) | |
new_plain = bytes(new_plain) | |
return new_plain | |
def block_encrypt(plaintext,key,iv): | |
aes = myAES(key) | |
block = len(plaintext)//16 | |
new_plain = exchange_plain(plaintext) | |
cipher = b'' | |
for i in range(block): | |
iv = aes.encrypt(iv) | |
cipher += xor(iv,new_plain[16*i:16*i+16]) | |
return cipher |
# 「Analyze」
针对题目给出附件有 my_encrypt.pyc
,只不过是 python3.9
的,不是很好反编译完全,在线网站只能够反编译得到大概,但看不到对 block_encrypt
以及 exchange_plain
中 for
循环内部的信息。
但是这道题,给出的块加密使用的 key
和 iv
都是在初始化阶段内容中就已经固定了的,在一次连接之中不会更改,那么其实我们就可以去猜这种特征的加密模式会有什么样的漏洞。倘若是 OFB
模式又或者是 CFB
模式,根据 CTF-Wiki
上这张图
我们就可以得知,是将 IV
加密之后在与明文异或,但是下一轮的 IV
是上一轮 IV
加密后的内容,那么,我们就可以通过这个弱点,将其攻破,任意密文解密。
而该道题,我们可以看到一个 exchange_plain
这个函数,那么他应该会是对明文进行操作改变,但是我们并不知道如何操作,只能去一个个试,猜出来他是针对明文每一个字节都左移了 1 位,那么,我们就可以尝试解密 flag
了,只要长度足够的进行已知明文攻击,就可以拿到加密过后的每组 IV
,与加密后的 flag
进行异或之后进行明文恢复操作就可以拿到 flag
.
# 「Exp」
from pwn import * | |
from Crypto.Util.number import * | |
from hashlib import sha256 | |
import string | |
from pwnlib.util.iters import mbruteforce | |
table = string.ascii_letters+string.digits | |
def pow(): | |
io.recvuntil("XXXX+") | |
suffix = io.recv(16).decode("utf8") | |
io.recvuntil("== ") | |
cipher = io.recvline().strip().decode("utf8") | |
proof = mbruteforce(lambda x: sha256((x + suffix).encode()).hexdigest() == | |
cipher, table, length=4, method='fixed') | |
io.sendlineafter("XXXX :", proof) | |
def pad(m): | |
padlen = 16 - len(m) % 16 | |
return m + padlen * bytes([padlen]) | |
def enc(plaintext): | |
print(io.recvuntil(b'[-]').decode()) | |
io.sendline(b"2") | |
print(io.recvuntil(b'[-] ').decode()) | |
io.sendline(plaintext) | |
io.recvuntil(b"CipherText:") | |
c = io.recvuntil(b'[+]')[:-4] | |
return c | |
def xor(msg1,msg2): | |
assert len(msg1)==len(msg2) | |
return long_to_bytes(bytes_to_long(msg1)^bytes_to_long(msg2)) | |
if __name__ == "__main__": | |
io = remote("127.0.0.1",10004) | |
pow() | |
print(io.recvuntil(b'[-] ').decode()) | |
io.sendline(b"1") | |
print(io.recvuntil(b"My Encrypted flag is:").decode()) | |
c = io.recvuntil(b'[+]')[1:-4] | |
cipherlen = len(c) - 1 | |
fakeplain = cipherlen * b'\x01' | |
blocksize = cipherlen//16 | |
newcipher = enc(fakeplain) | |
fakeplain = pad(fakeplain) | |
new_plain = [] | |
for i in fakeplain: | |
new_plain.append((i)<<1) | |
new_plain = bytes(new_plain) | |
s = (xor(new_plain,newcipher[:])) | |
fakeplain2 = (xor(s,c)) | |
new_plain = [] | |
for i in fakeplain2: | |
new_plain.append((i)>>1) | |
new_plain = bytes(new_plain) | |
print(new_plain) |
# MyCryptoSystem
# 「Description」
再来看看这个加密系统吧
# 「SourceCode」
from Crypto.Util.number import* | |
import random | |
from secret import flag | |
from hashlib import sha256 | |
import socketserver | |
import signal | |
import string | |
def trans_flag(flag): | |
new_flag = [] | |
for i in range(6): | |
new_flag.append(bytes_to_long(flag[i*7:i*7+7])) | |
return new_flag | |
kbits = 1024 | |
table = string.ascii_letters+string.digits | |
flag = trans_flag(flag) | |
def Setup(kbits): | |
p_bit = kbits//2 | |
q_bit = kbits - p_bit | |
while 1: | |
p = getPrime(p_bit) | |
p_tmp = (p-1)//2 | |
if isPrime(p_tmp): | |
break | |
while 1: | |
q = getPrime(q_bit) | |
q_tmp = (q-1)//2 | |
if isPrime(q_tmp): | |
break | |
N = p*q | |
while 1: | |
g = random.randrange(N*N) | |
if (pow(g,p_tmp * q_tmp,N*N) - 1)%N == 0 and (pow(g,p_tmp * q_tmp,N*N) - 1)//N >= 1 and (pow(g,p_tmp * q_tmp,N*N) - 1)//N <= N - 1: | |
break | |
public = (N,g) | |
return public,p | |
def KeyGen(public): | |
N,g = public | |
a = random.randrange(N*N) | |
h = pow(g,a,N*N) | |
pk = h | |
sk = a | |
return pk,sk | |
def Encrypt(public,pk,m): | |
N,g = public | |
r = random.randrange(N*N) | |
A = pow(g,r,N*N) | |
B = (pow(pk,r,N*N) * (1 + m * N)) % (N * N) | |
return A,B | |
def Add(public,dataCipher1,dataCipher2): | |
N = public[0] | |
A1,B1 = dataCipher1 | |
A2,B2 = dataCipher2 | |
A = (A1*A2)%(N*N) | |
B = (B1*B2)%(N*N) | |
return (A,B) | |
def hint(p): | |
_p = getPrime(2048) | |
_q = getPrime(2048) | |
n = _p*_q | |
e = 0x10001 | |
s = getPrime(300) | |
tmp = (160 * s ** 5 - 4999 * s ** 4 + 3 * s ** 3 +1) | |
phi = (_p-1)*(_q-1) | |
d = inverse(e,phi) | |
k = (_p-s)*d | |
enc = pow(p,e,n) | |
return (tmp,k,enc,n) | |
class Task(socketserver.BaseRequestHandler): | |
def _recvall(self): | |
BUFF_SIZE = 2048 | |
data = b'' | |
while True: | |
part = self.request.recv(BUFF_SIZE) | |
data += part | |
if len(part) < BUFF_SIZE: | |
break | |
return data.strip() | |
def send(self, msg, newline=True): | |
try: | |
if newline: | |
msg += b'\n' | |
self.request.sendall(msg) | |
except: | |
pass | |
def recv(self, prompt=b'SERVER <INPUT>: '): | |
self.send(prompt, newline=False) | |
return self._recvall() | |
def proof_of_work(self): | |
proof = (''.join([random.choice(table)for _ in range(20)])).encode() | |
sha = sha256(proof).hexdigest().encode() | |
self.send(b"[+] sha256(XXXX+" + proof[4:] + b") == " + sha ) | |
XXXX = self.recv(prompt = b'[+] Plz Tell Me XXXX :') | |
if len(XXXX) != 4 or sha256(XXXX + proof[4:]).hexdigest().encode() != sha: | |
return False | |
return True | |
def handle(self): | |
proof = self.proof_of_work() | |
if not proof: | |
self.request.close() | |
public,p = Setup(kbits) | |
signal.alarm(60) | |
pk = [] | |
for i in range(6): | |
pki,ski = KeyGen(public) | |
pk.append(pki) | |
msg = [123,456,789,123,456,789] | |
CipherPair = [] | |
for i in range(len(pk)): | |
TMP = Encrypt(public,pk[i],msg[i]) | |
CipherPair.append(((TMP),pk[i])) | |
CipherDate = [] | |
for i in range(len(pk)): | |
CipherDate.append(Add(public,Encrypt(public,pk[i],flag[i]),CipherPair[i][0])) | |
self.send(b'What do you want to get?\n[1]pk_list\n[2]public_parameters\n[3]hint_for_p\n[4]EncRypt_Flag\n[5]exit') | |
while 1: | |
option = self.recv() | |
if option == b'1': | |
self.send(b"[~]My pk_list is:") | |
self.send(str(pk).encode()) | |
elif option == b'2': | |
self.send(b"[~]My public_parameters is") | |
self.send(str(public).encode()) | |
elif option == b'3': | |
self.send(b"[~]My hint for p is") | |
self.send(str(hint(p)).encode()) | |
elif option == b'4': | |
self.send(b'[~]What you want is the flag!') | |
self.send(str(CipherDate).encode()) | |
else: | |
break | |
self.request.close() | |
class ThreadedServer(socketserver.ThreadingMixIn, socketserver.TCPServer): | |
pass | |
class ForkedServer(socketserver.ForkingMixIn, socketserver.TCPServer): | |
pass | |
if __name__ == "__main__": | |
HOST, PORT = '0.0.0.0', 10004 | |
print("HOST:POST " + HOST+":" + str(PORT)) | |
server = ForkedServer((HOST, PORT), Task) | |
server.allow_reuse_address = True | |
server.serve_forever() |
# 「Analyze」
一开始先是将 flag 每 7 位 bytes_to_long
之后组成一个 flag
的 list
,接着我们将每个重要的主体函数都对应转换成数学公式来看
- 其中 是一个安全位数参量,需要找到安全的 比特长的
RSA
模数 ,满足 以及 都是素数。去生成一个随机数 满足
- 随机生成私钥参数 ,并且计算 公钥
- 随机量 ,加密 得到两个参数
- 这里就只是进行了一个加法同态数据上的加密
题目给出 MENU
有 4 个选项,其中通过 hint_for_p
leak 了 ,通过二分拿到 ,计算 就能够拿到 ,到这里我们可以看出来其实这道题的加密系统很像 pallier,这里已经能够分解 了,那么必定是不安全的,虽然说他使用了任意的公钥加密。
paper:https://link.springer.com/content/pdf/10.1007%2Fb94617.pdf (37)
只需要去实现该篇论文中的另外一种解密方式就能够成功解密。
- 计算 , 接着计算
- 最终我们可以使用这些参数去拿到 m
# 「Exp」
from pwn import * | |
from Crypto.Util.number import * | |
from hashlib import sha256 | |
import string | |
from pwnlib.util.iters import mbruteforce | |
table = string.ascii_letters+string.digits | |
def pow(): | |
io.recvuntil("XXXX+") | |
suffix = io.recv(16).decode("utf8") | |
io.recvuntil("== ") | |
cipher = io.recvline().strip().decode("utf8") | |
proof = mbruteforce(lambda x: sha256((x + suffix).encode()).hexdigest() == | |
cipher, table, length=4, method='fixed') | |
io.sendlineafter("XXXX :", proof) | |
io = remote("0.0.0.0",10004) | |
pow() | |
io.interactive() | |
def getS(data): | |
left,right = 0,2**301 | |
for i in range(1000): | |
tmp = (left + right)//2 | |
if 160 * tmp ** 5 - 4999 * tmp ** 4 + 3 * tmp ** 3 +1-data > 0: | |
right = tmp | |
else: | |
left = tmp | |
return tmp | |
def getP(pdata): | |
tmp,k,c,n = pdata | |
s = getS(tmp) | |
e = 0x10001 | |
a = pow(3,e*k,n)-pow(3,1-s,n) | |
_p = GCD(a,n) | |
_q = n//_p | |
d = inverse(e,(_p-1)*(_q-1)) | |
return pow(c,d,n) | |
pdata = | |
pk = | |
public = | |
p = getP(pdata) | |
msg = [123,456,789,123,456,789] | |
secret = (p//2,public[0]//p//2) | |
k = (pow(public[1],secret[0]*secret[1],public[0]**2)-1) // public[0] | |
public = public[0],k,public[1] | |
def MDecrypt(public,pk,secret,A,B): | |
p_sec , q_sec = secret | |
N,k,g = public | |
h = pk | |
k_1 = inverse(k,N) | |
a = ((((pow(h,p_sec * q_sec,N**2) - 1) % (N**2) )//N )* k_1) % N | |
r = ((((pow(A,p_sec * q_sec,N**2) - 1) % (N**2) )//N )* k_1) % N | |
delta = pow(p_sec * q_sec ,-1 , N) | |
gamma = (a * r) % N | |
m = ((((pow(B * inverse(pow(g,gamma,N **2),N**2),p_sec * q_sec, N ** 2) - 1 ) %(N*N)) // N) * delta )%N | |
return m | |
print(len(pk)) | |
CipherDate = | |
for i in range(len(pk)): | |
A,B = CipherDate[i] | |
print(long_to_bytes(MDecrypt(public,pk[i],secret,A,B)-msg[i]).decode(),end='') |
# Referance
.pyc
在线反编译:https://tool.lu/pyc/
OFB
模式:https://wiki.x10sec.org/crypto/blockcipher/mode/ofb/
BCP
密码系统:https://link.springer.com/content/pdf/10.1007%2Fb94617.pdf (37)4