2024-NCTF-crypto

没啥时间写，复现一下

sign

题目：
srv.py：

from Crypto.Util.number import *
from util import *
from os import getenv
from Crypto.Util.Padding import pad
from random import Random
from Crypto.Cipher import AES
from hashlib import md5

string = open('secret.txt').read().strip().encode()
flag = getenv('FLAG').encode()

if __name__=='__main__':
    Keys = []
    for m in string:
        f = FHE()
        s = long_to_bytes(Random().getrandbits(20000))
        for i in s[4:]:
            Keys.extend(f.encrypt([i]))

        for i in s[:4]:
            Keys.extend(f.encrypt([i * (m & 0x03) % 0x101]))
            m >>= 2
        
    assert len(Keys) == 30000

    print(f'[+] Your ciphertext: {AES.new(md5(string).digest(),AES.MODE_ECB).encrypt(pad(flag,16)).hex()}')
    input(f'[+] The keys to retrieve the global internet connection are as follows:')
    for i in range(30000):
        print(f'[+] {Keys[i]}')

util.py：

from os import urandom
from Crypto.Util.number import *

def getrandint(n:int):
    return int.from_bytes(urandom(n//8+1)) % pow(2,n)

class FHE:
    def __init__(self):
        self.p = getPrime(77)
        self.pubkeys = []
        for _ in range(16):
            self.pubkeys.append(self.p * getrandint(177) + (getrandint(17) << 8))

    def encrypt(self,msg:list[int] | bytes):
        result = []
        for m in msg:
            tmp = 0
            shuffle_base = urandom(16)
            for i in shuffle_base:
                x,y = divmod(i,16)
                tmp += x*self.pubkeys[y] + y*self.pubkeys[x]
            result.append(tmp + m)
        return result

在srv.py中生成s这个20000bit的随机数，可以想到进行随机数预测，但是不能直接得到s，得到的是通过util.py加密后的s，那就需要先进行解密
util.py实际是AGCD问题，$result=p*A+256*B+m$
参考：AGCD近似最大公约数问题|独奏小屋
直接可以求出m(srv.py中的s的一个字节)，然后就可以进行$8 \times 2496$的随机数预测
exp：

from Crypto.Util.number import *
from random import *
import json
from Crypto.Cipher import AES
from hashlib import md5
from Crypto.Util.number import *
from random import *
from tqdm import *
from pwn import *

sh=remote("39.106.16.204",...)

sh.recvuntil(b'ciphertext: ')
ciphertext=sh.recvline().strip().decode()
sh.recvuntil(b' follows:')
sh.sendline(b'')
Keys=[]
for i in range(30000):
    sh.recvuntil(b'[+] ')
    key=sh.recvline().strip().decode()
    Keys.append(int(key))

sh.close()

assert len(Keys) == 30000
def construct_a_row(RNG):
    row = []
    for _ in range(19968 // 32):
        tmp = RNG.getrandbits(32)
        row = list(map(int, bin(tmp)[2:].zfill(32))) + row
    return row

# 构造线性方程组的矩阵
L = []
for i in trange(19968):
    state = [0] * 624
    temp = "0" * i + "1" * 1 + "0" * (19968 - 1 - i)
    for j in range(624):
        state[j] = int(temp[32 * j:32 * j + 32], 2)
    RNG = Random()
    RNG.setstate((3, tuple(state + [624]), None))
    L.append(construct_a_row(RNG))
# 将L转换为GF(2)上的矩阵（二进制域）
L = Matrix(GF(2), L)

def AGCD(xs, rho):
    k = len(xs)
    A = ZZ(pow(2, rho + 1))
    B = matrix(xs[1:])
    C = matrix.diagonal([-xs[0]] * (k - 1))
    M = matrix.block([[A, B], [ZZ(0), C]])
    L = M.LLL()
    q0 = ZZ(L[0, 0] / A).abs()
    e0 = ZZ(xs[0] % q0)
    p = ZZ((xs[0] - e0) / q0)
    return p


def MT19937_re(state):
    try:
        # 构造目标向量R 
        R = []
        for i in state:
            R += list(map(int, bin(i)[2:].zfill(8)))

        R = vector(GF(2), R)
        s = L.solve_left(R)  # 这里可能会抛出异常 

        # 将解转换为二进制字符串 
        init = "".join(list(map(str, s)))
        state = []
        # 将解重新分割成624个32位整数 
        for i in range(624):
            state.append(int(init[32 * i:32 * i + 32], 2))

            # 创建新的RNG并设置恢复出的状态
        RNG1 = Random()
        RNG1.setstate((3, tuple(state + [624]), None))

        return RNG1

    except Exception as e:
        print(f"[-]{e}")
        pass


ciphertext = long_to_bytes(ciphertext)
Keys = [...]

string = b""
for i in range(30000 // 2500):
    xs = Keys[i * 2500:(i + 1) * 2500]
    p = AGCD(xs[:40], 25)
    print(f"[+]found p:{p}")
    es = [(x % p) % 256 for x in xs]
    RNG = MT19937_re(es[:-4])
    print("[+]reverse MT19937")
    heads = [int(i) for i in long_to_bytes(RNG.getrandbits(20000))[:4]]
    m = 0
    for i in range(4)[::-1]:
        tmp = (pow(heads[i], -1, 0x101) * es[-4:][i]) % 0x101
        assert int(tmp).bit_length() <= 2
        m = (m << 2) + tmp
    m = long_to_bytes(int(m))
    string += m
    print(f"[+]get:{m}")
print(f"[+]string:{string}")
print(f"[+]flag: {AES.new(md5(string).digest(), AES.MODE_ECB).decrypt(ciphertext)}")

Arcahv

题目：

from Crypto.Util.number import *
from os import urandom,getenv
from functools import reduce
from Crypto.Cipher import AES

class LCG:
    def __init__(self,seed:int) -> None:
        self.p = getPrime(1024)
        self.a = getPrime(1023)
        self.b = getPrime(1023)
        self.status = seed

    def next(self) -> int:
        ret = self.status
        self.status = (self.status * self.a + self.b) % self.p
        return ret
    
def crystal_trick(m:bytes) -> bytes:
    m = bytearray(m)
    for i in range(len(m)):
        m[i] = reduce(lambda x,y: x^y^urandom(1)[0],m[:i],m[i])
    return m

class RSA:
    def __init__(self):
        p = getStrongPrime(1024)
        q = getStrongPrime(1024)
        self.p = p
        self.N = p * q
        self.e = 65537
        self.d = pow(self.e, -1, (p-1)*(q-1))

    def encrypt(self,m:int) -> int:
        return pow(m,self.e,self.N)
    
    def decrypt(self,c:int) -> int:
        return pow(c,self.d,self.N) 

class MyRSA1(RSA):
    def encrypt(self,m:bytes) -> bytes:
        return super().encrypt(int.from_bytes(m)).to_bytes(256)
    
    def decrypt(self,c:bytes) -> bytes:
        return super().decrypt(int.from_bytes(c)).to_bytes(256)

class MyRSA2(RSA):
    def encrypt(self,m:bytes) -> bytes:
        return pow(int.from_bytes(m),self.e,self.N).to_bytes(256,'little')
    
    def decrypt(self,c:bytes) -> bytes:
        m = pow(int.from_bytes(c),self.d,self.N).to_bytes(256,'little')
        print('Hibiscus is here to trick your decryption result!!')
        return crystal_trick(m)

menu = '''
Welcome to NCTF 2025 arcahv challenge!

--- Menu ---
[1] View encrypted flag and hint
[2] Play with the decryption orcale
[3] Get some random numbers for fun
[4] Exit

Your Option > '''


if __name__=='__main__':
    print('Loading, please wait...')
    
    # flag = open('flag.txt').read().strip().encode()
    flag = getenv('FLAG').encode()
    attempts = 75
    r1 = MyRSA1()
    r2 = MyRSA2()
    hint1 = r2.encrypt(r1.p.to_bytes(128))

    key = urandom(16)
    hint2 = AES.new(key,AES.MODE_ECB).encrypt(r1.N.to_bytes(256))

    def flag_and_hint():
        print(f'Encrypted flag: {r1.encrypt(flag).hex()}')
        print(f'Hint1: {hint1.hex()}')
        print(f'Hint2: {hint2.hex()}')

    def rsachal(): 
        global attempts

        print("Since you didn't v Hibiscus 50 on crazy thursday, Hibiscus decided to do some trick on your decryption result!")
        print(f'Your pubkey:({hex(r2.N)[2:]},{hex(r2.e)[2:]})')

        while attempts > 0:
            if input('Do you still want to try decryption(y/[n])?') != 'y':
                break

            c = bytes.fromhex(input(f'You have {attempts} remaining access to decryption orcale!\nYour ciphertext(in hex):'))
            print(f'Result: {r2.decrypt(c).hex()}')
            attempts -= 1
        
        if attempts == 0:
            print('Unfortunately, you are out of decryption attempts! Come back again on nctf2026 ~')

    
    def lcgchal():
        lcg = LCG(int.from_bytes(key))

        print('Tempering with LCG generator, please wait...')
        while urandom(1)[0] & 0xff:
            lcg.next()
        
        hexnums = ''.join(hex(lcg.next())[2:] for _ in range(5))
        if len(hexnums) % 16:
            hexnums = hexnums.zfill((len(hexnums) // 16 + 1) * 16)
        
        idx = 0
        while input('Do you want another unsigned long long number(y/[n])?') == 'y':
            print(int(''.join(hexnums[idx:idx+16]),16))
            idx = (idx + 16) % len(hexnums)

    def bye():
        print('Hope you have fun during the challenge XD:)')
        exit(0)

    fundc = {1:flag_and_hint,2:rsachal,3:lcgchal,4:bye}

    while True:
        opt = input(menu)
        if len(opt) == 0 or opt not in '1234':
            opt = '4'
        fundc[int(opt)]()

学习了一下RSA bytes orcale，通过Oracle返回明文的最后一个字节，进行解密
**RSA 选择明密文攻击 **写得很清楚
还有就是常规的给五组数据求lcg参数，求出来seed就是key
RSA bytes orcale部分exp：

inv = pow(n,-1,256)
c = hint1*pow(pow(256, e, n), 127, n) % n
k = 0
for _ in range(75):
    c = (c * pow(256, e, n)) % n
    io.sendline(long_to_bytes(c).hex().encode())#发送c
    tmp = bytes.fromhex(io.recvline()[8:].strip().decode())[0]#返回的明文最后一个字节
    tmp = -inv*tmp % 256
    k = k*256+tmp
 
ph = int((k+1)*n/256**(127+75))

lcg部分exp：

from Crypto.Util.number import *
x1 = 
x2 = 
x3 = 
x4 = 
x5 = 

x = [x1, x2, x3, x4, x5]
t = []

for i in range(1, len(x)):
    t.append(x[i] - x[i-1])

m = 0
for i in range(1, len(t)-1):
    m = GCD(t[i+1]*t[i-1] - t[i]*t[i], m)

m //= 2  # 注意这里
print(m)
assert isPrime(m)
a = (x3 - x2) * inverse(x2 - x1, m)
b = (x2 - a*x1) % m

inva = inverse(a, m)
 while True:
        seed=int((seed-b)*inverse(a,n) % n)
        if seed.bit_length()<=128:
            break
seed=long_to_bytes(seed)

X1crypsc -misc

题目：

from random import *
import time
import pyfiglet

text = "X1crypsc"
ascii_art = pyfiglet.figlet_format(text)
print(ascii_art)
time.sleep(1)
print('[+]I want to play a game.\n')
time.sleep(1)
print('[+]If you win the game, I will give you a gift:)\n')
time.sleep(1)
print('[+]But try to beat the monster first:)\n')
time.sleep(1)
print('[+]Good luck!\n')
print('[+]You got a weapon!\n')
damage_rng = ()
def regenerate_damage():
    global damage_rng
    base = getrandbits(16)
    add = getrandbits(16)
    damage_rng = (base ,base + add)
monster_health = getrandbits(64)
menu = '''
---Options---
[W]eapon
[A]ttack
[E]xit
'''
regenerate_damage()
print(menu)
HP = 3
while True:
    if monster_health <= 0:
        print('[+] Victory!!!')
        break
    if HP <= 0:
        print('[!] DEFEAT')
        exit(0)
    print(f'[+] Monster current HP:{monster_health}')
    print(f'[+] Your current HP: {HP}')
    opt = input('[-] Your option:')
    if opt == 'W':
        print(f'[+] Current attack value: {damage_rng[0]} ~ {damage_rng[1]}')
        if input('[+] Do you want to refresh the attack profile of the weapon([y/n])?') == 'y':
            regenerate_damage()
            print(f'[+] New weapon attack value: {damage_rng[0]} ~ {damage_rng[1]}')
    elif opt == 'A':
        print('[+] The monster sensed of an imminent danger and is about to teleport!!\n')
        print('[+] Now you have to aim at the monster\'s location to hit it!\n')
        print('[+]Input format: x y\n')
        x,y = map(int,input(f'[-] Provide the grid you\'re willing to aim:').split())
        if [x,y] ==  [randrange(2025),randrange(2025)]:
            dmg = min(int(randint(*damage_rng) ** (Random().random() * 8)),monster_health)
            print(f'[+] Decent shot! Monster was hevaily damaged! Damage value = {dmg}')
            monster_health -= dmg
        else:
            print("[+] Your bet didn't pay off, and the monster presented a counterattack on you!")
            HP -= 1     
    elif opt == 'E':
        print('[+] Bye~')
        exit(0)
    else:
        print('[!] Invalid input')
print('[+]Well done! You won the game!\n')
print('[+]And here is your gift: you got a chance to create a time capsule here and we\'ll keep it for you forever:)\n')

'''
[REDACTED]
'''

其实就是通过伤害提供的数据进行预测，预测出攻击范围
采用64 + 622 * 32 = 19968进行预测
exp：

from Crypto.Util.number import *
from Crypto.Util.number import *
from random import *
from tqdm import *
from pwn import *

r = remote("39.106.16.204",'')
######################################################## part1 recover MT and get seed
RNG = Random()

def construct_a_row(RNG):
        row = []
        bits = RNG.getrandbits(64)
        row += list(map(int, bin(bits)[2:].zfill(64)))
        for _ in range(622):
            # 获取 8 位随机数,右移 6 位只保留前 2 位
            bits = RNG.getrandbits(16)
            row += list(map(int, bin(bits)[2:].zfill(16)))
            bits = RNG.getrandbits(16)
            # 转换为二进制并填充到 2 位
            row += list(map(int, bin(bits)[2:].zfill(16)))

        return row


L = []
for i in trange(0,19968):

    state = [0]*624
    temp = "0"*i + "1"*1 + "0"*(19968-1-i)
    for j in range(624):
        state[j] = int(temp[32*j:32*j+32],2)
    RNG.setstate((3,tuple(state+[624]),None))
    L.append(construct_a_row(RNG))

L = Matrix(GF(2),L)
R = []
# c = []
r.recvuntil(b'HP:')
gift = (eval(r.recvline().strip().decode()))
gift = int((bin(gift)[2:].zfill(64)),2)
R += list(map(int, (bin(((gift)))[2:].zfill(64))))
for i in range(622):#832
    r.recvuntil(b"option:")
    r.sendline(b'W')
    r.recvuntil(b'value:')
    gift = (eval(r.recvuntil(b'~')[:-2].strip().decode()))
    gift1 = (eval(r.recvline().strip().decode()))- gift
    gift = int((bin(gift)[2:].zfill(16)),2)
    gift1 = int((bin(gift1)[2:].zfill(16)), 2)
    R += list(map(int, (bin(((gift)))[2:].zfill(16))))
    R += list(map(int, (bin(((gift1)))[2:].zfill(16))))
    r.sendline(b'y')
# print(R)
R = vector(GF(2),R)
s = L.solve_left(R)
# print(s)
# r.interactive()
# s = (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 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init = "".join(list(map(str,s)))
state = []
for i in range(624):
    state.append(int(init[32*i:32*i+32],2))
RNG1 = Random()
RNG1.setstate((3,tuple(state+[624]),None))
k = RNG1.getrandbits(64)
for i in range (623):
    k = RNG1.getrandbits(16)
    k1=RNG1.getrandbits(16)
# print(k)
# print(k1)
for i in range (3):
    r.recvuntil(b"option:")
    r.sendline(b'A')
    k = RNG1.randrange(2025)
    k1 = RNG1.randrange(2025)

print(r.recvline())
    # r.sendline(RNG1.getrandbits(16))

参考：
NCTF2024-Crypto|Naby
NCTF 2024|SeanDictionary