[De1CTF2019]Babylfsr

题目

import hashlib
from secret import KEY,FLAG,MASKassert(FLAG=="de1ctf{"+hashlib.sha256(hex(KEY)[2:].rstrip('L')).hexdigest()+"}")
assert(FLAG[7:11]=='1224')LENGTH = 256assert(KEY.bit_length()==LENGTH)
assert(MASK.bit_length()==LENGTH)def pad(m):pad_length = 8 - len(m)return pad_length*'0'+mclass lfsr():def __init__(self, init, mask, length):self.init = initself.mask = maskself.lengthmask = 2**(length+1)-1def next(self):nextdata = (self.init << 1) & self.lengthmask i = self.init & self.mask & self.lengthmask output = 0while i != 0:output ^= (i & 1)i = i >> 1nextdata ^= outputself.init = nextdatareturn outputif __name__=="__main__":l = lfsr(KEY,MASK,LENGTH)r = ''for i in range(63):b = 0for j in range(8):b = (b<<1)+l.next()r += pad(bin(b)[2:])with open('output','w') as f:f.write(r)

001010010111101000001101101111010000001111011001101111011000100001100011111000010001100101110110011000001100111010111110000000111011000110111110001110111000010100110010011111100011010111101101101001110000010111011110010110010011101101010010100101011111011001111010000000001011000011000100000101111010001100000011010011010111001010010101101000110011001110111010000011010101111011110100011110011010000001100100101000010110100100100011001000101010001100000010000100111001110110101000000101011100000001100010

解题
考点是伪随机LFSR

加密代码这个网址有：https://www.cnblogs.com/yhsy1002/p/6888895.html

先爆破掩码：

def test(padding):s = [int(x) for x in '001010010111101000001101101111010000001111011001101111011000100001100011111000010001100101110110011000001100111010111110000000111011000110111110001110111000010100110010011111100011010111101101101001110000010111011110010110010011101101010010100101011111011001111010000000001011000011000100000101111010001100000011010011010111001010010101101000110011001110111010000011010101111011110100011110011010000001100100101000010110100100100011001000101010001100000010000100111001110110101000000101011100000001100010'] + paddingM = matrix(GF(2), 256, 256)T = vector(GF(2), 256)for i in range(len(s) - 256):M[i] = s[i : i + 256]T[i] = s[i+256]try:mask = M.inverse() * Tprint(hex(int(''.join(map(str, (mask))), base=2)))except:returnfor x in itertools.product([0, 1], repeat = 8):test(list(x))

然后解题代码为

import itertools, hashlib, numpy as npdef int2bin(a, n):assert 0<=n and a < 2**nres = np.zeros(n, dtype = int)for x in range(n):res[n-x-1] = a % 2a = a // 2return res.tolist()def bin2int(a):return reduce(lambda x,y: x*2+y, a)def bitAnd(a, b):assert len(a) == len(b)return list(map(lambda x,y: int(x)&int(y), a, b))def test(padding):s = [int(x) for x in '001010010111101000001101101111010000001111011001101111011000100001100011111000010001100101110110011000001100111010111110000000111011000110111110001110111000010100110010011111100011010111101101101001110000010111011110010110010011101101010010100101011111011001111010000000001011000011000100000101111010001100000011010011010111001010010101101000110011001110111010000011010101111011110100011110011010000001100100101000010110100100100011001000101010001100000010000100111001110110101000000101011100000001100010'] + paddingM = matrix(GF(2), 256, 256)T = vector(GF(2), 256)for i in range(len(s) - 256):M[i] = s[i : i + 256]T[i] = s[i+256]try:mask = M.inverse() * Texcept:returnsuf = []for i in range(256):if bitAnd([0] + suf + s[0:255 - i], mask).count(1) % 2 == s[255 - i]:suf = [0] + sufelse:suf = [1] + sufkey = hex(bin2int(suf))[2:]sha = hashlib.sha256(key.encode()).hexdigest()if sha[:4] == '1224':print(sha)for x in itertools.product([0, 1], repeat = 8):test(list(x))

sage运行得到：1224473d5e349dbf2946353444d727d8fa91da3275ed3ac0dedeb7e6a9ad8619

flag{1224473d5e349dbf2946353444d727d8fa91da3275ed3ac0dedeb7e6a9ad8619}

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