Rating:

[hack.py](./hack.py)

Looking at [hack.py](./hack.py),

from Crypto.Util.number import *
from hashlib import md5

flag = "XXX"
assert len(flag) == 14

hack = 0

for char in flag:
hack*= ord(char)

print hack
#hack = 64364485357060434848865708402537097493512746702748009007197338675
#flag_to_submit = "MeePwnCTF{" + flag + "}"

We first try to factor the hack number: http://factordb.com/index.php?query=64364485357060434848865708402537097493512746702748009007197338675, so we see that it is factorable. The reason why we do this is because we know that hack is multiplied by the last character of the flag before its value is 64364485357060434848865708402537097493512746702748009007197338675, so the last character of the flag is one of the factors of 64364485357060434848865708402537097493512746702748009007197338675.

Assuming that the flag is printable ASCII characters, we don't have to search all 255 possible chars, just letters (upper and lowercase), numbers, and punctuation. Looking at the divisors of hack, we conclude that the possible values of our flag is [105, 107, 75, 35, 45, 63] or ['i', 'k', 'K', '#', '-', '?']. Now that we know what the last character of our flag could be, we still need to figure out pad in order to guess the other values of the characters of our flag.

Let's first rewrite hack. When the for loop runs for the first time, hack = ord(flag_1) * pad, here flag_1 just denotes the 1st character of the flag. The second time hack = ord(flag_2) * (hack + pad) = ord(flag_2) * (ord(flag_1 * pad) + pad). The third time hack = ord(flag_3) * (hack + pad) = ord(flag_3) * (ord(flag_2) * (ord(flag_1 * pad) + pad)) + pad). This continues 14 times, however note that we can factor out pad, meaning that pad also has to be a factor of 64364485357060434848865708402537097493512746702748009007197338675!. We know that md5 is 128 bits, or 16 bytes, so that means that pad will have a maximum value of 0xffffffffffffffffffffffffffffffff, so we just have to check the divisors of 64364485357060434848865708402537097493512746702748009007197338675 that are less than or equal to 0xffffffffffffffffffffffffffffffff.

So the plan is to loop through each candidate of pad and then get the possible values for the other characters of our flag, and then check if the 14-length string is our flag. We can check by just using the same hack.py, just modifying the last line to check if hack == 64364485357060434848865708402537097493512746702748009007197338675

The final code is in [solution.py](./solution.py). Things to note: I first try the last character of the flag as 63 or ? because it seems the most logical (I got lucky that it was the right one). If it wasn't right, then I'd have to change my code slightly to replace the occurences of 63 with my new guess for the last char. Also factorization doesn't contain all of the factors of 64364485357060434848865708402537097493512746702748009007197338675, rather the factors of 64364485357060434848865708402537097493512746702748009007197338675//63. I took out 63 from the factorization as pad can't take on any values that are divisible by 63, then that would mean that 64364485357060434848865708402537097493512746702748009007197338675 is divisible by 63^2 (which it isn't).

import itertools
from operator import mul
import copy
from Crypto.Util.number import *
from hashlib import md5

factorization = [(5, 2), (107, 1), (487, 1), (607, 1), (28429, 1), (29287, 1), (420577267963, 1), (3680317203978923, 1), (1002528655290265069, 1)]
values = [[(factor**e) for e in range(exp+1)] for (factor, exp) in factorization]
l = [];
printable = [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 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, 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, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 58, 59, 60, 61, 62, 63, 64, 91, 92, 93, 94, 95, 96, 123, 124, 125, 126, 32]

def getM(s, pr):
m = [];
for c in pr:
if s % c == 0:
m.append(c);
return m;

def hack(fla):
assert len(fla) == 14

hack = 0

for char in fla:
hack*= ord(char)

return hack == 64364485357060434848865708402537097493512746702748009007197338675

#print getM(64364485357060434848865708402537097493512746702748009007197338675, printable);

for xs in itertools.product(*values): #xs is a divisor of our number
sss = reduce(mul, xs, 1);
if ((sss <= 0xffffffffffffffffffffffffffffffff)):

news = 64364485357060434848865708402537097493512746702748009007197338675//63 - sss
mods = getM(news, printable);

if len(mods) > 0:
temps = copy.copy(news);
for mmm in mods:
news = news//mmm - sss;
mods2 = getM(news, printable);
if len(mods2) > 0:
temp2s = copy.copy(news);
for mmm2 in mods2:
news = news//mmm2 - sss;
mods3 = getM(news, printable);
if len(mods3) > 0:
temp3s = copy.copy(news);
for mmm3 in mods3:
news = news//mmm3 - sss;
mods4 = getM(news, printable);
if len(mods4) > 0:
temp4s = copy.copy(news);
for mmm4 in mods4:
news = news//mmm4 - sss;
mods5 = getM(news, printable);
if len(mods5) > 0:
temp5s = copy.copy(news);
for mmm5 in mods5:
news = news//mmm5 - sss;
mods6 = getM(news, printable);
if len(mods6) > 0:
temp6s = copy.copy(news);
for mmm6 in mods6:
news = news//mmm6 - sss;
mods7 = getM(news, printable);
if len(mods7) > 0:
temp7s = copy.copy(news);
for mmm7 in mods7:
news = news//mmm7 - sss;
mods8 = getM(news, printable);
if len(mods8) > 0:
temp8s = copy.copy(news);
for mmm8 in mods8:
news = news//mmm8 - sss;
mods9 = getM(news, printable);
if len(mods9) > 0:
temp9s = copy.copy(news);
for mmm9 in mods9:
news = news//mmm9 - sss;
mods10 = getM(news, printable);
if len(mods10) > 0:
temp10s = copy.copy(news);
for mmm10 in mods10:
news = news//mmm10 - sss;
mods11 = getM(news, printable);
if len(mods11) > 0:
temp11s = copy.copy(news);
for mmm11 in mods11:
news = news//mmm11 - sss;
mods12 = getM(news, printable);
if len(mods12) > 0:
temp12s = copy.copy(news);
for mmm12 in mods12:
news = news//mmm12 - sss;
mods13 = getM(news, printable);
if len(mods13) > 0:
temp13s = copy.copy(news);
for mmm13 in mods13:
news = news//mmm13 - sss;
mods14 = getM(news, printable);
flagg = chr(63) + chr(mmm) + chr(mmm2) + chr(mmm3) + chr(mmm4) + chr(mmm5) + chr(mmm6) + chr(mmm7) + chr(mmm8) + chr(mmm9) + chr(mmm10) + chr(mmm11) + chr(mmm12) + chr(mmm13);
if hack(flagg[::-1]):
print 'FOUND IT:', flagg[::-1], sss;
news = temp13s;
news = temp12s;
news = temp11s;
news = temp10s;
news = temp9s;
news = temp8s;
news = temp7s;
news = temp6s;
news = temp5s;
news = temp4s;
news = temp3s;
news = temp2s;
news = temps;

After running the code for a couple of minutes we get FOUND IT: [email protected]? 181900073144279366933091092045656603525. Our flag is MeePwnCTF{[email protected]?}.