# PicoCTF 2014 Write-ups

## Block - 130 (Cryptography)

#### Writeup by ZIceZ

Created: 2014-11-07 21:52:29

### Problem

Daedalus Corp has been using this script to encrypt it's data! We think this file contains a password to their command server. Can you crack it?

block.py

encrypted

### Hint

Is double encryption twice as secure?

### Overview

Find the keys through brute force using meet in the middle attack.

### Details

The encryption used is called substitution-permutation network, and the encryption algorithm is properly implemented. However, the python program adds "message: " to the beginning of every data being encrypted. Check out line 96 in the python program. This means that we know the text and the cipher text of the first 8 characters of the encrypted file. But we only need the first 3 characters to figure out the key because the encryption encrypts three characters at a time.

A special trait of substitution-permutation network is that even if an adversary obtains the text and the cipher text it's still impossible to figure out the key used to encrypted. Thus, we have to brute force the key, but a key in this case is only $2^{24}$ bits long which is very brute force-able. Although, the encryption uses two keys, so one would think that $2^{48}$ calculation is needed crack the key. This is where meet in the middle attack comes in.

Since we have the text and the cipher, we can use meet in the middle to reduces the amount of calculation needed to crack both keys.

The encryption algorithm does this:

Text ---- encryption with key 1 ---> (something) ---- encryption with key 2 ---> Ciphertext


The attack works by creating a table of all possible value of (something) with all the possible combinations of key 1. Then we decrypt the ciphertext by guessing value of key 2 back and cross checking the resulting value with the table generated with key 1. When we get a match of what we decrypted with a value in the table generated, we will find out the correct value of key 1 and key 2.

Meet in the middle attack:

Text ----- some key 1 ----> (something) == (something) <------ some key 2 ---- Ciphertext


Instead of doing $2^{48}$ calculations, we have essentially done two $2^{24}$ calculations instead which is only $2^{25}$ calculations. However, this takes much more memory. On my computer it takes a few gigabytes, as opposed to straight decryption, which takes less than one megabyte. It is an example of a space-time trade off.

Make sure to run the following script in pypy, which is a dropin replacement for python that is much faster than vanilla python. My brute forcing python code

from block import encrypt_data, decrypt_data
plain_text = 'message: '
cipher_text = '\xa1\x98\xa4\x03\x85\x81\xc5\x10\x9e'

data = {}
for i in xrange(0, 16**6):
data[encrypt_data(plain_text, i)] = i

for i in xrange(0, 16**6):
try:
print ('{0:x} {1:x}'.format(data[decrypt_data(cipher_text, i)], i))
except KeyError:
pass


On my computer it uses 1 core of the CPU and 3 gigabytes of RAM and 3 minutes of time. This script should output.

9b3ce2 41013


With the keys, it's trivial to decrypt the file and get the flag.

python block.py decrypt 9b3ce2 41013 encrypted decrypted
cat decrypted


### Flag

e67db97764f9da3d818243dd8cc8b3