# PicoCTF 2014 Write-ups

## ZOR - 50 (Cryptography)

Created: 2014-11-13 09:26:47

### Problem

Daedalus has encrypted their blueprints! Can you get us the password?

ZOR.py

encrypted

### Hint

The password gets reduced to a one byte XOR key. That's only 256 possible keys!

### Overview

Use a frequency analysis and make the most common character in the cipher text decrypt to space (the most common character in most plaintexts). Ignore th password function and XOR the data directly.

### Details

XOR has the rare property that it is its own inverse. If $m \oplus k = c$, then $m \oplus c = k$. This means if we have a known piece of the plaintext message $m$, and a known piece of the ciphertext, $c$, (and we know it is an XOR encryption), then we can deduce the key, $k$.

The most common character in the cipher text probably decodes to the most common character in English. The most common character in most English plaintexts is usually space. It occurs about twice as often as e according to some pages. The most common character in cipher text is a bit harder to get. Luckily, python has a really nice Counter class.

from collections import Counter

frequency = Counter()
with open('encrypted', 'r') as f:
for ch in data:
frequency[ch] += 1

c = frequency.most_common(10)[0][0]
m = ' '
print (repr(a) + ' decrypts to ' + repr(m))


Output:

'\xb2' decrypts to ' '


This gets the most common characters in the cipher text, c. We want to find a k such that m decrypts to c. In other words find $k$ such that $m \oplus k = c$. We have stated above that XOR is its own inverse, so $m \oplus c = k$.

def xor(input_data, key):
result = ""
for ch in input_data:
result += chr(ord(ch) ^ ord(key))
return result

k = xor(c, m)


Now that we know k, we can decrypt the whole message.

print (xor(data, k))


Output:

This message is for Daedalus Corporation only. Our blueprints for the

Notice we never actually use the encrypt or decrypt function we are provided with. Guessing the password for these is a bit harder. The hint says "that's only 256 possible keys." They mean instead of trying to guess the password which has several million (possibly infinite) keys, we can guess the key for the xor part, which has only 256 possible keys. To do this, we just did a simple frequency analysis. The entire script described in this write-up can be found here.
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