Set 1

Challenge 1 - Convert hex to base64

import base64 
base64.b64encode("49276d206b696c6c696e6720796f757220627261696e206c696b65206120706f69736f6e6f7573206d757368726f6f6d".decode("hex"))

Challenge 2 - Fixed XOR

from itertools import cycle

def xor_mb(message, key):
    return''.join(chr(ord(m_byte)^ord(k_byte)) for m_byte,k_byte in zip(message, cycle(key)))

xor_mb("1c0111001f010100061a024b53535009181c".decode('hex'), "686974207468652062756c6c277320657965".decode('hex')).encode('hex')

Challenge 3 - Single-byte XOR cipher

from collections import Counter
message = "1b37373331363f78151b7f2b783431333d78397828372d363c78373e783a393b3736".decode('hex')
cnt = Counter(message)
cnt.most_common(3)
for vv in cnt.most_common(7):
    for char in "ETAOIN SHRDLU".lower():
        key = chr(ord(vv[0]) ^ ord(char))
        print key, xor_mb(message, key)

Challenge 4 - Detect single-character XOR

• Solution using limited frequency analysis approach

import string
from collections import Counter
from itertools import cycle

def xor_mb(message, key):
        return''.join(chr(ord(m_byte)^ord(k_byte)) for m_byte,k_byte in zip(message, cycle(key)))

printset = set(string.printable)
messages = open("4.txt", 'r').readlines()

for line in messages:
    message = line.rstrip().decode('hex')
    cnt = Counter(message)
    for vv in cnt.most_common(3):
            for char in "ETAOINSHRDLU".lower():
                key = chr(ord(vv[0]) ^ ord(char))
                temp = xor_mb(message, key)
                if set(temp).issubset(printset) and temp[-1] == "\n":
                    print key, temp

• https://dbjergaard.github.io/posts/matasano_set_1.html recommends chi-squared. Cool concept but super slow in Python. Would not recommend.
• Pearson's chi-squared test
• Chi-square distribution introduction | Probability and Statistics | Khan Academy
• Pearson's chi square test (goodness of fit) | Probability and Statistics | Khan Academy

chi-squared approach

```Python import math import string

from collections import Counter from itertools import cycle

Source http://jsbin.com/kaxoxajige/1/edit?js,output

expected = [0.08167,0.01492,0.02782,0.04253,0.12702,0.02228,0.02015,0.06094,0.06966,0.00153,0.00772, 0.04025,0.02406,0.06749,0.07507,0.01929,0.00095,0.05987,0.06327,0.09056,0.02758,0.00978, 0.02360,0.00150,0.01974,0.00074]

Source -h https://hflog.wordpress.com/2014/04/01/how-to-perform-a-chi-squared-goodness-of-fit-test-in-python

def gf(x): #Play with these values to adjust the error of the approximation. upper_bound=100.0 resolution=1000000.0
step=upper_bound/resolution val=0 rolling_sum=0 while val<=upper_bound: rolling_sum+=step(val(x-1)2.7182818284590452353602874713526624977**(-val)) val+=step return rolling_sum

def ilgf(s,z): val=0 for k in range(0,100): val+=(((-1)k)*z(s+k))/(math.factorial(k)*(s+k)) return val

def chisquarecdf(x,k): return 1-ilgf(k/2,x/2)/gf(k/2)

def chisquare(observed_values,expected_values): test_statistic=0 for observed, expected in zip(observed_values, expected_values): test_statistic+=(float(observed)-float(expected))**2/float(expected) df=len(observed_values)-1 return test_statistic, chisquarecdf(test_statistic,df)

def frequency(message): message = message.lower().strip(" ") freq = [] length = len(message) for char in "abcdefghijklmnopqrstuvwxyz": freq.append(float(message.count(char)) / length) return freq

def xor_mb(message, key): return''.join(chr(ord(m_byte)^ord(k_byte)) for m_byte,k_byte in zip(message, cycle(key)))

printset = set(string.printable) messages = open("4.txt", 'r').readlines()

for line in messages: message = line.rstrip().decode('hex') for key in range(0 ,256): temp = xor_mb(message, chr(key)) temp_freq = frequency(temp) chi, tt = chisquare(temp_freq, expected) print chi, tt, temp ```