Bad Cipher (50 points/ 82 solves)

Problem statement:

My friend insisted on using his own cipher program to encrypt this flag, but I don’t think it’s very secure. Unfortunately, he is quite good at Code Golf, and it seems like he tried to make the program as short (and confusing!) as possible before he sent it.
I don’t know the key length, but I do know that the only thing in the plaintext is a flag. Can you break his cipher for me?
Encryption Program
Encrypted Flag

My opinion:

Again… why the Reverse Engineering tag, this time we were given an obfuscated python code that encrypts an input string using a key. THIS IS CRYPTO!
Anyway, the vulnerability was that we knew the first bytes of the flag and that gave us a part of the key

Understanding the encryption:

We were supplied with an encrypted flag=473c23192d4737025b3b2d34175f66421631250711461a7905342a3e365d08190215152f1f1e3d5c550c12521f55217e500a3714787b6554and some code that encrypted the flag:

message = "[REDACTED]"
key = ""

r,o,u,x,h=range,ord,chr,"".join,hex
def e(m,k):
l=len(k);s=[m[i::l]for i in r(l)]
for i in r(l):
a,e=0,""
for c in s[i]:
a=o(c)^o(k[i])^(a>>2)
e+=u(a)
s[i]=e
return x(h((1<<8)+o(f))[3:]for f in x(x(y)for y in zip(*s)))

print(e(message,key))

Firstly, I couldn’t bare reading that so I took the time to deobfuscate the code:

message = ""
key = ""

def encrypt(message,key):
L=len(key)
s=[message[i::L] for i in range(L)]
for i in range(L):
act=0
enc=""
for c in s[i]:
act=ord(c)^ord(key[i])^(act>>2)
enc+=chr(act)
s[i]=enc
return ''.join( hex(ord(y))[2:] for y in ''.join(''.join(x) for x in zip(*s)))

print encrypt(message,key)

Ok, now let’s understand the encryption:

NOTE : The encryption works properly only if the message’s length is a multiple of the key’s length (this is due to zip(*s)), I’ll explain it a bit later.

NOTE : h((1<<8)+o(f))[3:] and hex(ord(y))[2:] give the same output since (1<<8) is 256 and that’s 0x100 in hex, so h((1<<8)+o(f)) will always be 0x1XX

The encryption function takes a key and a message.
It then creates the matrix s of size len(key) x (len(message)/len(key)) which pretty much is the message written like a normal text that moves to a new row when there is no space left on the current row, except the rows and columns are reversed (see the following example).

>>> import sys
>>> message='thisismymessage!'
>>> key='Akey'
>>> L=len(key)
>>> s=[message[i::L] for i in range(L)]
>>> for i in range(len(s)):
... for j in range(len(s[i])):
... sys.stdout.write(s[i][j])
... sys.stdout.write('\n')
...
tima
hseg
imse
sys!

Now, for every line of the matrix s the following process is applyied:

for i in range(L):
act=0
enc=""
for c in s[i]:
act=ord(c)^ord(key[i])^(act>>2)
enc+=chr(act)
s[i]=enc

1. The i-th byte of the key is used in a xor encryption.
2. Each byte of the ciphertext is dependent of the previous byte.

After that, the last line of the encrypt function returns the hex of the string ''.join(''.join(x) for x in zip(*s)) which means it reverses the process that generated s in the first place, so the message’s bytes are in the same order both in ciphertext and plaintext!

NOTE : Let’s talk about zip(*s), the zip() function stops when the shortest array reaches it’s end. So if len(message) is not a multiple of len(key) the last bytes of the message will be ignored (see the python documentation). This was a huge help in solving the problem since now we know now that the key’s lenght divides 56.

Finding the key length:

Now we know that the key’s lenght might be: 1, 2, 4, 7, 8, 14, 28 or 56, most probably it will be either 4, 7, 8 or 14 so let’s try them one by one:

Sice we know the first 6 bytes of the flag: tjctf{, we can check 4 by hand and see if it’s wrong:

1. The first byte of the key is hex(ord('t')^int('47',16))=='0x33' or '3'
2. If the key length was 4 then at the 5-th byte hex(int('2d',16)^ord('3')^(int('47',16)>>2)==0xf should be 'f' or 0x66, so the key is longer than 4.
3. Now we can find the first 6 bytes of the key:

>>> x=['47','3c','23','19','2d','47']
>>> x=[int(y,16) for y in x]
>>> flag='tjctf{'
>>> key=''.join(chr(ord(flag[i])^x[i]) for i in range(len(x)))
>>> key
'[email protected]<'

For the other lenghts I wrote a script that will give us a partially decrypted flag for each length:

def transform(msg):
out=''
for i in range(0,len(msg),2):
out+=chr(int(msg[i:i+2],16))
return out

def decrypt(msg,l):
flag='tjctf{'+(l-6)*'\xff'
key=[]
for i in range(len(flag)):
key.append(chr(ord(msg[i])^ord(flag[i])))
keylen=len(key)
dec=''
act=[0 for i in range(keylen)]
for i in range(len(msg)):
if(i>=keylen):
act[i%keylen]=ord(msg[i])^ord(key[i%keylen])^(ord(msg[i-keylen])>>2)
else:
act[i]=ord(msg[i])^ord(key[i])
dec+=chr(act[i%keylen])
print list(dec)

print 'Msg Len:',len(transform(message))

decrypt(transform(message),7)
decrypt(transform(message),8)
decrypt(transform(message),14)

And the output is:

Msg Len: 56
['t', 'j', 'c', 't', 'f', '{', '\xff', ' ', '\x02', 's', 'F', 't', ':', '\x9a', 'U', '\x02', 'X', 'W', 'c', '>', '\xce', 'l', '\\', '<', 'd', 'v', '\x17', '\xf2', '\x14', '\r', 'V', 'u', 'D', '#', '\xd2', '\x11', '^', '\\', 'V', '\x17', 'l', '\xc1', '*', '\x03', 'X', '7', '}', 'W', '\x9b', '=', 'u', 'S', '\x00', '8', 'F', '\x88']
['t', 'j', 'c', 't', 'f', '{', '\xff', '\xff', 'y', 'b', 'e', '_', 'W', 'r', '\xa3', '\xbf', '3', 'i', 'n', 'g', '_', 'm', '\xcb', '\x94', '3', 'n', 'c', 'R', 'y', 'p', '\xc6', '\xfa', '0', 'N', '_', 'M', 'Y', '5', '\xf7', '\xa7', 'f', '_', 'W', '4', 'S', 'n', '\xe6', '\x94', 'v', '_', 's', 'm', '4', 'R', '\xa5', '\xb6']
['t', 'j', 'c', 't', 'f', '{', '\xff', '\xff', '\xff', '\xff', '\xff', '\xff', '\xff', '\xff', 'D', '\x1b', '^', 'Z', 'e', '*', '\xd4', '\xbb', '\xa8', '\xb3', '\xdc', '\xf2', '\xc7', '\x89', '\x1c', '\x1b', 'M', 'x', '@', '(', '\xd9', '\xc3', '\xbd', '\xc4', '\xee', '\x9a', '\xb7', '\xa3', ',', '\x13', ']', '>', 'j', 'G', '\x9d', '\xfc', '\x94', '\xd7', '\xa5', '\xa7', '\x98', '\xf7']

Ok so it’s clear that the key’s length is 8.

Finding the flag:

Now we have a lot of info about the flag: tjctf{��ybe_Wr��3ing_m˔3ncRyp��0N_MY5��f_W4Sn��v_sm4R�� and we know the key’s length, the flag pretty much says maybe writing my encryption myself wasn't very smart, so I tried to write it in leet. Eventually I tried tjctf{m4 as the first 8 bytes and ran decrypt.py and done!

Flag: tjctf{m4ybe_Wr1t3ing_mY_3ncRypT10N_MY5elf_W4Snt_v_sm4R7}