# Challenge 19: Break fixed-nonce CTR mode using substitutions¶

Take your CTR encrypt/decrypt function and fix its nonce value to 0. Generate a random AES key.

In successive encryptions (not in one big running CTR stream), encrypt each line of the base64 decodes of the following, producing multiple independent ciphertexts:

SSBoYXZlIG1ldCB0aGVtIGF0IGNsb3NlIG9mIGRheQ==
Q29taW5nIHdpdGggdml2aWQgZmFjZXM=
RnJvbSBjb3VudGVyIG9yIGRlc2sgYW1vbmcgZ3JleQ==
RWlnaHRlZW50aC1jZW50dXJ5IGhvdXNlcy4=
SSBoYXZlIHBhc3NlZCB3aXRoIGEgbm9kIG9mIHRoZSBoZWFk
T3IgcG9saXRlIG1lYW5pbmdsZXNzIHdvcmRzLA==
T3IgaGF2ZSBsaW5nZXJlZCBhd2hpbGUgYW5kIHNhaWQ=
UG9saXRlIG1lYW5pbmdsZXNzIHdvcmRzLA==
QW5kIHRob3VnaHQgYmVmb3JlIEkgaGFkIGRvbmU=
T2YgYSBtb2NraW5nIHRhbGUgb3IgYSBnaWJl
VG8gcGxlYXNlIGEgY29tcGFuaW9u
QXJvdW5kIHRoZSBmaXJlIGF0IHRoZSBjbHViLA==
QmVpbmcgY2VydGFpbiB0aGF0IHRoZXkgYW5kIEk=
QnV0IGxpdmVkIHdoZXJlIG1vdGxleSBpcyB3b3JuOg==
QWxsIGNoYW5nZWQsIGNoYW5nZWQgdXR0ZXJseTo=
QSB0ZXJyaWJsZSBiZWF1dHkgaXMgYm9ybi4=
VGhhdCB3b21hbidzIGRheXMgd2VyZSBzcGVudA==
SW4gaWdub3JhbnQgZ29vZCB3aWxsLA==
SGVyIG5pZ2h0cyBpbiBhcmd1bWVudA==
VW50aWwgaGVyIHZvaWNlIGdyZXcgc2hyaWxsLg==
V2hhdCB2b2ljZSBtb3JlIHN3ZWV0IHRoYW4gaGVycw==
V2hlbiB5b3VuZyBhbmQgYmVhdXRpZnVsLA==
U2hlIHJvZGUgdG8gaGFycmllcnM/
VGhpcyBtYW4gaGFkIGtlcHQgYSBzY2hvb2w=
QW5kIHJvZGUgb3VyIHdpbmdlZCBob3JzZS4=
VGhpcyBvdGhlciBoaXMgaGVscGVyIGFuZCBmcmllbmQ=
V2FzIGNvbWluZyBpbnRvIGhpcyBmb3JjZTs=
SGUgbWlnaHQgaGF2ZSB3b24gZmFtZSBpbiB0aGUgZW5kLA==
U28gZGFyaW5nIGFuZCBzd2VldCBoaXMgdGhvdWdodC4=
VGhpcyBvdGhlciBtYW4gSSBoYWQgZHJlYW1lZA==
QSBkcnVua2VuLCB2YWluLWdsb3Jpb3VzIGxvdXQu
SGUgaGFkIGRvbmUgbW9zdCBiaXR0ZXIgd3Jvbmc=
VG8gc29tZSB3aG8gYXJlIG5lYXIgbXkgaGVhcnQs
WWV0IEkgbnVtYmVyIGhpbSBpbiB0aGUgc29uZzs=
SGUsIHRvbywgaGFzIHJlc2lnbmVkIGhpcyBwYXJ0
SW4gdGhlIGNhc3VhbCBjb21lZHk7
SGUsIHRvbywgaGFzIGJlZW4gY2hhbmdlZCBpbiBoaXMgdHVybiw=
VHJhbnNmb3JtZWQgdXR0ZXJseTo=
QSB0ZXJyaWJsZSBiZWF1dHkgaXMgYm9ybi4=



(This should produce 40 short CTR-encrypted ciphertexts).

Because the CTR nonce wasn't randomized for each encryption, each ciphertext has been encrypted against the same keystream. This is very bad.

Understanding that, like most stream ciphers (including RC4, and obviously any block cipher run in CTR mode), the actual "encryption" of a byte of data boils down to a single XOR operation, it should be plain that:

CIPHERTEXT-BYTE XOR PLAINTEXT-BYTE = KEYSTREAM-BYTE



And since the keystream is the same for every ciphertext:

CIPHERTEXT-BYTE XOR KEYSTREAM-BYTE = PLAINTEXT-BYTE (ie, "you don't say!")



Attack this cryptosystem piecemeal: guess letters, use expected English language frequence to validate guesses, catch common English trigrams, and so on.

Don't overthink it. Points for automating this, but part of the reason I'm having you do this is that I think this approach is suboptimal.

Okay, so I don't understand what they expect from us here.

As soon as I start thinking about it I end up solving it in the way they describe in challenge 20.

Well they say that the only purpose of this challenge is to show you how much better the other method is, so let's just go to the next challenge.

# Challenge 20: Break fixed-nonce CTR statistically¶

In this file find a similar set of Base64'd plaintext. Do with them exactly what you did with the first, but solve the problem differently.

Instead of making spot guesses at to known plaintext, treat the collection of ciphertexts the same way you would repeating-key XOR.

Obviously, CTR encryption appears different from repeated-key XOR, but with a fixed nonce they are effectively the same thing.

To exploit this: take your collection of ciphertexts and truncate them to a common length (the length of the smallest ciphertext will work).

Solve the resulting concatenation of ciphertexts as if for repeating- key XOR, with a key size of the length of the ciphertext you XOR'd.

In [1]:
import os
from base64 import b64decode

from libmatasano import aes_128_ctr_transform

with open('data/20.txt') as f:
data = [b64decode(line) for line in f]

key = os.urandom(16)

ctxts = [aes_128_ctr_transform(line, key, nonce=0)
for line in data]


Take the following example with three-letters messages being encrypted with the same key and the same nonce. Say the keystream generated with this key and nonce happens to start with ZJK (that is, three bytes encoding the letters "ZJK" in ASCII encoding).

  key:  Z J K
msg 1:  L O L
msg 2:  F O O
msg 3:  B A R
etc...



Here is the intuition of the attack: we take the first byte of every ciphertext and concatenate them together. The result is a long list of letters all XORed against the same byte (in our example, Z). We can then re-use the attack we designed in challenge 3 against "single-byte XOR cipher".

Let us verify that our attack against "single-bye XOR cipher" works well against a "column" of ciphertext bytes:

In [5]:
# Python has a very useful "zip" builtin function
# that perfectly fits our need here
# let's just first show how it works
# note that the 'zip' function stop at the length of the shortest input
list(zip('abc', 'def', 'ghijkl'))

Out[5]:
[('a', 'd', 'g'), ('b', 'e', 'h'), ('c', 'f', 'i')]
In [8]:
from libmatasano import attack_single_byte_xor

# The 'next' builtin function will take the first element outputed by the zip function
# (zip is actually an Python iterator)
# the '*' operator before ctxt will unpack the elements of the 'ctxt' variable
# as multiple arguments of the function (see how we called zip in the previous cell)
l = next(zip(*ctxts))

attack_single_byte_xor(l)

Out[8]:
{'message': b'icbysmhdfttfwftsmtmihsiclmytapmobyinywkocitssiibssaf\x07sr\x07yata',
'nb_letters': 58,
'key': b'8'}

Beautiful, right ?

Of course the message we got is meaningless, but this is supposed to be a concatenation of the first letter of each message, so this is not surprising.

So we just do this for every "column" and then we recompose the first message by taking the first letter of every column and so on...

In [10]:
columns = [ attack_single_byte_xor(l)['message'] for l in zip(*ctxts) ]

for msg in zip(*columns):
print(bytes(msg).decode())

i'm rated "R"...this is a warning, ya better void / P
cuz I came back to attack others in spite- / Strike l
but don't be afraid in the dark, in a park / Not a sc
ya tremble like a alcoholic, muscles tighten up / Wha
suddenly you feel like your in a horror flick / You g
music's the clue, when I come your warned / Apocalyps
haven't you ever heard of a MC-murderer? / This is th
death wish, so come on, step to this / Hysterical ide
friday the thirteenth, walking down Elm Street / You
this is off limits, so your visions are blurry / All
terror in the styles, never error-files / Indeed I'm
for those that oppose to be level or next to this / I
worse than a nightmare, you don't have to sleep a win
flashbacks interfere, ya start to hear: / The R-A-K-I
then the beat is hysterical / That makes Eric go get
soon the lyrical format is superior / Faces of death
mC's decaying, cuz they never stayed / The scene of a
the fiend of a rhyme on the mic that you know / It's
melodies-unmakable, pattern-unescapable / A horn if w
i bless the child, the earth, the gods and bomb the r
hazardous to your health so be friendly / A matter of
shake 'till your clear, make it disappear, make the n
if not, my soul'll release! / The scene is recreated,
lyrics of fury! A fearified freestyle! / The "R" is i
make sure the system's loud when I mention / Phrases
you want to hear some sounds that not only pounds but
then nonchalantly tell you what it mean to me / Stric
and I don't care if the whole crowd's a witness! / I'
program into the speed of the rhyme, prepare to start
open your mind, you will find every word'll be / Furi
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i wake ya with hundreds of thousands of volts / Mic-t
novocain ease the pain it might save him / If not, Er
yo Rakim, what's up? / Yo, I'm doing the knowledge, E
well, check this out, since Norby Walters is our agen
kara Lewis is our agent, word up / Zakia and 4th and
okay, so who we rollin' with then? We rollin' with Ru
check this out, since we talking over / This def beat
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so I dig into my pocket, all my money is spent / So I
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but now I learned to earn 'cuz I'm righteous / I feel
search for a nine to five, if I strive / Then maybe I
so I walk up the street whistlin' this / Feelin' out
a pen and a paper, a stereo, a tape of / Me and Eric
fish, which is my favorite dish / But without no mone
Cuz I don't like to dream about gettin' paid / So I
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Cause my girl is definitely mad / 'Cause it took us
yo, I hear what you're saying / So let's just pump th
and count our money / Yo, well check this out, yo Eli
turn down the bass down / And let the beat just keep
and we outta here / Yo, what happened to peace? / Pea