# Aes 128, CTR mode, Counter Mode, Hmac, mac Assume Alice and Bob are communicating using 'MAC then Encrypt' paradigm. Specifically, they are using HMAC with SHA256 as the hash function and the output is truncated to 40 bits. They are using AES-128 in CTR mode as the blockcipher. Specifically, they do the following:

C=<IV, ENC(M II MAC(M, IV PAD) II PAD)>


I understand this. If we consider the message is 200 bits long. So the first block has 128 bits, the second block has 72 bits of the message, 40 bits of MAC and 16 bits padding. Padding scheme: 16 bits is 2 bytes (0X02). (0X0Z) for all Z bytes.

What I want to know is that if Eve has no idea that the original message is 200 bit long, but Eve knows it's 2 blocks long after 40 bit MAC was added and it is padded.

How will Eve know the length of the message? Will it be done by flipping the last bit and looking for padding error and using the padding algorithm? Or will we try padding oracle attack??

• So how can eve know the length of the message? Thats confusing me. – AnswerFinder95 Dec 4 '17 at 10:01
• This looks like an assignment to me. What have you tried? What is the difference between flipping the bit and a padding oracle attack? – Maarten Bodewes Dec 4 '17 at 10:39
• @MaartenBodewes we had a similar assignment question in which we had to find if there is a padding error or MAC error. I am using the same script for my project thesis but i need to research first on the workings and all possibilities. To my knowledge both padding oracle attack and bit flipping are the similar, i did research on padding oracle attack for CBC mode. I know in padding oracle we flip a bit and then send it to oracle to know if it returns good padding or bad padding, that way we can defeat the system. – AnswerFinder95 Dec 4 '17 at 10:44
• I think forcing a specific length for Z is the only way to go. So you flip bits in such a way that an error is generated (or not) depending on the guessed bits of Z. But the exercise is rather weird, as CTR mode doesn't require any padding in the first place - it probably stresses the fact that MAC-then-encrypt is dangerous even if you use CTR mode, or that plaintext / padding oracle attacks can be performed not just on ECB/CBC if the protocol involves padding. – Maarten Bodewes Dec 4 '17 at 13:26
• I can show you the original assignment question if you want to see that in reference to this. – AnswerFinder95 Dec 5 '17 at 4:18

# Finding the message size knowing the padding size

With CTR mode the length of the ciphertext is the same as the length of the plaintext, because what you do is XORing bit-by-bit the message with the keystream.

So the length of the second component of C minus the padding length and MAC length is the length of the message.

Quick Python example:

import os

# https://cryptography.io
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import hashes, hmac
from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes

backend = default_backend()

M = os.urandom(200//8)
MAC_KEY = os.urandom(hashes.SHA256.digest_size)
AES_KEY = os.urandom(32)
IV = os.urandom(16)

h = hmac.HMAC(MAC_KEY, hashes.SHA256(), backend=default_backend())
# truncated to 40 bits = 5 bytes
MAC = h.finalize()[:5]

cipher = Cipher(algorithms.AES(AES_KEY), modes.CTR(IV), backend=backend)
encryptor = cipher.encryptor()
C = (IV, encryptor.update(M + MAC + PAD) + encryptor.finalize())

print('length of message: %i bits' % (8*(len(C) - len(PAD) - len(MAC))))
# out: length of message: 200 bits


# Finding the padding size using the oracle

EDIT: added this question from comment of OP.

Another property of CTR mode is that flipping a bit in the ciphertext flips the corresponding bit in the plaintext.

So if you flip say the last bit of C you will modify the padding and get a "padding error"; while if you flip a bit that correspond to MAC you get a "MAC error".

As a result if flipping the i-th bit gives you a "MAC error" while flipping the i+1-th bit gives you a "padding error" then the padding starts at bit i+1 and you gets the padding length and its value.

Continuing my Python example:

class PaddingError(Exception):
pass

class MacError(Exception):
pass

def oracle(ctxt):
decryptor = cipher.decryptor()
ptxt = decryptor.update(ctxt) + decryptor.finalize()
m = ptxt[:25]
mac = ptxt[25:30]

# i'm cheating
elif mac != MAC:
return MacError
elif m != M:
return 'Message was modified'
else:
return 'OK'

def flip(x, i):
"returns x with its i-th bit flipped (starts at 0)"
return bytes([ x[j]^mask if j==(i//8) else x[j] for j in range(len(x)) ])

oracle(flip(C, len(C)*8-16))

oracle(flip(C, len(C)*8-17))
# out: MacError


# Finding the last byte of the MAC

EDIT added from another comment of OP

When you know the padding length, you know where is the last byte of the MAC, and because of the CTR mode you are able to modify it by XORing it against some byte of your choice.

So you pick a random byte and you XOR it against the last byte of the MAC, and you send the result to the oracle.

Normally you should get a "MAC error", but if the modified MAC byte ends up being the same as the PAD bytes (for instance 0x02 in your example) you should get a "Padding error" instead.

Let B be the byte you used to get this "Padding error", we now know that:

MAC[-1] ^ B = 0x02


(where ^ denotes bit-wise XOR as in Python)

Thus:

MAC[-1] = 0x02 ^ B

• Thanks. I guess this is it. Although lets say if in my scenario Eve knows the padding scheme but does not know the pad size. What would be the possible way to find the length then? – AnswerFinder95 Dec 5 '17 at 10:37
• @AnswerFinder95 added how to find the padding length using the oracle. – Cédric Van Rompay Dec 5 '17 at 11:19
• Just one last issue. Can this way be used to determine the last byte of the MAC? – AnswerFinder95 Dec 5 '17 at 17:34
• @AnswerFinder95 added how to find the last byte of the MAC – Cédric Van Rompay Dec 6 '17 at 17:20