In this exercise you will perform a timing attack against CBC-MAC.

You are given access to a CBC-MAC $\mathsf{Verify}$ oracle, which tests whether the received tag matches the one computed using the secret key. Timing attacks exploit naive equality comparisons between the received and computed MACs (for example, the comparison is done byte by byte; more checks means more latency).

Your task is to produce a forged tag for the message 'Hristos a inviat' without knowing the key. Do this by iterating through all possible values for a specific byte; when the oracle's latency for a certain value seems larger than the rest, it suggests that the equality test returned True and the oracle passed to the next byte.

Try to start by finding the first byte and checking your result with the timing attack.

You can use time.clock() before and after each oracle query to measure its runtime.

TODO1: Implement the CBC-MAC function.

TODO2: Implement the MAC time verification attack and obtain the desired MAC without knowing the key.

timing.py

import sys
import random
import string
import time
import itertools
import operator
import base64
 
from Crypto.Cipher import AES
from Crypto.Hash import SHA256
 
def slow_foo():
    p = 181
    k = 2
    while k < p:
        if p % k == 0:
            return
        k += 1
 
def aes_enc(k, m):
  """ 
  Encrypt a message m with a key k in ECB mode using AES as follows:
  c = AES(k, m)
 
  Args:
    m should be a bytestring multiple of 16 bytes (i.e. a sequence of characters such as 'Hello...' or '\x02\x04...')
    k should be a bytestring of length exactly 16 bytes.
 
  Return:
    The bytestring ciphertext c
  """
  aes = AES.new(k)
  c = aes.encrypt(m)
 
  return c
 
def aes_dec(k, c):
  """
  Decrypt a ciphertext c with a key k in ECB mode using AES as follows:
  m = AES(k, c)
 
  Args:
    c should be a bytestring multiple of 16 bytes (i.e. a sequence of characters such as 'Hello...' or '\x02\x04...')
    k should be a bytestring of length exactly 16 bytes.
 
  Return:
    The bytestring message m
  """
  aes = AES.new(k)
  m = aes.decrypt(c)
 
  return m
 
def aes_enc_cbc(k, m, iv):
  """
  Encrypt a message m with a key k in CBC mode using AES as follows:
  c = AES(k, m)
 
  Args:
    m should be a bytestring multiple of 16 bytes (i.e. a sequence of characters such as 'Hello...' or '\x02\x04...')
    k should be a bytestring of length exactly 16 bytes.
    iv should be a bytestring of length exactly 16 bytes.
 
  Return:
    The bytestring ciphertext c
  """
  aes = AES.new(k, AES.MODE_CBC, iv)
  c = aes.encrypt(m)
 
  return c
 
def aes_dec_cbc(k, c, iv):
  """
  Decrypt a ciphertext c with a key k in CBC mode using AES as follows:
  m = AES(k, c)
 
  Args:
    c should be a bytestring multiple of 16 bytes (i.e. a sequence of characters such as 'Hello...' or '\x02\x04...')
    k should be a bytestring of length exactly 16 bytes.
    iv should be a bytestring of length exactly 16 bytes.
 
  Return:
    The bytestring message m
  """
  aes = AES.new(k, AES.MODE_CBC, iv)
  m = aes.decrypt(c)
 
  return m
 
def aes_cbc_mac(k, m):
  """
  Compute a CBC-MAC of message m with a key k using AES as follows:
  t = AES-CBC-MAC(k=(k1,k2), m),
  where k1 is used for the raw-CBC operation and k2 is used for the final
  encryption.
 
  k1 and k2 are derived from k as follows:
  [k1|k2] = SHA256(k | "CBC MAC keys")
 
  Note: the IV for CBC in this case will be 0.
 
  Args:
    m should be a bytestring multiple of 16 bytes (i.e. a sequence of characters such as 'Hello...' or '\x02\x04...')
    k should be a bytestring of length exactly 16 bytes.
 
  Return:
    The bytestring MAC t, of 16 bytes.
  """
 
  #Require good size
  m = m.ljust(16)
  k = k.ljust(16)
 
  #Derive the keys for raw-CBC and for the final tag
  #[k1 | k2] = SHA256(k + "CBC MAC keys")
 
  #Get the MAC:
  #1 - Do aes-CBC with k1 and iv=0, then keep only last block (last 16 bytes) of encryption
  #2 - Perform another AES encryption (simple, without CBC) on the last block from #1 using k2
  #t = tag
  t = 16*'\x00'
 
  return t
 
def verify(message, tag):
  key = 'Cozonace si oua '
 
  # Get correct tag
  goodtag = aes_cbc_mac(key, message)
 
  # Compare tags
  for i in range(16):
    # Artificially extend byte comparison duration
    slow_foo()
    if tag[i] != goodtag[i]:
      return False
 
  return True
 
 
def main():
  message = 'Hristos a inviat'
 
  # Step 1. Iterate through all possible first byte values, and call the
  # Verify oracle for each of them
  tag = 16*'\x00'
  verify(message, tag)
 
  # Step 2. Store the byte that caused the longest computation time
 
  # Step 3. Continue the operation for each byte (except the last)
 
  # Step 4. Guess the last byte, and query the oracle with the complete tag
  mytag = '???'
  result = verify(message, mytag)
  if result == True:
    print "Found tag: " + mytag
 
if __name__ == "__main__":
  main()

In this first exercise we'll see how to compute hashes using the OpenSSL command line interface.

You can interact with the OpenSSL utilities in two ways:

• directly from bash, by using the openssl command followed by the desired command and parameters
• from the OpenSSL console, by using the openssl command without additional arguments. You can close the console by calling quit or exit.

If the manual pages are correctly installed, you can consult the documentation via man <command_name> (e.g. man md5).

Hashes are often used to check the integrity of downloaded files. We will now use OpenSSL to compute the MD5 and SHA-1 hashes of this page.

Download this page by running:

linux$ wget http://ocw.cs.pub.ro/courses/sasc/laboratoare/09 -O sasc.html

Use OpenSSL to compute the MD5 and SHA-1 hashes of the newly downloaded file; print the output in hexadecimal.

To check your results, you can use md5sum or sha1sum as an alternative way of computing the same hashes.

In this second exercise we'll use the command line to compute an HMAC, with SHA-1 as the hashing algorithm.

Recall from the lecture that for HMAC to be secure, we need to sample a random key $k \gets \mathcal{K}$.

We can generate random bytes using openssl rand. To compute HMACs, check the documentation for openssl dgst.

For this exercise, use OpenSSL commands to:

1. generate a 16 byte random key
2. use the key to compute the SHA-1 HMAC of the page downloaded in the previous exercise

In this exercise you will implement the Birthday attack on SHA-1 from the previous lab using OpenSSL. The goal is to obtain a collision in the first four bytes of the hash.

In contrast to previous labs, this time we'll use C. You can implement the attack from scratch, or start from our archive here.

To compute a digest, you might find the code below useful:

    SHA_CTX context;
    SHA1_Init(&context);
    SHA1_Update(&context, buffer, length);
    SHA1_Final(md, &context); /* md must point to at least 20 bytes of valid memory */

linux$ ./config --prefix=/home/student/local --openssldir=/home/student/local/openssl
linux$ make
linux$ make install_sw

LDFLAGS=-L/home/student/local/lib -lcrypto
CFLAGS=-Wall -g -I/home/student/local/include