Alice and Bob are exchanging with encrypted messages. To encrypt data, they use the Present cipher with an 80-bit secret key in ECB format. Bob prepared eight files for Alice, without headers, encrypted using the Present algorithm with the same secret key. He has sent the files themselves and hash values of the headers to Alice.
Help Alice decipher the message from Bob by associating each image with it's corresponding header.
To solve this problem we will be calculating the aproximate dimensions (number of pixels) of each image and matching each possible dimension with the correspoding header, if any.
- Collect aproximate number of pixels in each image by reading the encrypted file's size.
files_folder = 'task1'
for file in os.listdir(files_folder):
file_path = os.path.join(files_folder, file)
with open(file_path, 'r', encoding='latin-1') as f:
content = f.read()
nr_pixels.append(len(content) // 3)-
Since Present cipher is a block cipher, it encrypts data in 64-bit chunks (8 bytes). Therefore, it is possible that the file has been padded up to a file size that is a multiple of 8 bytes.
-
To account for those cases, we will consider that up to 2 pixels (6 bytes) have been added extra due to padding. Any more than 2 pixels would be too much, as it doesn't make sense for the encryption to append more than 8 bytes.
for image_index in range(len(nr_pixels)):
for padding_length in range(3):
possible_dimensions = getDivisorsPair(nr_pixels[image_index] - padding_length)
possible_hashed_headers = []
dimensions = []
for dimension in possible_dimensions:
hashed_header = sha256(f"P6 {dimension[0]} {dimension[1]} 255")
dimensions.append((dimension[0], dimension[1]))
possible_hashed_headers.append(hashed_header)
if dimension[0] != dimension[1]:
hashed_header = sha256(f"P6 {dimension[1]} {dimension[0]} 255")
dimensions.append((dimension[1], dimension[0]))
possible_hashed_headers.append(hashed_header)📎Output
Image: 0, Header number: 2, Header: aa1...bb5, Dimensions: 512 x 512 px
Image: 1, Header number: 6, Header: bd0...81d, Dimensions: 598 x 605 px
Image: 2, Header number: 4, Header: 77a...cb6, Dimensions: 585 x 577 px
Image: 3, Header number: 3, Header: 70f...450, Dimensions: 525 x 489 px
Image: 4, Header number: 0, Header: 602...71d, Dimensions: 400 x 433 px
Image: 5, Header number: 5, Header: 456...c01, Dimensions: 513 x 613 px
Image: 6, Header number: 7, Header: 372...305, Dimensions: 465 x 464 px
Image: 7, Header number: 1, Header: f40...7d5, Dimensions: 559 x 530 px
Using the same strategy as Bob, create your own encrypted images, extracting the file header. You can implement this using any other block cypher.
We will achieve this by generating a set of images and and associated hashed header. We will than solve the problem with the method presented in task 1. Afterwards, the new problem could again be solved by Alice.
- Generate images and associated headers using Python Imaging Library (PIL).
def generate_image_with_letter(letter):
image_size = generate_random_size()
image = Image.new('RGB', image_size)
draw = ImageDraw.Draw(image)
draw.text((100, 100), letter)
return image
def generate_files(letters):
random.seed(int(time.time()))
sizes = []
headers = []
letter_frequency = {}
for letter in letters:
if letter == ' ':
continue
letter_image = generate_image_with_letter(letter) # generate an image
file_path = f'task2/original/{letter}'
if letter in letter_frequency:
letter_frequency[letter] += 1
# generate asociated header
letter_image.save(f'{file_path}{letter_frequency[letter]}.ppm', 'PPM')
else:
letter_frequency[letter] = 0
letter_image.save(f'{file_path}.ppm', 'PPM')
sizes.append(letter_image.size)
# hash headers
for size in sizes:
hashed_header = sha256_hash(f"P6 {size[0]} {size[1]} 255")
headers.append(hashed_header)
return sizes, headers
message = "RADU SI MARIA"
sizes, headers = generate_files(message)- Encrypt images. We chose AES encryption.
def encrypt_files():
key = os.urandom(16)
cipher = Cipher(algorithms.AES(key), modes.ECB())
folder_path = 'task2/original'
for filename in os.listdir(folder_path):
file_path = os.path.join(folder_path, filename)
with open(file_path, 'rb') as file:
plaintext = file.read()
encryptor = cipher.encryptor()
padder = padding.PKCS7(algorithms.AES.block_size).padder()
padded_data = padder.update(plaintext) + padder.finalize()
ciphertext = encryptor.update(padded_data) + encryptor.finalize()
with open(f'task2/encrypted/{filename}', 'wb') as encrypted_file:
encrypted_file.write(ciphertext)- Hash headers with 256
for size in sizes:
hashed_header = sha256_hash(f"P6 {size[0]} {size[1]} 255")
headers.append(hashed_header)At this point Alice and attempt to solve the problem with the provided encrypted images and headers.
Headers: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