#### Permutation Cipher

I
```"""
The permutation cipher, also called the transposition cipher, is a simple encryption
technique that rearranges the characters in a message based on a secret key. It
divides the message into blocks and applies a permutation to the characters within
each block according to the key. The key is a sequence of unique integers that
determine the order of character rearrangement.

For more info: https://www.nku.edu/~christensen/1402%20permutation%20ciphers.pdf
"""

import random

def generate_valid_block_size(message_length: int) -> int:
"""
Generate a valid block size that is a factor of the message length.

Args:
message_length (int): The length of the message.

Returns:
int: A valid block size.

Example:
>>> random.seed(1)
>>> generate_valid_block_size(12)
3
"""
block_sizes = [
block_size
for block_size in range(2, message_length + 1)
if message_length % block_size == 0
]
return random.choice(block_sizes)

def generate_permutation_key(block_size: int) -> list[int]:
"""
Generate a random permutation key of a specified block size.

Args:
block_size (int): The size of each permutation block.

Returns:
list[int]: A list containing a random permutation of digits.

Example:
>>> random.seed(0)
>>> generate_permutation_key(4)
[2, 0, 1, 3]
"""
digits = list(range(block_size))
random.shuffle(digits)
return digits

def encrypt(
message: str, key: list[int] | None = None, block_size: int | None = None
) -> tuple[str, list[int]]:
"""
Encrypt a message using a permutation cipher with block rearrangement using a key.

Args:
message (str): The plaintext message to be encrypted.
key (list[int]): The permutation key for decryption.
block_size (int): The size of each permutation block.

Returns:
tuple: A tuple containing the encrypted message and the encryption key.

Example:
>>> encrypted_message, key = encrypt("HELLO WORLD")
>>> decrypted_message = decrypt(encrypted_message, key)
>>> decrypted_message
'HELLO WORLD'
"""
message = message.upper()
message_length = len(message)

if key is None or block_size is None:
block_size = generate_valid_block_size(message_length)
key = generate_permutation_key(block_size)

encrypted_message = ""

for i in range(0, message_length, block_size):
block = message[i : i + block_size]
rearranged_block = [block[digit] for digit in key]
encrypted_message += "".join(rearranged_block)

return encrypted_message, key

def decrypt(encrypted_message: str, key: list[int]) -> str:
"""
Decrypt an encrypted message using a permutation cipher with block rearrangement.

Args:
encrypted_message (str): The encrypted message.
key (list[int]): The permutation key for decryption.

Returns:
str: The decrypted plaintext message.

Example:
>>> encrypted_message, key = encrypt("HELLO WORLD")
>>> decrypted_message = decrypt(encrypted_message, key)
>>> decrypted_message
'HELLO WORLD'
"""
key_length = len(key)
decrypted_message = ""

for i in range(0, len(encrypted_message), key_length):
block = encrypted_message[i : i + key_length]
original_block = [""] * key_length
for j, digit in enumerate(key):
original_block[digit] = block[j]
decrypted_message += "".join(original_block)

return decrypted_message

def main() -> None:
"""
Driver function to pass message to get encrypted, then decrypted.

Example:
>>> main()
Decrypted message: HELLO WORLD
"""
message = "HELLO WORLD"
encrypted_message, key = encrypt(message)

decrypted_message = decrypt(encrypted_message, key)
print(f"Decrypted message: {decrypted_message}")

if __name__ == "__main__":
import doctest

doctest.testmod()
main()
```