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(d) Write down the authenticated encryption algorithm based on the same design but using different keys for the encryption and the MAC. Explain why the attack from part (c) cannot be done when the authenticated encryption algorithm uses different keys.

Question

(d) Write down the authenticated encryption algorithm based on the same design but using different keys for the encryption and the MAC. Explain why the attack from part (c) cannot be done when the authenticated encryption algorithm uses different keys.

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Solution

The authenticated encryption algorithm that uses different keys for encryption and MAC (Message Authentication Code) can be written as follows:

  1. Generate two different keys, K1 for encryption and K2 for MAC.
  2. Encrypt the plaintext message M using key K1 to get the ciphertext C.
  3. Compute the MAC of the ciphertext C using key K2 to get the tag T.
  4. The output of the authenticated encryption algorithm is the pair (C, T).

The attack from part (c) cannot be done when the authenticated encryption algorithm uses different keys because the attacker does not have access to both keys. In the case where the same key is used for both encryption and MAC, if the attacker gets hold of the key, they can both decrypt the ciphertext and forge the MAC. However, when different keys are used, even if the attacker gets hold of one key, they cannot perform both actions. For example, if they get the encryption key, they can decrypt the ciphertext but cannot forge the MAC because they do not have the MAC key. Similarly, if they get the MAC key, they can forge the MAC but cannot decrypt the ciphertext because they do not have the encryption key. This significantly increases the security of the authenticated encryption algorithm.

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