Question

Topic: Encrypt-then-authenticate scheme, Cryptography

Let Π^E = (Gen^E, Enc^E, Dec^E) be an encryption scheme and Π^M = (Gen^M, Mac^M, Vrfy^M) be a MAC scheme.

(b) Prove that Π is unforgeable for any encryption scheme Π^E (even if not CPA-secure) and any secure MAC scheme Π^M (even if not strongly secure).

Answer 1

SOLUTION-

(b) If ENC is a symmetric encryption scheme secure in the sense
of IND-CPA and MAC is a secure MAC family then method EtA(ENC, MAC)
implements secure channels.

• Encryption then authenticate provides integrity of Ciphertext. Assuming the MAC shared secret has not been compromised, it is ble to deduce whether a given ciphertext is indeed authentic or has been forged; for example, in public-key cryptography anyone can send you messages. EtM ensures you only read valid messages.
• Plaintext integrity.
• If the cipher scheme is maliable we need not be so concerned since the MAC will filter out this invalid ciphertext.
• The MAC does not provide any information on the plaintext since, assuming the output of the cipher appears random, so does the MAC. In other words, we haven't carried any structure from the plaintext into the MAC.

The function snd represents the operations and transformations applied
to a message by its sender in order to protect it from adversarial action over
the communication links. Namely, when a message m is to be transmitted from
party P to party Q under a session s established between these parties, the
function snd is applied to m and, possibly, to additional information such as a
message identifier. The definition of snd typically consists of the application of
some combination of a MAC and symmetric encryption keyed via the session
key. The function rcv describes the action at the receiving end for “decoding”
and verifying incoming messages, and it typically involves the verification of a
MAC and/or the decryption of an incoming ciphertext.

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