In this problem, we will compare the security services that are provided by digi

Question

In this problem, we will compare the security services that are provided by digital signatures (DS) and message authentication codes (MAC).We assume that Oscar is able to observe all messages send from Alice to Bob and vice versa. Oscar has no knowledge of any keys but the public one in case of DS. State whether and how (i) DS and (ii) MAC protect against each attack.The value auth(x) is computed with a DS or a MAC algorithm, respectively. a. (Message integrity) Alice sends a message x Transfer $1000 to Mark in the clear and also sends auth(x) to Bob. Oscar intercepts the message and replaces Mark with Oscar.Will Bob detect this?

Explanation / Answer

Alice knows that she will want to send a single 128-bit message to Bob. for this, Alice and Bob first select a 128-bit key k {0, 1} 128 uniformly at random. When alice send a message x {0, 1} 128 to Bob, Alice considers two ways of doing so. She can use the key as a one time pad, sending Bob k x. Alternatively, she can use AES to encrypt x. Recall that AES is a 128-bit block cipher which can use a 128-bit key, so in this case she would encrypt x as a single block and send Bob AESk(x).

Assume Eve will see either k x or AESk(x), that Eve knows an initial portion of x (a standard header), and that she wishes to recover the remaining portion of x.

If Eve has time to try out every possible key k {0, 1} 128, then in this condition-They would be equally secure. Either way, Eve would not be able to learn the unknown portion of x.(Even after trying every possible key (including the actual one), Eve will have no way of recognizing the correct plaintext or even narrowing down the possibilities in any way.)

A MAC can only be verified with the secret key used to generate it, but a digital signature can be verified with the public key of the party that signed the message.

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