Suppose Alice has four blocks of plaintext, P_{o}, -P_{1}, P_{2}, -P_{3}· She computes a MAC using key K\, and then CBC encrypts the data using key K2 to obtain C_{0},C_{1},C_{2},C_{3}. Alice sends the IV, the ciphertext, and the MAC to Bob. Trudy intercepts the message and replaces C\ with X so that Bob receives IV, C$,X, 62,63, and the MAC. Bob attempts to verify the integrity of the data by decrypting (using key K2) and then computing a MAC (using key K_{1}) on the putative plaintext.

a. Show that Bob will detect Trudy’s tampering.

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b. Suppose that Alice and Bob only share a single symmetric key K. They agree to let K_{1}= K and K_{2} = K (BY, where Y is known to Alice, Bob, and Trudy. Assuming Alice and Bob use the same scheme as above, does this create any security problem?

Suppose that Alice and Bob have access to two secure block ciphers, say, Cipher A and Cipher B, where Cipher A uses a 64-bit key, while Cipher B uses a 128-bit key. Alice prefers Cipher A, while Bob wants the additional security provided by a 128-bit key, so he insists on Cipher B. As a compromise, Alice proposes that they use Cipher A, but they encrypt each message twice, using two independent 64-bit keys. Assume that no shortcut attack is available for either cipher.

Is Alice’s approach as secure as Bob’s?

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