1. Suppose that we use a block cipher to encrypt according to the rule
C0 = IV E(P0, K),C1 = C0 E(P1, K), C2 = C1 E(P2, K),
What is the corresponding decryption rule? Are there any security advantages or disadvantages to this mode compared to CBC mode?
2. Suppose Alice has four blocks of plaintext, P0, P1, P2 and P3 and she computes a MAC (Students can assume CBC MAC) using the key K. Alice sends the initialization vector, denoted IV, the plaintext blocks and the MAC to Bob. However, Trudy intercepts the message and replaces P1 with X so that Bob receives IV, P0. X, P2, P3, and the MAC.
a. Precisely what does Bob compute when he attempts to verify the MAC?
b. Show that Bob will almost certainly detect Trudys tampering.
c. What is the probability that Bob does not detect Trudys tampering?
3. Counter (CTR) mode allows block ciphers to be used like stream ciphers. The CTR mode encryption formula is Ci = Pi E(1V+i , K ), and decryption rule is Pi = Ci E(1V+i, K ) .
a. Explain how to do random access on data encrypted using CTR mode
b. Explain how to do random access on data encrypted using CBC mode
c. Which is better for random access, CTR mode or CBC mode, and why?
4. Suppose that Alice and Bob always choose the same IV.
a. Discuss one security problem this creates if CBC mode is used.
b. Discuss one security problem this creates if CTR mode is used
c. If the same IV is always used, why is CBC mode preferable to CTR mode?
5. Consider a Feistel Cipher with four rounds. Then P = (L0, R0) is the plaintext. What is the ciphertext C = (L4,R4), in terms of (L0, R0), for each of the following round functions?
a. F(Ri-1, Ki) = X, where X is a constant
b. F(Ri-1, Ki) = Ri-1
c. F(Ri-1, Ki) = Ri-1 Ki
d. F(Ri-1, Ki) = Ri-1 +Ki (mod 232), where Ri-1 and Ki are 32-bit quantities
6. Trudy wants to attack a block cipher that has a 64-bit key and 64-bit blocks. Each time she attacks this cipher, she can conduct a chosen plaintext attack and the cipher is used in ECB mode.
a. Suppose Trudy does an exhaustive key search each time she attacks the cipher. If she conducts the attack 220 times, what is the total work, the storage requirement, and the success probability?
b. Suppose Trudy pre-computes E(P,K) for a selected plaintext P and every possible key K . For each attack, Trudy chooses the same plaintext P and obtains the corresponding ciphertext C. Then she
simply looks up C in her pre-computed list to obtain the key K. If she again conducts the attack 220 times, what is the total work, the storage requirement, and the success probability?
c. Suppose Trudy implements Hellmans TMTO attack and, as suggested in the text, she chooses T = m = t = 264/3. If she conducts the attack 220 times, what is the total work, the storage requirement and the success probability?
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