INTE1127: Frontiers of Applied Cryptography - IT Assignment Help

Assignment Task:

Task:

1. Consider a block cipher encryption algorithm given by y = EK(x) with x the plaintext, y the ciphertext and K the key. Let K ∈ {0, 1} k , and x, y ∈ {0, 1} n , with EK : {0, 1} n → {0, 1} n .

(a) What is the keylength of this cipher? What is the blocklength of this cipher? How many possible keys exist for this cipher? How many possible plaintext blocks exist for this cipher?

(b) State the precise mathematical conditions on the encryption map- pings EK(·), as K varies over {0, 1} k , which ensures that the cipher can be used to obtain a valid plaintext x for every valid (cipher- text,key) pair (y, K).

(c) i. Describe how a brute force attack on this block cipher based on an exhaustive key search would proceed. Write the attack in the form of simple pseudocode fragment, making clear what is the input to the attack algorithm and what its output is.

ii. Derive the expected and the worst case time complexity of this attack. Also state and justify the memory and data complexity
for the attack. Evaluate these complexities for the case k = n = 128, as in modern block ciphers.
Note: You may use expressions of the form 2a I don’t expect decimal expansions of huge numbers.
(d) Let k = 3d. Assume that you can command a cluster of 2d processors in order to perform a parallel key search.
i. Let the processors be numbered as P0, P1, . . . , P2 d−1 . Describe a decomposition of the key space K = {0, 1} k , into subsets = K0, . . . , K2 d−1
, so that this attack can be carried out efficiently.
Derive the worst case and average case time complexity of this attack.
ii. Was there a free lunch? Did we actually do less work to find the key in this case? Explain.

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