2016 09 28

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Cryptography and Architectures for Computer Security Exam Code: 095947 (old 090959), A.Y. 2015–2016, Semester: 2 Prof. G. Pelosi September 28th, 2016 – Exam Session Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Surname: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Student ID: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Signature: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time: 2h:30’. Use of textbooks, notes, phones or Internet connected devices is not allowed. Prior to turn in your paper, write your name on any additional sheet and sign it. Question 1 [2 pts] Alice uses a block cipher Enc having 64-bit block size and 64-bit key size. She is worried that the key size is too small to prevent brute force attacks. Therefore, she decides to improve the encryption scheme employing 2 independent 64-bit keys: (k0,k1), and encrypting her messages as: c = Enck0(m)⊕k1, m,c ∈{ 0, 1}64 • Assume that the adversary gets access to a few plaintext/ciphertext pairs and is indeed able to perform a brute-force attack on the original encryption scheme Enc and recover the key with a known plaintext attack . Show that he can also break the “improved” scheme and recover the Alice’s extended key. Solution: Considering 2 pairs of plaintexts and ciphertexts (m1,c 1), (m2,c 2) for each possible value of k0 compute k1 =c1⊕ Enck0(m1) and check if k1 =c2⊕ Enck0(m2) holds The adversary needs to compute every value of Enck0(m1) and Enck0(m2), thus the cost for obtaining the extended key with 128-bit is only doubled with respect to a bruteforce of the 64-bit key of the original cipher. Question 2 [3 pts] Consider a file encrypted with a given mode of operation and the…