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Cryptography and Architectures for Computer Security Exam Code: 095947 (old 090959), A.Y. 2014–2015, Semester: 2 Prof. G. Pelosi July 22nd, 2015 – 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 [3 pts] Consider a Vigen` ere Cipher. Each (lower-case) letter of the English alphabet is put into one-to- one correspondence with the integer denoting its position, i.e.: a=0, b=1, ... , z=25. The key k=(k1,k 2,...,k m), 0≤ki≤ 25 is composed by m≥ 2 letters and is employed to perform a block encryption of the plaintext message x=(x1,x 2,...,x m,x m+1,... ), with 0≤xi≤ 25, as follows: c=(x1+k1 mod 26, ... , xm+km mod 26, xm+1+k1 mod 26, ... ) • Show how to apply a Known Plaintext Attack • Describe how to execute a Ciphertext-Only Attack • How is it possible to design a Perfectly Secure Cipher employing a Vigen` ere Cipher? Solution: see lectures, or book, ... Question 2 [3 pts] Let p be a large prime and g be a generator of ( Z∗ p,·). Suppose we are considering the function h : Z↦→ Z∗ p for use as a hash function, where h(x) = gx modp, assuming x to be an arbitrary binary string interpreted as a positive integer number, i.e.: x∈Z, x≥0. Note that the compression property of typical hash functions is satisfied by the above definition as messages x of arbitrary bit-length are hashed into a fixed…