# CS458 Problem Set 2 solved

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## Description

Problem 1
We now consider the relation between passwords and key size. For this purpose we consider a cryptosystem
where the user enters a key in the form of a password.
a. Assume a password consisting of 8 letters, where each letter is encoded by the ASCII scheme (7 bits
per character, i.e., 128 possible characters). What is the size of the key space which can be constructed
b. What is the corresponding key length in bits?
c. Assume that most users use only the 26 lowercase letters from the alphabet instead of the full 7 bits
of the ASCII-encoding. What is the corresponding key length in bits in this case?
Problem 2
One important property which makes DES secure is that the S-boxes are nonlinear. How would you verify
(not prove of course) the non-linearity of S-box 1 of DES using the following input pairs
1. x1 = 000000 , x2 = 000001
2. x1 = 111111 , x2 = 100000
S-Box 1 of DES
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7
1 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8
2 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0
3 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13
Problem 3
Explain the self-healing property of cipher block chaining mode?
Problem 4
Perform encryption using the RSA algorithm, for the following:
1. p = 3, q = 11, e = 7, M = 5
2. p = 5, q = 17, e = 3, M = 9
Problem 5
Perform decryption using the RSA algorithm, for p = 11, q = 13, e = 11; C = 106
Problem 6
In a public-key system using RSA, you intercept the ciphertext C =10 sent to a user whose public key is
e=5 , n=35 . What is the plaintext M ?
1
Problem 7
Alice and Bob use the Diffie-Hellman key exchange technique with a common prime p = 71 and a primitive
root α = 7 .
1. If Alice has private key kpr,A = 5 , what is Alice’s public key kpub,A?
2. If Bob has private key kpr,B = 12 , what is Bob’s public key kpub,B?
3. What is the shared secret key?
2