[Solved] CS458 Problem Set 2- Relation between passwords and key size

CS458Problem Set 2Problem 1We now consider the relation between passwords and key size. For this purpose we consider a cryptosystemwhere 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 bitsper character, i.e., 128 possible characters). What is the size of the key space which can be constructedby such passwords?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 bitsof the ASCII-encoding. What is the corresponding key length in bits in this case?Problem 2One 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 pairs1. x1 = 000000 , x2 = 0000012. x1 = 111111 , x2 = 100000S-Box 1 of DES0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 71 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 82 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 03 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13Problem 3Explain the self-healing property of cipher block chaining mode?Problem 4Perform encryption using the RSA algorithm, for the following:1. p = 3, q = 11, e = 7, M = 52. p = 5, q = 17, e = 3, M = 9Problem 5Perform decryption using the RSA algorithm, for p = 11, q = 13, e = 11; C = 106Problem 6In a public-key system using RSA, you intercept the ciphertext C =10 sent to a user whose public key ise=5 , n=35 . What is the plaintext M ?1Problem 7Alice and Bob use the Die-Hellman key exchange technique with a common prime p = 71 and a primitiveroot  = 7 .1. If Alice has private key kpr,A = 5 , what is Alices public key kpub,A?2. If Bob has private key kpr,B = 12 , what is Bobs public key kpub,B?3. What is the shared secret key?2