1) Determine the expanded key length (in terms of the number of words) for AES when we use key of length 256 bits. Also, draw the overall structure of AES for a 256-bit key. Show all the inputs and outputs (similar to the overall structure shown for AES with a 128-bit key).
2) Derive the 32-bit output for the 48-bit input using the S-Box table given for DES

48-bit input

3) Would it be possible to reduce the key search space for 56-bit key-based DES from O(256) to O(255) using a "known plaintext attack" and the bit-wise complement property of DES? Why or why not? Justify your answer.

4 Suppose the DES f function (Feistel function) maps every 32-bit input R (regardless of the value of the input K) to 32-bit string of 1s. Given that the input to a round j is Lj-1 and Rj-1, determine what would DES compute after every two rounds and after every four rounds? [Hint: Use the XOR properties - A A = 0; A 1 = A′; A 0 = A]

5)Given the following state array (in hex.) for an AES encryption round:

52        6b        7c        8d

74        99        14        2a

fb         a2        b3        c2

54        8d        1c        93

(a) Perform the Sub Bytes step followed by the Shift Rows step and write the output array (in hex.)

(b) When the output array of (a) is subjected to the AES Mix Columns step, write the output value of the byte in the third row and second column of the product array. Show all the steps.

6) (25 pts) RSA Algorithm: Let p = 7 and q = 11.
a) Determine the encryption and decryption keys. Your encryption key of choice (e) should be above 6.
b) Show the decryption for a ciphertext 9. You should use the decryption key found using the Extended Euclid's algorithm in step (a).