Recall that for a block cipher, a key schedule algorithm determines the subkey for each round, based on the key K. Let K = (K0,K1,K2K55) be a 56-bit DES key.

a. List the 48 bits for each of the 16 DES subkeys K1, K2, ., K16, in terms of the key bits Ki.

b. Make a table that contains the number of subkeys in which each key bit ki is used.

c. Can you design a DES key schedule algorithm in which each key bit is used an equal number of times?