CRYPTOGRAPHY DES 1 DES2

Consider a new block cipher, DES2, that consists only of two rounds of the Feistel structure (com- pared to 16 rounds for the noemal use of DES) of DES. DES2 has the same block and key size as DES. For this question, you should consider the DES round function F as a black box that takes two inputs, a 32-bit data segment and a 48-bit round key, and produces a 32-bit output. Do not look inside the S-boxes for this problem. Do not look at the key scheduling algorithm for this problem. Suppose you have a large number of plaintext-ciphertext pairs for DES2 under a single unknown key. Give an algorithm for recovering the 48-bit round key for round 1 and the 48-bit round key for round 2. Your algorithm should require fewer operations than an exhaustive search for the entire 56-bit DES key.