Show that DES decryption is inverse of DES encryption?

Answer 1

The reasoning for the Feistel cipher, as shown in Figure 3.6 applies in the case of

DES. We only have to show the effect of the IP and IP-1 functions. For encryption,

the input to the final IP-1 is RE16 LE16. The output of that stage is the ciphertext.

On decryption, the first step is to take the ciphertext and pass it through IP. Because

IP is the inverse of IP-1, the result of this operation is just RE16 LE16, which is

equivalent to LD0 RD0. Then, we follow the same reasoning as with the Feistel

cipher to reach a point where LE0 = RD16 and RE0 = LD16. Decryption is completed

by passing LD0 RD0 through IP-1. Again, because IP is the inverse of IP-1, passing

the plaintext through IP as the first step of encryption yields LD0 RD0, thus

showing that decryption is the inverse of encryption.