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.