Question

Suppose the DES F function mapped every 32-bit input R, regardless of the value of the input K, to
a) 32-bit string of ones,
b) bitwise complement of R.

1. What function would DES then compute?
2. How would the decryption look like?

3. Show that DES decryption is, in fact, the inverse of DES encryption.

Hint:

Use the following properties of the XOR operation:

(A XOR B) XOR C = A XOR (B XOR C)

A XOR A = 0

A XOR 0 = A

A XOR 1 = bitwise complement of A

where

A, B, C are n-bit strings of bits
0 is an n-bit string of zeros
1 is an n-bit string of ones

Answer 1

Figure 1:

Figure 2: