Suppose the DES F function mapped every 32-bit input R, regardless of the value of the input

Question:

Suppose the DES F function mapped every 32-bit input R, regardless of the value of the input $\mathrm{K}$, to

a. 32-bit string of ones

b. bitwise complement of $\mathrm{R}$

Hint: Use the following properties of the XOR operation:

1. What function would DES then compute?

2. What would the decryption look like?

\[
\begin{gathered}
(A \oplus B) \oplus C=A \oplus(B \oplus C) \\
A \oplus A=\mathbf{0} \\
A \oplus 0=A
\end{gathered}
\]
$A \oplus \mathbf{1}=$ bitwise complement of $A$
where
$A, B, C$ are $n$-bit strings of bits
$\mathbf{0}$ is an $n$-bit string of zeros
$\mathbf{1}$ is an $n$-bit string of one