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