Problem 5.16 in this pdf, from the book: Christof Paar, Jan Pelzl, Understanding Cryptography
5.16. This is your chance to break a cryptosystem. As we know by now, cryptography is a tricky business. The following problem illustrates how easy it is to turn a strong scheme into a weak one with minor modifications. We saw in this chapter that key whitening is a good technique for strengthening block ciphers against brute-force attacks. We now look at the following variant of key whitening against DES, which we’ll call DESA: $$\operatorname{DESA}_{k,k_1} (x) \underset{\text{def}}= \operatorname{DES}_k(x)⊕k_1$$ Even though the method looks similar to key whitening, it hardly adds to the security. Your task is to show that breaking the scheme is roughly as difficult as a brute-force attack against single DES. Assume you have a few pairs of plaintext– ciphertext.