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 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: DESA_k, k1(x) = 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-cyphertext