Question: Suppose we are given a plaintext-ciphertext pair (m, c) such that c = DESk(m) is the encryption of m under some unknown secret 56-bit key

Suppose we are given a plaintext-ciphertext pair (m, c) such that c = DESk(m) is the encryption of m under some unknown secret 56-bit key k.

a) Show that from (m, c) we obtain immediatelywithout having to invoke an encryption or decryption oraclea plaintext-ciphertext pair (m, c) for the bit-wise complement k 156 of k.

b) Can the observation in (a) be exploited to expedite an exhaustive key search against DES?

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