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For DES, suppose that key k converts plaintext p into ciphertext c. If k’ represents the bitwise complement of the key k, p’ represents the bitwise complement of the plaintext p, and c’ represents the bitwise complement of the ciphertext c, show that key k’ would convert plaintext p’ into ciphertext c’.

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Are you asking us how to show the key complement property of DES? What have you attempted? –  poncho Jan 31 at 19:38
Hint: in this drawing of DES, and this one detailing a round, highlight was complementing $P$ and $K$ complements. Then, after understanding what happens, use induction for a formal proof. For bonus points: when and how is this exploitable by an attacker? –  fgrieu Jan 31 at 19:52
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