This is a cryptology question from the textbook Introduction to Modern Cryptography by Katz and Lindell.

6.10 Show that DES has the property that DESk(z) = DESk(2) for ev- ery key k and input x (where 2 denotes the bitwise complement of z) (This is called the complementarity property of DES.) Does this repre- sent a serious vulnerability in the use of triple-DES as a pseudorandom permutation? Explain. 6.10 Show that DES has the property that DESk(z) = DESk(2) for ev- ery key k and input x (where 2 denotes the bitwise complement of z) (This is called the complementarity property of DES.) Does this repre- sent a serious vulnerability in the use of triple-DES as a pseudorandom permutation? Explain