It is known that DES has the key-complementation property. That is, given any key $k$ and any message $m\in\{0,1\}^{64}$ $$\operatorname{DES}_k(m)=\overline{\operatorname{DES}_\overline k(\overline m)}$$
By using this property, show that the key search of DES can be sped up by a factor of two.
