Strength of Double DES

However, this is susceptible to a Meet-in-the-Middle attack:

• For $C=E(K_2,E(K_1,P))$, let $X=E(K_1,P)=D(K_2,C)$.
• Given known $P$ and $C$, encrypt $P$ for all possible $2^{56}$ possible $K_1$.
• Store in table, sorted by $X$.
• Decrypt $C$ with all $2^{56}$ possible $K_2$ and look for a match.
• Each hit is a candidate solution, validated with additional plain/cipher-text pair.
• A known plaintext attack against double DES will succeed with effort on the order of $2^{56}$ operations.