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Actually, because of DESX works, the meet-in-the-middle attack can be optimized to take $2^{119}$ $DES$ (and no $DES^{-1}$ operations), and no additional storage. Here is how it works: let us assume that we have three known plaintext/ciphertext pairs $(P_1, C_1)$, $(P_2, C_2)$ and $(P_3, C_3)$. We know that: $$C_1 = K_2 \oplus DES( K, K_1 \oplus P_1 )$$ ...

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