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The block cipher DESX is defined by DESXk.k1.ka(x) = k2 ⊕ DESk(k1 ⊕ x), where ⊕ denotes bitwise exclusive-or. This construction was first suggested by Ron Rivest as a computationally-cheap way to protect DES against exhaustive key-search attacks. This paper proves, in a formal model, that the DESX construction is sound. We show that, when F is an idealized block cipher, FXk.k1.k2(x)= K2 ⊕ Fk(k1 ⊕ x) is substantially more resistant to key search than is F. In fact, our analysis says that FX has an effective key length of at least ϰ+n - 1 - lg m bits, where ϰ, is the key length of F, n is the block Iength, and m bounds the number of (x, FXk(x)) pairs the adversary can obtain.

How to Protect DES Against Exhaustive Key Search