Security Ampliication by Composition: the Case of Doubly-iterated, Ideal Ciphers

We i n v estigate, in the Shannon model, the security of constructions corresponding to double and two-key triple DES. That is, we consider F k1 F k2 and F k1 F ,1 k2 F k1 with the component functions being ideal ciphers. This models the resistance of these constructions to generic" attacks like meet in the middle attacks. We obtain the rst proof that composition actually increases the security in some meaningful sense. We compute a bound on the probability of breaking the double cipher as a function of the number of computations of the base cipher made, and the number of examples of the composed cipher seen, and show that the success probability is the square of that for a single key cipher. The same bound holds for the two-key triple cipher. The rst bound is tight and shows that meet in the middle is the best possible generic attack against the double cipher.