A Synthetic Indifferentiability Analysis of Interleaved Double-Key Even-Mansour Ciphers

Iterated Even-Mansour scheme (IEM) is a generalization of the basic 1-round proposal (ASIACRYPT ’91). The scheme can use one key, two keys, or completely independent keys. Most of the published security proofs for IEM against relate-key and chosen-key attacks focus on the case where all the round-keys are derived from a single master key. Whereas results beyond this barrier are relevant to the cryptographic problem whether a secure blockcipher with key-size twice the block-size can be built by mixing two relatively independent keys into IEM and iterating sufficiently many rounds, and this strategy actually has been used in designing blockciphers for a long-time. This work makes the first step towards breaking this barrier and considers IEM with Interleaved Double independent round-keys: IDEMr((k1, k2),m) = ki ⊕ (Pr(. . . k1 ⊕ P2(k2 ⊕ P1(k1 ⊕m)) . . .)), where i = 2 when r is odd, and i = 1 when r is even. As results, this work proves that 15 rounds can achieve (full) indifferentiability from an ideal cipher with O(q/2) security bound. This work also proves that 7 rounds is sufficient and necessary to achieve sequential-indifferentiability (a notion introduced at TCC 2012) with O(q/2) security bound, so that IDEM7 is already correlation intractable and secure against any attack that exploits evasive relations between its input-output pairs.