International Association
for Cryptologic Research

The iterated Even-Mansour cipher is a construction of a block cipher from $r$ public permutations $P_1,\\ldots,P_r$ which abstracts in a generic way the structure of key-alternating ciphers. The indistinguishability of this construction from a truly random permutation by an adversary with oracle access to the inner permutations $P_1,\\ldots,P_r$ has been investigated in a series of recent papers. This construction has also been shown to be (fully) indifferentiable from an ideal cipher for a sufficient number of rounds (five or twelve depending on the assumptions on the key-schedule). In this paper, we extend this line of work by considering the resistance of the iterated Even-Mansour cipher to xor-induced related-key attacks (i.e., related-key attacks where the adversary is allowed to xor any constant of its choice to the secret key) and to chosen-key attacks. For xor-induced related-key attacks, we first provide a distinguishing attack for two rounds, assuming the key-schedule is linear. We then prove that for a linear key-schedule, three rounds yield a cipher which is secure against xor-induced related-key attacks up to $O(2^{\\frac{n}{2}})$ queries of the adversary, whereas for a nonlinear key-schedule, one round is sufficient to obtain a similar security bound. We also show that the iterated Even-Mansour cipher with four rounds offers some form of provable resistance to chosen-key attacks, which is the minimal number of rounds to achieve this property. The main technical tool that we use to prove this result is \\emph{sequential indifferentiability}, a weakened variant of (full) indifferentiability introduced by Mandal \\emph{et al.} (TCC~2010).