Resistance against Adaptive Plaintext-Ciphertext Iterated Distinguishers

Decorrelation Theory deals with general adversaries who are mounting iterated attacks, i.e., attacks in which an adversary is allowed to make d queries in each iteration with the aim of distinguishing a random cipher C from the ideal random cipher C^*. A bound for a non-adaptive iterated distinguisher of order d, who is making plaintext (resp. ciphertext) queries, against a 2d-decorrelated cipher has already been derived by Vaudenay at EUROCRYPT '99. He showed that a 2d-decorrelated cipher resists against iterated non-adaptive distinguishers of order d when iterations have almost no common queries. More recently, Bay et al. settled two open problems arising from Vaudenay's work at CRYPTO '12, yet they only consider non-adaptive iterated attacks. Hence, a bound for an adaptive iterated adversary of order d, who can make both plaintext and ciphertext queries, against a 2d-decorrelated cipher has not been studied yet. In this work, we study the resistance against this distinguisher and we prove the bound for an adversary who is making adaptive plaintext and ciphertext queries depending on the previous queries to an oracle.