Resistance against Iterated Attacks by Decorrelation Revisited

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)

Abstract

Iterated attacks are comprised of iterating adversaries who can make d plaintext queries, in each iteration to compute a bit, and are trying to distinguish between a random cipher C and the ideal random cipher \(C^*\) based on all bits. In EUROCRYPT ’99, Vaudenay showed that a 2d-decorrelated cipher resists to iterated attacks of order d when iterations make almost no common queries. Then, he first asked what the necessary conditions are for a cipher to resist a non-adaptive iterated attack of order d. Secondly, he speculated that repeating a plaintext query in different iterations does not provide any advantage to a non-adaptive distinguisher. We close here these two long-standing open problems.

We show that, in order to resist non-adaptive iterated attacks of order d, decorrelation of order \(2d-1\) is not sufficient. We do this by providing a counterexample consisting of a cipher decorrelated to the order \(2d-1\) and a successful non-adaptive iterated attack of order d against it.

Moreover, we prove that the aforementioned claim is wrong by showing that a higher probability of having a common query between different iterations can translate to a high advantage of the adversary in distinguishing C from \(C^*\). We provide a counterintuitive example consisting of a cipher decorrelated to the order 2d which can be broken by an iterated attack of order 1 having a high probability of common queries.

Keywords

Random Function Block Cipher Linear Cryptanalysis Probabilistic Encryption Newton Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  1. 1.EPFLLausanneSwitzerland

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