The Iterated Random Permutation Problem with Applications to Cascade Encryption

@article{Minaud2015TheIR,
  title={The Iterated Random Permutation Problem with Applications to Cascade Encryption},
  author={Brice Minaud and Yannick Seurin},
  journal={IACR Cryptology ePrint Archive},
  year={2015},
  volume={2015},
  pages={504}
}
We introduce and study the iterated random permutation problem, which asks how hard it is to distinguish, in a black-box way, the rth power of a random permutation from a uniformly random permutation of a set of size N . We show that this requires Ω(N) queries (even for a two-sided, adaptive adversary). As a direct application of this result, we show that cascading a block cipher with the same key cannot degrade its security (as a pseudorandom permutation) more than negligibly. 

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