**A Simple Proof of a Distinguishing Bound of Iterated Uniform Random Permutation**

*Mridul Nandi*

**Abstract: **Let P be chosen uniformly from the set P := Perm(S), the set of all permutations over a set S of size N. In Crypto 2015, Minaud and Seurin proved that for any unbounded time adversary A, making at most q queries, the distinguishing advantage between P^r (after sampling P, compose it for r times) and P, denoted Delta(P^r ; P), is at most (2r + 1)q/N. In this paper we provide an alternative simple proof of this result for an upper bound 2q(r+1)^2/N by using well known coefficient H-technique.

**Category / Keywords: **secret-key cryptography / iterated random permutation, blockcipher, cascade encryption.

**Date: **received 10 Jun 2015

**Contact author: **mridul nandi at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20150618:194356 (All versions of this report)

**Short URL: **ia.cr/2015/579

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