[Resource Topic] 2015/579: A Simple Proof of a Distinguishing Bound of Iterated Uniform Random Permutation

Resource Secret-key cryptography
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Welcome to the resource topic for 2015/579

Title:
A Simple Proof of a Distinguishing Bound of Iterated Uniform Random Permutation

Authors: 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.

ePrint: https://eprint.iacr.org/2015/579

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