TY - JOUR

T1 - Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation

AU - Tsaban, Boaz

PY - 2003/7

Y1 - 2003/7

N2 - P ∈ SN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is Θ(N) if one does not use queries of the form Pm(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form Pm(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold.

AB - P ∈ SN is a fast forward permutation if for each m the computational complexity of evaluating Pm(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in SN is Θ(N) if one does not use queries of the form Pm(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form Pm(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold.

KW - Cycle structure

KW - Fast forward permutations

KW - Permutation graphs

KW - Pseudorandom permutations

UR - http://www.scopus.com/inward/record.url?scp=0037635114&partnerID=8YFLogxK

U2 - 10.1016/S0196-6774(03)00017-8

DO - 10.1016/S0196-6774(03)00017-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0037635114

SN - 0196-6774

VL - 47

SP - 104

EP - 121

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 2

ER -