International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: Permutation graphs, fast forward permutations, and

Authors:
Boaz Tsaban
Download:
URL: http://eprint.iacr.org/2003/138
Search ePrint
Search Google
Abstract: A permutation $P\in S_N$ is a \emph{fast forward permutation} if for each $m$ the computational complexity of evaluating $P^m(x)$ 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 $S_N$ is $\Theta(N)$ if one does not use queries of the form $P^m(x)$, but is only $\Theta(1)$ 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 $P^m(x)$ 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.
BibTeX
@misc{eprint-2003-11853,
  title={Permutation graphs, fast forward permutations, and},
  booktitle={IACR Eprint archive},
  keywords={foundations /},
  url={http://eprint.iacr.org/2003/138},
  note={Journal of Algorithms 47 (2), 104--121. tsaban@math.huji.ac.il 12250 received 16 Jul 2003},
  author={Boaz Tsaban},
  year=2003
}