**On the Construction of Pseudo-Random Permutations: Luby-Rackoff Revisited**

*Moni Naor and Omer Reingold*

**Abstract: **Luby and Rackoff showed a method for constructing a pseudo-random permutation
from a pseudo-random function. The method is based on composing four
(or three for weakened security) so called Feistel permutations
each of which requires the evaluation of a pseudo-random function.
We reduce somewhat the complexity of the construction
and simplify its proof of security by showing
that two Feistel permutations are sufficient together with initial
and final pair-wise independent permutations.
The revised construction and proof provide a framework in which
similar constructions may be brought up and their security can
be easily proved.
We demonstrate this by presenting some additional adjustments
of the construction that achieve the following:
1. Reduce the success probability of the adversary.
2. Provide a construction of pseudo-random permutations with large input
size using pseudo-random functions with small input size.
3. Provide a construction of a pseudo-random permutation
using a single pseudo-random function.

**Category / Keywords: **

**Publication Info: **Appeared in the THEORY OF CRYPTOGRAPHY LIBRARY and has been included in the ePrint Archive.

**Date: **received August 1st, 1996. Revised Feb 17th, 1997.

**Contact author: **reingold at wisdom weizmann ac il

**Available format(s): **Postscript (PS) | Compressed Postscript (PS.GZ) | BibTeX Citation

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