Constructing Pseudo-Random Permutations with a Prescribed Structure

We show how to construct pseudo-random permutations that satisfy a certain cycle restriction, for example that the permutation be cyclic (consisting of one cycle containing all the elements) or an involution (a self-inverse permutation) with no fixed points. The construction can be based on any (unrestricted) pseudo-random permutation. The resulting permutations are defined succinctly and their evaluation at a given point is efficient. Furthermore, they enjoy a fast forward property, i.e. it is possible to iterate them at a very small cost. Received 10 August 2000 and revised 30 September 2000 Online publication 9 April 2001