Algorithmic pseudo-random permutations for large sequences

permdata = createRandomPermutation(numobjects, nrounds) create a pseudo-random permutation

% PERMDATA = createRandomPermutation(NUMOBJECTS, NROUNDS) generates a
% struct representing a pseudo-random permutation of the sequence
% 1:NUMOBJECTS.
%
% The permutation is generated algorithmically, so there is no need to
% hold it in memory. This is useful for pseudo-random permutations which
% are too large to be generated with randperm. The parameter NUMOBJECTS
% can be very large, provided that floating point arithmetic errors keep
% below 0.5 (for example, it works for the range 1:1e12).
%
% It is essentially a slow, quick-and-dirty implementation of a
% substitution-perturbation network (essentially a randomly generated,
% probably non-secure block cipher with custom block-length). Surely
% there are simpler ways to generate good pseudo-random perturbations,
% but I am no expert...
% See:
% http://en.wikipedia.org/wiki/Format-preserving_encryption#FPE_from_cycle_walking
% http://en.wikipedia.org/wiki/Substitution-permutation_network
%
% The parameter NROUNDS specifies the number os stages of the network.
%
% Example: To generate a permutation of the sequence 1:1e8, first
% generate a random substitution-perturbation network (in
% this example, with 10 stages:
%
% permdata = createRandomPermutation(1e8, 10);
%
% Then, to generate the n-th element of the permuted sequence,
% use:
%
% m = permdata.encode(permdata, n);
%
% Example: create a random permutation of the sequence 1:10000 and check
% that it is, effectively, a permutation
%
% permdata = createRandomPermutation(10000, 10);
% x = (1:permdata.numobjects)';
% y = zeros(size(x));
% for k=1:numel(y);
% y(k) = permdata.encode(permdata, x(k));
% end
% yy = sort(y);
% isequal(x, yy)
% plot(x,y,'.'); grid on;
%
% Copyright (C) Jose David Fernandez Rodriguez 2012