You can't use anything that will provide a uniform random distribution. It has to be at least a binomially distributed random, and at best a time-distributed fractional poisson distribution.

I'm using the built in poisson distribution randomiser built into R with some jiggery pokery to make it a poisson time-distributed random(really share based) instead of the standard poisson distribution http://stat.ethz.ch/R-manual/R-patched/library/stats/html/Poisson.html. Ryouiki has a bespoke poisson randomiser built on mersenne twister as a random seeder.