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Pseudorandom number generators are often composed to yield pseudorandom function generators. We will introduce a model in which it should be possible to demonstrate a lower bound on the number of times a pseudorandom function generator must query an oracle for a pseudorandom number generator.
Weakly pseudorandom function generators are often composed in rounds to produce adaptively pseudorandom function generators. Non-adaptively pseudorandom function generators were introduced to model the weakly secure function generators. In [18], using an assumption related to the non-uniform DDH assumption, it is shown that the composition of non-adaptively pseudorandom function generators is not adaptively pseudorandom in general. We will show that the assumption given in [18] can be weakened to the more standard non-uniform DDH assumption, yielding a stronger result.