Sparse Pseudorandom Distributions

Pseudorandom distributions on n-bit strings are ones which cannot be effi- ciently distinguished from the uniform distribution on strings of the same length. Namely, the expected behavior of any polynomial-time algorithm on a pseudorandom input is (almost) the same as on a random (i.e. uniformly chosen) input. Clearly, the uni- form distribution is a pseudorandom one. But do such trivial cases exhaust the notion of pseudorandomness? Under certain intractability assumptions the existence of pseudoran- dom generators was proven, which in turn implies the existence of non-trivial pseudoran- dom distributions. In this paper we investigate the existence of pseudorandom distribu- tions, using no unproven assumptions.