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Let's say I have $k$ distributions, where $k$ is polynomially large, $D_1, D_2, \ldots, D_k$ such that each $D_i$ is computationally indistinguishable from the uniform distribution.

Is it true that the distribution $D_1 D_2 \ldots D_k$ is also computationally indistinguishable from $k$ copies of the uniform distribution?

This trivially holds if each $D_i$ is efficiently samplable. But let's say they are not.

Does the fact still remain true, by some clever way to bypass the samplability requirement?

BlackHat18
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1 Answers1

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This is a very interesting question. I looked around and found a paper called Computational Indistinguishability: A Sample Hierarchy by Goldreich and Sudan. This contains a proof that it doesn't hold.

Yehuda Lindell
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