Characterizing pseudoentropy and simplifying pseudorandom generator constructions

@article{Vadhan2011CharacterizingPA,
  title={Characterizing pseudoentropy and simplifying pseudorandom generator constructions},
  author={Salil P. Vadhan and Colin Jia Zheng},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2011},
  volume={18},
  pages={141}
}
We provide a characterization of pseudoentropy in terms of hardness of sampling: Let (X,B) be jointly distributed random variables such that B takes values in a polynomial-sized set. We show that B is computationally indistinguishable from a random variable of higher Shannon entropy given X if and only if there is no probabilistic polynomial-time S such that (X,S(X)) has small KL divergence from (X,B). This can be viewed as an analogue of the Impagliazzo Hardcore Theorem (FOCS '95) for Shannon… CONTINUE READING

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