Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A note on computational indistinguishability
Information Processing Letters
Journal of Computer and System Sciences
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Bounds on the Efficiency of Generic Cryptographic Constructions
SIAM Journal on Computing
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
A Leakage-Resilient Mode of Operation
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
2-Source Extractors under Computational Assumptions and Cryptography with Defective Randomness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Cryptographic extraction and key derivation: the HKDF scheme
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Leftover Hash Lemma, revisited
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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Computational extractors are efficient procedures that map a source of sufficiently high min-entropy to an output that is computationally indistinguishable from uniform. By relaxing the statistical closeness property of traditional randomness extractors one hopes to improve the efficiency and entropy parameters of these extractors, while keeping their utility for cryptographic applications. In this work we investigate computational extractors and consider questions of existence and inherent complexity from the theoretical and practical angles, with particular focus on the relationship to pseudorandomness. An obvious way to build a computational extractor is via the "extract-then-prg" method: apply a statistical extractor and use its output to seed a PRG. This approach carries with it the entropy cost inherent to implementing statistical extractors, namely, the source entropy needs to be substantially higher than the PRG's seed length. It also requires a PRG and thus relies on one-way functions. We study the necessity of one-way functions in the construction of computational extractors and determine matching lower and upper bounds on the "black-box efficiency" of generic constructions of computational extractors that use a one-way permutation as an oracle. Under this efficiency measure we prove a direct correspondence between the complexity of computational extractors and that of pseudorandom generators, showing the optimality of the extract-then-prg approach for generic constructions of computational extractors and confirming the intuition that to build a computational extractor via a PRG one needs to make up for the entropy gap intrinsic to statistical extractors. On the other hand, we show that with stronger cryptographic primitives one can have more entropy- and computationally-efficient constructions. In particular, we show a construction of a very practical computational extractor from any weak PRF without resorting to statistical extractors.