• Corpus ID: 14335618

A modular framework for randomness extraction based on Trevisan's construction

@article{Mauerer2012AMF,
  title={A modular framework for randomness extraction based on Trevisan's construction},
  author={Wolfgang Mauerer and Christopher Portmann and Volkher B. Scholz},
  journal={ArXiv},
  year={2012},
  volume={abs/1212.0520}
}
Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random numbers---required, for instance, by cryptographic protocols, numerical simulations, or randomised computations. Trevisan's extractor raised considerable theoretical interest not only because of its data parsimony compared to other constructions, but particularly because… 

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References

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Here, it is shown that the well-known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information and exploited the modularity of this paradigm to give several concrete extractor constructions.

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This work proposes a general “sample-then-extract” approach to constructing locally computable extractors: use essentially any randomness-efficient sampler to select bits from the input and then apply any extractor to the selected bits.

Encryption against Storage-Bounded Adversaries from On-Line Strong Extractors

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It is shown that an encryption scheme with such nice properties can be derived immediately from any strong randomness extractor, a function which extracts randomness from a slightly random source, so that its output and its seed together are almost random.

Does Privacy Require True Randomness?

This work completely resolves the question of private-key encryption, where parties wish to encrypt a b-bit value using a shared secret key sampled from some imperfect source of randomness S, and shows that if such n-bit source S allows for a secure encryption of b bits, then one can deterministically extract nearly b almost perfect random bits from S.

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It is proved that certain extractors are suitable for key expansion in the bounded-storage model where the adversary has a limited amount of quantum memory.

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It is shown that, using the simpler Nisan--Wigderson generator and standard error-correcting codes, one can build even better extractors with the additional advantage that both the construction and the analysis are simple and admit a short self-contained description.

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