On extractors and exposure-resilient functions for sublogarithmic entropy
نویسندگان
چکیده
منابع مشابه
On Extractors and Exposure-Resilient Functions for Sublogarithmic Entropy
We study deterministic extractors for bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions for small min-entropy. That is, of the n bits given as input to the function, k n bits are uniformly random and unknown to the adversary. We show that a random function is a resilient function with high probability if and only if k is at least roughly logn. In contrast, we show...
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Resilient and exposure-resilient functions are functions whose output appears random even if some portion of their input is either revealed or fixed. We explore an alternative way of characterizing these objects that ties them explicitly to the theory of randomness extractors and simplifies current proofs of basic results. We also describe the inclusions and separations governing the various cl...
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We give an efficient deterministic algorithm that extracts Ω(n2γ) almost-random bits from sources where n 1 2 +γ of the n bits are uniformly random and the rest are fixed in advance. This improves upon previous constructions, which required that at least n/2 of the bits be random in order to extract many bits. Our construction also has applications in exposure-resilient cryptography, giving exp...
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Last time we proved the Leftover Hash Lemma, which states that if X is a random variable with universe U and H∞(X) ≥ k, ε > 0, and H is a universal hash family of size 2 with output length l = k − 2 log(1/ε), then Ext(x, h) = h(x) is a (k, ε/2) extractor with seed length d and output length m. In other words, Ext(x, h) extracts l bits from x that are ε-close to uniform, with ε = 12 √ 2−l. For a...
متن کاملZero-Fixing Extractors for Sub-Logarithmic Entropy
An (n, k)-bit-fixing source is a distribution on n bit strings, that is fixed on n − k of the coordinates, and jointly uniform on the remaining k bits. Explicit constructions of bit-fixing extractors by Gabizon, Raz and Shaltiel [SICOMP 2006] and Rao [CCC 2009], extract (1 − o(1)) · k bits for k = poly log n, almost matching the probabilistic argument. Intriguingly, unlike other well-studied so...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2012
ISSN: 1042-9832
DOI: 10.1002/rsa.20424