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- W4302309683 abstract "We study deterministic extractors for oblivious bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions with small min-entropy: of the function's n input bits, k << n bits are uniformly random and unknown to the adversary. We simplify and improve an explicit construction of extractors for bit-fixing sources with sublogarithmic k due to Kamp and Zuckerman (SICOMP 2006), achieving error exponentially small in k rather than polynomially small in k. Our main result is that when k is sublogarithmic in n, the short output length of this construction (O(log k) output bits) is optimal for extractors computable by a large class of space-bounded streaming algorithms. Next, we show that a random function is an extractor for oblivious bit-fixing sources with high probability if and only if k is superlogarithmic in n, suggesting that our main result may apply more generally. In contrast, we show that a random function is a static (resp. adaptive) exposure-resilient function with high probability even if k is as small as a constant (resp. log log n). No explicit exposure-resilient functions achieving these parameters are known." @default.
- W4302309683 created "2022-10-06" @default.
- W4302309683 creator A5016656677 @default.
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- W4302309683 date "2010-03-21" @default.
- W4302309683 modified "2023-09-29" @default.
- W4302309683 title "On Extractors and Exposure-Resilient Functions for Sublogarithmic Entropy" @default.
- W4302309683 doi "https://doi.org/10.48550/arxiv.1003.4029" @default.
- W4302309683 hasPublicationYear "2010" @default.
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