| Abstract |
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We give an efficient deterministic algorithm which extracts \Omega (n^{2\gamma } ) almost-random bits from sources where n^{\frac{1}{2} + \gamma } of the n bits are uniformly random and the rest are fixed in advance. This improves on previous constructions which required that at least n/2 of the bits be random. Our construction also gives explicit adaptive exposure-resilient functions and in turn adaptive all-or-nothing transforms. For sources where instead of bits the values are chosen from [d], for d > 2, we give an algorithm which extracts a constant fraction of the randomness. We also give bounds on extracting randomness for sources where the fixed bits can depend on the random bits. .
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 Additional Information
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Citation:
Jesse Kamp, David Zuckerman,
"Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography,"
focs,
p. 92,
44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03),
2003
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