Extractors: Low Entropy Requirements Colliding With Non-Malleability
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The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about 1/2, the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability. (2) Constructions where one source is uniform, and the other can have small min-entropy rate, and the extractor guarantees non-malleability when the uniform source is tampered. (3) Constructions where both sources have entropy rate very close to 1 and the extractor guarantees non-malleability against the tampering of both sources. We introduce a new notion of collision resistant extractors and in using it we obtain a strong two source non-malleable extractor where we require the first source to have 0.8 entropy rate and the other source can have min-entropy polylogarithmic in the length of the source. We show how the above extractor can be applied to obtain a non-malleable extractor with output rate 1/2, which is optimal. We also show how, by using our extractor and extending the known protocol, one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal.
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