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### Paper:

TR21-150 | 7th November 2021 21:08

#### Extractors: Low Entropy Requirements Colliding With Non-Malleability

TR21-150
Authors: Eldon Chung, Maciej Obremski, Divesh Aggarwal
Publication: 7th November 2021 22:13
Keywords:

Abstract:

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 $\frac 1 2$, 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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