Extractors: Low Entropy Requirements Colliding With Non-Malleability

TL;DR

This paper introduces a new class of collision resistant extractors that enable the construction of non-malleable extractors with lower entropy requirements, achieving optimal output rate and enhanced security against tampering.

Contribution

The paper presents a novel notion of collision resistant extractors and leverages it to develop a strong two-source non-malleable extractor with reduced entropy requirements.

Findings

Achieved a non-malleable extractor with one source at 0.8 entropy rate and polylogarithmic min-entropy in the other.

Constructed a non-malleable extractor with an optimal output rate of 1/2.

Extended the extractor to improve privacy amplification security against memory tampering.

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.