Extractors: Low Entropy Requirements Colliding With Non-Malleability
This addresses a foundational problem in cryptography for secure key derivation and privacy amplification, offering significant improvements over prior constructions by reducing entropy needs while maintaining non-malleability.
The paper tackles the problem of constructing non-malleable two-source extractors with low entropy requirements, introducing a new notion of collision resistant extractors to achieve a strong two-source non-malleable extractor where one source has 0.8 entropy rate and the other has polylogarithmic min-entropy, and applying it to obtain an optimal output rate of 1/2 and near-optimal privacy amplification against memory tampering.
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.