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 21, 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