We make progress in the following three problems: 1. Constructing optimal seeded non-malleable extractors; 2. Constructing optimal privacy amplification protocols with an active adversary, for any possible security parameter; 3. Constructing extractors for independent weak random sources, when the min-entropy is extremely small (i.e., near logarithmic).

For the first ... more >>>

A typical obstacle one faces when constructing pseudorandom objects is undesired correlations between random variables. Identifying this obstacle and constructing certain types of "correlation breakers" was central for recent exciting advances in the construction of multi-source and non-malleable extractors. One instantiation of correlation breakers is correlation breakers with advice. These ... more >>>

This paper offers the following contributions:

* We construct a two-source extractor for quasi-logarithmic min-entropy. That is, an extractor for two independent $n$-bit sources with min-entropy $\widetilde{O}(\log{n})$. Our construction is optimal up to $\mathrm{poly}(\log\log{n})$ factors and improves upon a recent result by Ben-Aroya, Doron, and Ta-Shma (ECCC'16) that can handle ... more >>>

A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications, including seeded or seedless non-malleable extractors, two source extractors, (bipartite) Ramsey graphs, privacy amplification protocols with an active adversary, non-malleable codes and many more. These connections essentially show ... more >>>