Randomness extractors and error correcting codes are fundamental objects in computer science. Recently, there have been several natural generalizations of these objects, in the context and study of tamper resilient cryptography. These are \emph{seeded non-malleable extractors}, introduced by Dodis and Wichs \cite{DW09}; \emph{seedless non-malleable extractors}, introduced by Cheraghchi and Guruswami ... more >>>

A non-malleable extractor is a seeded extractor with a very strong guarantee - the output of a non-malleable extractor obtained using a typical seed is close to uniform even conditioned on the output obtained using any other seed. The first contribution of this paper consists of two new and improved ... more >>>

We construct non-malleable extractors with seed length $d = O(\log{n}+\log^{3}(1/\epsilon))$ for $n$-bit sources with min-entropy $k = \Omega(d)$, where $\epsilon$ is the error guarantee. In particular, the seed length is logarithmic in $n$ for $\epsilon> 2^{-(\log{n})^{1/3}}$. This improves upon existing constructions that either require super-logarithmic seed length even for constant ... 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 >>>

In this paper we give improved constructions of several central objects in the literature of randomness extraction and tamper-resilient cryptography. Our main results are:

(1) An explicit seeded non-malleable extractor with error $\epsilon$ and seed length $d=O(\log n)+O(\log(1/\epsilon)\log \log (1/\epsilon))$, that supports min-entropy $k=\Omega(d)$ and outputs $\Omega(k)$ bits. Combined with ... 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 >>>