Gil Cohen

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 >>>

Avraham Ben-Aroya, Eshan Chattopadhyay, Dean Doron, Xin Li, Amnon Ta-Shma

We show a reduction from the existence of explicit t-non-malleable

extractors with a small seed length, to the construction of explicit

two-source extractors with small error for sources with arbitrarily

small constant rate. Previously, such a reduction was known either

when one source had entropy rate above half [Raz05] or ...
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Tom Gur, Igor Shinkar

A (k,\eps)-non-malleable extractor is a function nmExt : {0,1}^n x {0,1}^d -> {0,1} that takes two inputs, a weak source X~{0,1}^n of min-entropy k and an independent uniform seed s in {0,1}^d, and outputs a bit nmExt(X, s) that is \eps-close to uniform, even given the seed s and the ... more >>>

Eshan Chattopadhyay, Jesse Goodman, Vipul Goyal, Xin Li

Randomness extraction is a fundamental problem that has been studied for over three decades. A well-studied setting assumes that one has access to multiple independent weak random sources, each with some entropy. However, this assumption is often unrealistic in practice. In real life, natural sources of randomness can produce samples ... more >>>

Oded Goldreich, Avi Wigderson

A graph $G$ is called {\em self-ordered}\/ (a.k.a asymmetric) if the identity permutation is its only automorphism.

Equivalently, there is a unique isomorphism from $G$ to any graph that is isomorphic to $G$.

We say that $G=(V,E)$ is {\em robustly self-ordered}\/ if the size of the symmetric difference ...
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Divesh Aggarwal, Bhavana Kanukurthi, SaiLakshmiBhavana Obbattu, Maciej Obremski, Sruthi Sekar

At ITCS 2010, Dziembowski, Pietrzak, and Wichs introduced Non-malleable Codes (NMCs). Non-malleability is one of the strongest and most challenging notions of security considered in cryptography and protects against tampering attacks. In the context of coding schemes, non-malleability requires that it be infeasible to tamper the codeword of a message ... more >>>

Eldon Chung, Maciej Obremski, Divesh Aggarwal

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 ...
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