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Electronic Colloquium on Computational Complexity

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Reports tagged with correlation breakers:
TR16-114 | 30th July 2016
Gil Cohen

Two-Source Extractors for Quasi-Logarithmic Min-Entropy and Improved Privacy Amplification Protocols

Revisions: 1

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 >>>

TR21-075 | 4th June 2021
Eshan Chattopadhyay, Jesse Goodman, Jyun-Jie Liao

Affine Extractors for Almost Logarithmic Entropy

We give an explicit construction of an affine extractor (over $\mathbb{F}_2$) that works for affine sources on $n$ bits with min-entropy $k \ge~ \log n \cdot (\log \log n)^{1 + o(1)}$. This improves prior work of Li (FOCS'16) that requires min-entropy at least $\mathrm{poly}(\log n)$.

Our construction is ... more >>>

TR21-147 | 22nd October 2021
Eshan Chattopadhyay, Jyun-Jie Liao

Extractors for Sum of Two Sources

Revisions: 1

We consider the problem of extracting randomness from \textit{sumset sources}, a general class of weak sources introduced by Chattopadhyay and Li (STOC, 2016). An $(n,k,C)$-sumset source $\mathbf{X}$ is a distribution on $\{0,1\}^n$ of the form $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_C$, where $\mathbf{X}_i$'s are independent sources on $n$ bits ... more >>>

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