Related papers: An explicit two-source extractor with min-entropy …
We continue the study of constructing explicit extractors for independent general weak random sources. The ultimate goal is to give a construction that matches what is given by the probabilistic method --- an extractor for two independent…
In a recent breakthrough \cite{CZ15}, Chattopadhyay and Zuckerman gave an explicit two-source extractor for min-entropy $k \geq \log^C n$ for some large enough constant $C$. However, their extractor only outputs one bit. In this paper, we…
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…
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…
We explicitly construct the first nontrivial extractors for degree $d \ge 2$ polynomial sources over $\mathbb{F}_2^n$. Our extractor requires min-entropy $k\geq n - \tilde{\Omega}(\sqrt{\log n})$. Previously, no constructions were known,…
Randomness extractors are algorithms that distill weak random sources into near-perfect random numbers. Two-source extractors enable this distillation process by combining two independent weak random sources. Raz's extractor (STOC '05) was…
We study the problem of extracting random bits from weak sources that are sampled by algorithms with limited memory. This model of small-space sources was introduced by Kamp, Rao, Vadhan and Zuckerman (STOC'06), and falls into a line of…
Non-malleable extractors are generalizations and strengthening of standard randomness extractors, that are resilient to adversarial tampering. Such extractors have wide applications in cryptography and explicit construction of extractors.…
We propose a new model of a weakly random source that admits randomness extraction. Our model of additive sources includes such natural sources as uniform distributions on arithmetic progressions (APs), generalized arithmetic progressions…
A long line of work in the past two decades or so established close connections between several different pseudorandom objects and applications. These connections essentially show that an asymptotically optimal construction of one central…
A random variable $X$ is an $(n,k)$-zero-fixing source if for some subset $V\subseteq[n]$, $X$ is the uniform distribution on the strings $\{0,1\}^n$ that are zero on every coordinate outside of $V$. An $\epsilon$-extractor for…
Constructing explicit RIP matrices is an open problem in compressed sensing theory. In particular, it is quite challenging to construct explicit RIP matrices that break the square-root bottleneck. On the other hand, providing explicit…
We identify a new notion of pseudorandomness for randomness sources, which we call the average bias. Given a distribution $Z$ over $\{0,1\}^n$, its average bias is: $b_{\text{av}}(Z) =2^{-n} \sum_{c \in \{0,1\}^n} |\mathbb{E}_{z \sim…
Dodis and Wichs introduced the notion of a non-malleable extractor to study the problem of privacy amplification with an active adversary. A non-malleable extractor is a much stronger version of a strong extractor. Previously, there are…
We continue a line of work on extracting random bits from weak sources that are generated by simple processes. We focus on the model of locally samplable sources, where each bit in the source depends on a small number of (hidden) uniformly…
The following is a near complete set of notes of Bourgain's 1988 paper "Almost Sure Convergence and Bounded Entropy." Both entropy results are treated, as is one application. The proofs here are essentially those of Bourgain's.
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 $\epsilon$…
We provide a unified method for constructing explicit distributions which are difficult for restricted models of computation to generate. Our constructions are based on a new notion of robust extractors, which are extractors that remain…
One of the earliest models of weak randomness is the Chor-Goldreich (CG) source. A $(t,n,k)$-CG source is a sequence of random variables $X=(X_1,\dots,X_t)\sim(\{0,1\}^n)^t$, where each $X_i$ has min-entropy $k$ conditioned on any fixing of…
We construct explicit deterministic extractors for polynomial images of varieties, that is, distributions sampled by applying a low-degree polynomial map $f : \mathbb{F}_q^r \to \mathbb{F}_q^n$ to an element sampled uniformly at random from…