Related papers: Two-Source and Affine Non-Malleable Extractors for…
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 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…
In 2005 Bourgain gave the first explicit construction of a two-source extractor family with min-entropy rate less than $1/2$. His approach combined Fourier analysis with innovative but inefficient tools from arithmetic combinatorics and…
We construct efficient, unconditional non-malleable codes that are secure against tampering functions computed by small-depth circuits. For constant-depth circuits of polynomial size (i.e. $\mathsf{AC^0}$ tampering functions), our codes…
We initiate the study of multi-source extractors in the quantum world. In this setting, our goal is to extract random bits from two independent weak random sources, on which two quantum adversaries store a bounded amount of information. Our…
How to generate provably true randomness with minimal assumptions? This question is important not only for the efficiency and the security of information processing, but also for understanding how extremely unpredictable events are possible…
Non-malleable coding, introduced by Dziembowski, Pietrzak and Wichs (ICS 2010), aims for protecting the integrity of information against tampering attacks in situations where error-detection is impossible. Intuitively, information encoded…
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…
We introduce a framework for obtaining tight mixing times for Markov chains based on what we call restricted modified log-Sobolev inequalities. Modified log-Sobolev inequalities (MLSI) quantify the rate of relative entropy contraction for…
Non-malleable codes were introduced by Dziembowski, Pietrzak, and Wichs (JACM 2018) as a generalization of standard error correcting codes to handle severe forms of tampering on codewords. This notion has attracted a lot of recent research,…
We study the tasks of deterministically condensing and extracting from Online Non-Oblivious Symbol Fixing (oNOSF) sources, a natural model of defective randomness where extraction is impossible in many parameter regimes [AORSV,…
Seeded extractors are fundamental objects in pseudorandomness and cryptography, and a deep line of work has designed polynomial-time seeded extractors with nearly-optimal parameters. However, existing constructions of seeded extractors with…
Multi-source-extractors are functions that extract uniform randomness from multiple (weak) sources of randomness. Quantum multi-source-extractors were considered by Kasher and Kempe (for the quantum-independent-adversary and the…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Non-malleable secret sharing was recently proposed by Goyal and Kumar in independent tampering and joint tampering models for threshold secret sharing (STOC18) and secret sharing with general access structure (CRYPTO18). The idea of making…
An extractor is a function E that is used to extract randomness. Given an imperfect random source X and a uniform seed Y, the output E(X,Y) is close to uniform. We study properties of such functions in the presence of prior quantum…
We study deterministic extractors for oblivious bit-fixing sources (a.k.a. resilient functions) and exposure-resilient functions with small min-entropy: of the function's n input bits, k << n bits are uniformly random and unknown to the…
Fuzzy extractors (FE) are cryptographic primitives that extract reliable cryptographic key from noisy real world random sources such as biometric sources. The FE generation algorithm takes a source sample, extracts a key and generates some…
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…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…