Related papers: Quantum-Proof Extractors: Optimal up to Constant F…
We construct a strong extractor against quantum storage that works for every min-entropy $k$, has logarithmic seed length, and outputs $\Omega(k)$ bits, provided that the quantum adversary has at most $\beta k$ qubits of memory, for any…
Many constructions of randomness extractors are known to work in the presence of quantum side information, but there also exist extractors which do not [Gavinsky {\it et al.}, STOC'07]. Here we find that spectral extractors $\psi$ with a…
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Furthermore they are also a useful tool in quantum Shannon…
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 $\epsilon$…
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…
Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security…
A $(k,\varepsilon)$-non-malleable extractor is a function ${\sf nmExt} : \{0,1\}^n \times \{0,1\}^d \to \{0,1\}$ that takes two inputs, a weak source $X \sim \{0,1\}^n$ of min-entropy $k$ and an independent uniform seed $s \in \{0,1\}^d$,…
We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015]. 1) We construct the…
The recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in several seemingly different topics. These include seeded…
We make progress in the following three problems: 1. Constructing optimal seeded non-malleable extractors; 2. Constructing optimal privacy amplification protocols with an active adversary, for any security parameter; 3. Constructing…
Quantum-proof randomness extraction is essential for handling quantum side information possessed by a quantum adversary, which is widely applied in various quantum cryptography tasks. In this study, we introduce a real-time two-source…
The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness…
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 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,…
We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$.…
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…
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…
Consider a general quantum stochastic source that emits at discrete time steps quantum pure states which are chosen from a finite alphabet according to some probability distribution which may depend on the whole history. Also, fix two…
Randomness extraction involves the processing of purely classical information and is therefore usually studied in the framework of classical probability theory. However, such a classical treatment is generally too restrictive for…
Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…