Related papers: Quantum-proof multi-source randomness extractors i…
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…
We study the problem of constructing multi-source extractors in the quantum setting, which extract almost uniform random bits against quantum side information collected from several initially independent classical random sources. This is a…
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…
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…
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 the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
Two-source extractors aim to extract randomness from two independent sources of weak randomness. It has been shown that any two-source extractor which is secure against classical side information remains secure against quantum side…
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…
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…
Randomness extraction is of fundamental importance for information-theoretic cryptography. It allows to transform a raw key about which an attacker has some limited knowledge into a fully secure random key, on which the attacker has…
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…
Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose…
The generation of random numbers via quantum processes is an efficient and reliable method to obtain true indeterministic random numbers that are of vital importance to cryptographic communication and large-scale computer modeling. However,…
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts---a randomness source and its readout. The source is…
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…
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…
Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of…
Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a…
How much cryptographically-secure randomness can be extracted from a quantum state? This fundamental question probes the absolute limits of quantum random number generation (QRNG) and yet, despite the technological maturity of QRNGs, it…