Explicit two-source extractors and resilient functions

  title={Explicit two-source extractors and resilient
  author={Chattopadhyay and Zuckerman},
  journal={Annals of Mathematics},
An explicit two-source extractor with min-entropy rate near 4/9
An improved analysis of one of Bourgain's extractors is given which shows that it in fact extracts from sources with min-entropy rate near $\frac{21}{44} =.477\ldots', and a variant of this extractor is constructed which is shown to have the advantage of exponential small error which is important in some applications.
Constructions in Ramsey theory
A superexponential lower bound is proved for the classical 4-uniform Ramsey number r_4(5,n) and an upper bound for the hypergraph Erd\H os-Rogers function f^k_{k+1, k+2}(N) is proved that is an iterated $(k-13)$-fold logarithm in $N$.
Efficient Distributed Coin-tossing Protocols
This model considers an adversary who monitors the protocol's communication and intervenes at most once by restarting the processor who just broadcast her message, and proves the existence of coin-tossing protocols that achieve the same tolerance as the threshold protocols using a smaller number of processors.
Extractors: Low Entropy Requirements Colliding With Non-Malleability
A new notion of collision resistant extractors is introduced and in using it a strong two source non-malleable extractor is obtained and one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal.
Privacy Amplification with Tamperable Memory via Non-malleable Two-source Extractors
The classical problem of privacy amplification is extended to a setting where the active adversary is also allowed to fully corrupt the internal memory of one of the honest parties, Alice and Bob, before the execution of the protocol, thereby resolving a long-standing open question.
Private Weakly-Random Sequences from Human Heart Rate for Quantum Amplification
It is found that the heart can be treated as a good enough, and private by its nature, source of randomness that every human possesses and can be used as input to quantum device-independent randomness amplification protocols.
Communication for Generating Correlation: A Unifying Survey
Progress-to-date on manipulating correlated random variables in a distributed setting is described and pertinent measures, achievability results, limits of performance, and point to new directions are laid out.
Explicit Designs and Extractors
This work gives significantly improved explicit constructions of three related pseudorandom objects and establishes a new, simple framework for extracting from adversarial sources of locality $0 as well as improving low-error extractors for these sources.
Guest Column
Randomness is a valuable resource in computation and Monte Carlo simulations of complex systems such as the stock market or weather prediction systems, and Cryptography is another area that crucially relies on access to random bits.
Large cliques and independent sets all over the place
The (probabilistic) construction gives rise to new examples of Ramsey graphs, which while having no very large homogenous subsets contain both cliques and independent sets of size $\log n$ in any small subset of vertices, very far from being true in random graphs.