Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Journal of Computer and System Sciences
Perfect information leader election in log * n+0(1) rounds
Journal of Computer and System Sciences
Privacy Amplification Secure Against Active Adversaries
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Noncryptographic Selection Protocols
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors for a constant number of polynomially small min-entropy independent sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
SIAM Journal on Computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Non-malleable extractors and symmetric key cryptography from weak secrets
Proceedings of the forty-first annual ACM symposium on Theory of computing
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
2-Source Extractors under Computational Assumptions and Cryptography with Defective Randomness
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Improved Constructions of Three Source Extractors
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Privacy Amplification and Non-malleable Extractors via Character Sums
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Distributed computing with imperfect randomness
DISC'05 Proceedings of the 19th international conference on Distributed Computing
Design extractors, non-malleable condensers and privacy amplification
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Non-malleable Extractors with Short Seeds and Applications to Privacy Amplification
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
Non-malleable Extractors, Two-Source Extractors and Privacy Amplification
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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We study the problem of constructing explicit extractors for independent general weak random sources. For weak sources on n bits with min-entropy k, perviously the best known extractor needs to use at least log n/log k independent sources [22, 3]. In this paper we give a new extractor that only uses O(log(log n/log k))+O(1) independent sources. Thus, our result improves the previous best result exponentially. We then use our new extractor to give improved network extractor protocols, as defined in [14]. The network extractor protocols also give new results in distributed computing with general weak random sources, which dramatically improve previous results. For example, we can tolerate a nearly optimal fraction of faulty players in synchronous Byzantine agreement and leader election, even if the players only have access to independent n-bit weak random sources with min-entropy as small as k=polylog(n). Our extractor for independent sources is based on a new condenser for somewhere random sources with a special structure. We believe our techniques are interesting in their own right and are promising for further improvement.