Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Deterministic Extractors for Affine Sources over Large Fields
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Deterministic extractors for small-space sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
Computational Complexity
A 2-Source Almost-Extractor for Linear Entropy
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Extracting Computational Entropy and Learning Noisy Linear Functions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Deterministic extractors for independent-symbol sources
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Our data, ourselves: privacy via distributed noise generation
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Generalized strong extractors and deterministic privacy amplification
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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An (n, k)-bit-fixing source is a distribution X over {0, 1}n such that there is a subset of k variables in X1, . . .,Xn which are uniformly distributed and independent of each other, and the remaining n - k variables are fixed. A deterministic bit-fixing source extractor is a function E : {0, 1}^n . {0, 1}^m which on an arbitrary (n, k)-bit-fixing source outputs m bits that are statistically-close to uniform. Recently, Kamp and Zuckerman [13] gave a construction of deterministic bit-fixing source extractor that extracts 驴(k虏/n) bits, and requires k \sqrt n. In this paper we give constructions of deterministic bit-fixing source extractors that extract (1 - o(1))k bits whenever k (log n)^c for some universal constant c 0. Thus, our constructions extract almost all the randomness from bit-fixing sources and work even when k is small. For k 驴 \sqrt n the extracted bits have statistical distance 2^{ - n^{\Omega (1)} } from uniform, and for k 驴 \sqrt n the extracted bits have statistical distance k^{ - \Omega (1)} from uniform. Our technique gives a general method to transform deterministic bit-fixing source extractors that extract few bits into extractors which extract almost all the bits.