Privacy amplification by public discussion
SIAM Journal on Computing - Special issue on cryptography
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Tiny families of functions with random properties: a quality-size trade-off for hashing
Proceedings of the workshop on Randomized algorithms and computation
Dense quantum coding and a lower bound for 1-way quantum automata
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computing with Very Weak Random Sources
SIAM Journal on Computing
Bounds for Dispersers, Extractors, and Depth-Two Superconcentrators
SIAM Journal on Discrete Mathematics
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Correcting errors without leaking partial information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Kakeya Sets, New Mergers and Old Extractors
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Generalized privacy amplification
IEEE Transactions on Information Theory - Part 2
On the power of quantum memory
IEEE Transactions on Information Theory
The Bounded-Storage Model in the Presence of a Quantum Adversary
IEEE Transactions on Information Theory
Near-optimal extractors against quantum storage
Proceedings of the forty-second ACM symposium on Theory of computing
Two-source extractors secure against quantum adversaries
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Quantum-resilient randomness extraction
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
Certifiable quantum dice: or, true random number generation secure against quantum adversaries
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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In the classical privacy amplification problem Alice and Bob share information that is only partially secret towards an eavesdropper Charlie. Their goal is to distill this information to a shorter string that is completely secret. The classical privacy amplification problem can be solved almost optimally using extractors. An interesting variant of the problem, where the eavesdropper Charlie is allowed to keep quantum information rather than just classical information, was introduced by Konig, Maurer and Renner. In this setting, the eavesdropper Charlie may entangle himself with the input (without changing it) and the only limitation Charlie has is that it may keep at most b qubits of storage. A natural question is whether there are classical extractors that are good even against quantum storage. Recent work has shown that some classical extractors miserably fail against quantum storage. At the same time, it was shown that some other classical extractors work well even against quantum storage, but all these extractors had a large seed length that was either as large as the extractor output, or as large as the quantum storage available to the eavesdropper. In this paper we show that a modified version of Trevisan's extractor is good even against quantum storage, thereby giving the first such construction with logarithmic seed length. The technique we use is a combination of Trevisan's approach of constructing an extractor from a black-box pseudorandom generator, together with locally list-decodable codes and previous work done on quantum random access codes.