Journal of Computer and System Sciences
Journal of Computer and System Sciences
Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
Computing with Very Weak Random Sources
SIAM Journal on Computing
List decoding algorithms for certain concatenated codes
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Privacy Amplification Secure Against Active Adversaries
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Extractors: optimal up to constant factors
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
SIAM Journal on Computing
Kakeya Sets, New Mergers and Old Extractors
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Key Agreement from Close Secrets over Unsecured Channels
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
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)
Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Privacy amplification with asymptotically optimal entropy loss
Proceedings of the forty-second ACM symposium on Theory of computing
Privacy Amplification and Non-malleable Extractors via Character Sums
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Robust fuzzy extractors and authenticated key agreement from close secrets
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Non-malleable Extractors with Short Seeds and Applications to Privacy Amplification
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
New independent source extractors with exponential improvement
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We introduce a new combinatorial object, called a design extractor, that has both the properties of a design and an extractor. We give efficient constructions of such objects and show that they can be used in several applications. Improving the output length of known non-malleable extractors. Non-malleable extractors were introduced in [DW09] to study the problem of privacy amplification with an active adversary. Currently, only two explicit constructions are known [DLWZ11, CRS11]. Both constructions work for n bit sources with min-entropy k n/2. However, in both constructions the output length is smaller than the seed length, while the probabilistic method shows that to achieve error e, one can use O(log n+log (1/e)) bits to extract up to k/2 output bits. In this paper, we use our design extractor to give an explicit non-malleable extractor for min-entropy k n/2, that has seed length O(log n+log (1/e)) and output length Ω(k). Non-malleable condensers. We introduce and define the notion of a non-malleable condenser. A non-malleable condenser is a generalization and relaxation of a non-malleable extractor. We show that similar as extractors and condensers, non-malleable condensers can be used to construct non-malleable extractors. We then show that our design extractor already gives a non-malleable condenser for min-entropy k n/2, with error e and seed length O(log (1/e)). A new optimal protocol for privacy amplification. More surprisingly, we show that non-malleable condensers themselves give optimal privacy amplification protocols with an active adversary. In fact, the non-malleable condensers used in these protocols are much weaker compared to non-malleable extractors, in the sense that the entropy rate of the condenser's output does not need to increase at all. This suggests that one promising next step to achieve better privacy amplification protocols may be to construct non-malleable condensers for smaller min-entropy. As a by-product, we also obtain a new explicit 2-round privacy amplification protocol with optimal entropy loss and optimal communication complexity for min-entropy kn/2, without using non-malleable extractors.