Article

Generalized strong extractors and deterministic privacy amplification

Authors:

Ueli MaurerAuthors Info & Claims

IMA'05: Proceedings of the 10th international conference on Cryptography and Coding

Pages 322 - 339

https://doi.org/10.1007/11586821_22

Published: 19 December 2005 Publication History

Abstract

Extracting essentially uniform randomness from a somewhat random source X is a crucial operation in various applications, in particular in cryptography where an adversary usually possesses some partial information about X. In this paper we formalize and study the most general form of extracting randomness in such a cryptographic setting. Our notion of strong extractors captures in particular the case where the catalyst randomness is neither uniform nor independent of the actual extractor input. This is for example important for privacy amplification, where a uniform cryptographic key is generated by Alice and Bob sharing some partially secret information X by exchanging a catalyst R over an insecure channel accessible to an adversary Eve. Here the authentication information for R creates, from Eve's viewpoint, a dependence between X and R. We provide explicit constructions for this setting based on strong blenders. In addition, we give strong deterministic randomness extractors for lists of random variables, where only an unknown subset of the variables is required to have some amount of min-entropy.

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Cited By

Chattopadhyay EGoodman JGoyal VLi XMakarychev KMakarychev YTulsiani MKamath GChuzhoy J(2020)Extractors for adversarial sources via extremal hypergraphsProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3357713.3384339(1184-1197)Online publication date: 22-Jun-2020
https://dl.acm.org/doi/10.1145/3357713.3384339
Dodis YRistenpart TVadhan S(2012)Randomness condensers for efficiently samplable, seed-dependent sourcesProceedings of the 9th international conference on Theory of Cryptography10.1007/978-3-642-28914-9_35(618-635)Online publication date: 19-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28914-9_35
Shaltiel R(2011)An introduction to randomness extractorsProceedings of the 38th international conference on Automata, languages and programming - Volume Part II10.5555/2027223.2027226(21-41)Online publication date: 4-Jul-2011
https://dl.acm.org/doi/10.5555/2027223.2027226
Show More Cited By

Index Terms

Generalized strong extractors and deterministic privacy amplification
1. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image Guide Proceedings

IMA'05: Proceedings of the 10th international conference on Cryptography and Coding

December 2005

459 pages

ISBN:354030276X

Editor:
Nigel P. Smart
Dept. Computer Science, University of Bristol, Woodland Road, Bristol, United Kingdom

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 December 2005

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Cited By

Chattopadhyay EGoodman JGoyal VLi XMakarychev KMakarychev YTulsiani MKamath GChuzhoy J(2020)Extractors for adversarial sources via extremal hypergraphsProceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3357713.3384339(1184-1197)Online publication date: 22-Jun-2020
https://dl.acm.org/doi/10.1145/3357713.3384339
Dodis YRistenpart TVadhan S(2012)Randomness condensers for efficiently samplable, seed-dependent sourcesProceedings of the 9th international conference on Theory of Cryptography10.1007/978-3-642-28914-9_35(618-635)Online publication date: 19-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28914-9_35
Shaltiel R(2011)An introduction to randomness extractorsProceedings of the 38th international conference on Automata, languages and programming - Volume Part II10.5555/2027223.2027226(21-41)Online publication date: 4-Jul-2011
https://dl.acm.org/doi/10.5555/2027223.2027226
Lee CLu CTsai S(2010)Deterministic extractors for independent-symbol sourcesIEEE Transactions on Information Theory10.1109/TIT.2010.207901256:12(6501-6512)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1109/TIT.2010.2079012
Kamp JRao AVadhan SZuckerman DKleinberg J(2006)Deterministic extractors for small-space sourcesProceedings of the thirty-eighth annual ACM symposium on Theory of Computing10.1145/1132516.1132613(691-700)Online publication date: 21-May-2006
https://dl.acm.org/doi/10.1145/1132516.1132613
Lee CLu CTsai S(2006)Deterministic extractors for independent-symbol sourcesProceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I10.1007/11786986_9(84-95)Online publication date: 10-Jul-2006
https://dl.acm.org/doi/10.1007/11786986_9

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