Reusable Fuzzy Extractors for Low-Entropy Distributions
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Author(s)
Canetti, Ran
Fuller, Benjamin
Paneth, Omer
Reyzin, Leonid
Smith, Adam
Date Issued
November 2020
Journal
Journal of Cryptology
Publisher
Springer Science and Business Media LLC
Citation
Canetti, Ran et al. "Reusable Fuzzy Extractors for Low-Entropy Distributions." Journal of Cryptology 34, 1 (November 2020): 2 © 2020 International Association for Cryptologic Research
Version
Author's final manuscript
Abstract
Fuzzy extractors (Dodis et al., in Advances in cryptology—EUROCRYPT 2014, Springer, Berlin, 2014, pp 93–110) convert repeated noisy readings of a secret into the same uniformly distributed key. To eliminate noise, they require an initial enrollment phase that takes the first noisy reading of the secret and produces a nonsecret helper string to be used in subsequent readings. Reusable fuzzy extractors (Boyen, in Proceedings of the 11th ACM conference on computer and communications security, CCS, ACM, New York, 2004, pp 82–91) remain secure even when this initial enrollment phase is repeated multiple times with noisy versions of the same secret, producing multiple helper strings (for example, when a single person’s biometric is enrolled with multiple unrelated organizations). We construct the first reusable fuzzy extractor that makes no assumptions about how multiple readings of the source are correlated. The extractor works for binary strings with Hamming noise; it achieves computational security under the existence of digital lockers (Canetti and Dakdouk, in Advances in cryptology—EUROCRYPT 2008, Springer, Berlin, 2008, pp 489–508). It is simple and tolerates near-linear error rates. Our reusable extractor is secure for source distributions of linear min-entropy rate. The construction is also secure for sources with much lower entropy rates—lower than those supported by prior (nonreusable) constructions—assuming that the distribution has some additional structure, namely, that random subsequences of the source have sufficient minentropy. Structure beyond entropy is necessary to support distributions with low entropy rates. We then explore further how different structural properties of a noisy source can be used to construct fuzzy extractors when the error rates are high, building a computationally secure and an information-theoretically secure construction for large-alphabet sources.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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DOI of Published Version
https://doi.org/10.1007/s00145-020-09367-8
