When are Fuzzy Extractors Possible?

Benjamin Fuller; Leonid Reyzin; Adam Smith

Paper 2014/961

When are Fuzzy Extractors Possible?

Benjamin Fuller, Leonid Reyzin, and Adam Smith

Abstract

Fuzzy extractors (Dodis et al., SIAM J. Computing 2008) convert repeated noisy readings of a high-entropy secret into the same uniformly distributed key. A minimum condition for the security of the key is the hardness of guessing a value that is similar to the secret, because the fuzzy extractor converts such a guess to the key. We codify this quantify this property in a new notion called fuzzy min-entropy. We ask: is fuzzy min-entropy sufficient to build fuzzy extractors? We provide two answers for different settings. 1) If the algorithms have precise knowledge of the probability distribution $W$ that defines the noisy source is a sufficient condition for information-theoretic key extraction from $W$. 2) A more ambitious goal is to design a single extractor that works for all possible sources. This more ambitious goal is impossible: there is a family of sources with high fuzzy min-entropy for which no single fuzzy extractor is secure. This is true in three settings: a) for standard fuzzy extractors, b) for fuzzy extractors that are allowed to sometimes be wrong, c) and for secure sketches, which are the main ingredient of most fuzzy extractor constructions.

Note: This work is now appearing in IEEE Transactions on Information Theory 2020 and a conference version appeared Asiacrypt 2016. This version contains all proofs and technical details.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Minor revision. 2020 IEEE Transactions on Information Theory. Conference Version is in 2016 Asiacrypt.
DOI: 10.1109/TIT.2020.2984751
Keywords: Fuzzy extractors secure sketches information theory biometric authentication error-tolerance key derivation error-correcting codes
Contact author(s): benjamin fuller @ uconn edu
History: 2020-08-26: last of 8 revisions; 2014-11-25: received; See all versions
Short URL: https://ia.cr/2014/961
License: CC BY

BibTeX

@misc{cryptoeprint:2014/961,
      author = {Benjamin Fuller and Leonid Reyzin and Adam Smith},
      title = {When are Fuzzy Extractors Possible?},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/961},
      year = {2014},
      doi = {10.1109/TIT.2020.2984751},
      url = {https://eprint.iacr.org/2014/961}
}