digital lockers

Reusable Fuzzy Extractors for Low-Entropy Distributions

Ran Canetti, Benjamin Fuller, Omer Paneth, Leonid Reyzin, and Adam Smith.  Reusable Fuzzy Extractors for Low-Entropy Distributions. Eurocrypt 2016.

Previous titles were “Reusable Fuzzy Extractors via Digital Lockers” and “Key Derivation From Noisy Sources With More Errors Than Entropy.”


Fuzzy extractors (Dodis et al., Eurocrypt 2004) 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, CCS 2004) 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 only prior construction assumed a very specific, unrealistic class of correlations). The extractor works for binary strings with Hamming noise; it achieves computational security under assumptions on the security of hash functions or in the random oracle model. It is simple and efficient 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. We show that such structural assumptions are necessary to support 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, providing a computationally secure and an information-theoretically secure construction for large-alphabet sources.

Strong Key Derivation from Noisy Sources

My Ph.D. has been completed and defended.  It is titled Strong Key Derivation from Noisy Sources.  It is largely drawn from three papers Computational Fuzzy ExtractorsReusable Fuzzy Extractors for Low-Entropy Distributions, and When are Fuzzy Extractors Possible?  Those papers are more up-to-date than my Ph.D.  My Ph.D does contain a cohesive summary of the results that can be useful as an introduction.