Pseudoentropic Isometries

Abstract

Fuzzy extractors (Dodiset al., Eurocrypt 2004) turn a noisy secret into a stable, uniformly distributed key. Reusable fuzzy extractors remain secure when multiple keys are produced from a single noisy secret (Boyen, CCS 2004). Boyen showed information-theoretically secure reusable fuzzy extractors are subject to strong limitations. Simoens et al. (IEEE S&P, 2009) then showed deployed constructions suffer severe security breaks when reused. Canetti et al. (Eurocrypt 2016) used computational security to sidestep this problem, building a computationally secure reusable fuzzy extractor that corrects a sublinear fraction of errors. We introduce a generic approach to constructing reusable fuzzy extractors. We define a new primitive called a reusable pseudoentropic isometry that projects an input metric space to an output metric space. This projection preserves distance and entropy even if the same input is mapped to multiple output metric spaces. A reusable pseudoentropy isometry yields a reusable fuzzy extractor by 1) randomizing the noisy secret using the isometry and 2) applying a traditional fuzzy extractor to derive a secret key. We propose reusable pseudoentropic isometries for the set difference and Hamming metrics. The set difference construction is built from composable digital lockers (Canetti and Dakdouk, Eurocrypt 2008). For the Hamming metric, we show that the second construction of Canetti et al.(Eurocrypt 2016) can be seen as an instantiation of our framework. In both cases, the pseudoentropic isometry's reusability requires noisy secrets distributions to have entropy in each symbol of the alphabet. Our constructions yield the first reusable fuzzy extractors that correct a constant fraction of errors. We also implement our set difference solution and describe two use cases.