Continuous-Source Fuzzy Extractors: Source Uncertainty And Insecurity
2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)(2019)
摘要
Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy source into the same uniformly distributed key. The functionality of a fuzzy extractor outputs the key when provided with a value close to the original reading of the source. A necessary condition for security, called fuzzy min-entropy, is that the probability of every ball of values of the noisy source is small.Many noisy sources are best modeled using continuous metric spaces. To build continuous-source fuzzy extractors, prior work assumes that the system designer has a good model of the distribution (Verbitskiy et al., IEEE TIFS 2010). However, it is impossible to build an accurate model of a high entropy distribution just by sampling from the distribution.Model inaccuracy may be a serious problem. We demonstrate a family of continuous distributions W that is impossible to secure. No fuzzy extractor designed for W extracts a meaningful key from an average element of W. This impossibility result is despite the fact that each element W is an element of W has high fuzzy min-entropy. We show a qualitatively stronger negative result for secure sketches, which are used to construct most fuzzy extractors.Our results are for the Euclidean metric and are information-theoretic in nature. To the best of our knowledge all continuous-source fuzzy extractors argue information-theoretic security.Fuller, Reyzin, and Smith showed comparable negative results for a discrete metric space equipped with the Hamming metric (Asiacrypt 2016). Continuous Euclidean space necessitates new techniques.
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关键词
continuous-source fuzzy extractors,high entropy distribution,high fuzzy min-entropy,source uncertainty,uniformly distributed key,noisy source,continuous distributions,Euclidean metric,information-theoretic,discrete metric space
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