Paper 2018/461

Continuous-Source Fuzzy Extractors: Source uncertainty and security

Benjamin Fuller and Lowen Peng

Abstract

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 V that is impossible to secure. No fuzzy extractor designed for V extracts a meaningful key from an average element of V. This impossibility result is despite the fact that each element W in V 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.