Paper 2014/605

On the Possibilities and Limitations of Computational Fuzzy Extractors

Kenji Yasunaga and Kosuke Yuzawa

Abstract

Fuller et~al. (Asiacrypt 2013) studied on computational fuzzy extractors, and showed, as a negative result, that the existence of a computational ``secure sketch'' implies the existence of an information-theoretically secure sketch with slightly weaker parameters. In this work, we show a similar negative result such that the existence of a computational fuzzy extractor satisfying a certain computational condition implies the existence of an information-theoretic fuzzy extractor with slightly weaker parameters. The condition is that the generation procedure of the fuzzy extractor can be efficiently invertible. This result implies that to circumvent the limitations of information-theoretic fuzzy extractors, we need to employ computational fuzzy extractors in which the generation procedure cannot be efficiently invertible. As positive results, we present a construction of computational fuzzy extractor based on a leakage-resilient key encapsulation mechanism and a construction based on a strong decisional Diffie-Hellman assumption.