On the Possibilities and Limitations of Computational Fuzzy Extractors

We present positive and negative results of fuzzy extractors with computational security. As a negative result, we show that, under a certain computational condition, the existence of a computational fuzzy extractor implies the existence of an information-theoretic fuzzy extractor with slightly weaker parameters. The condition is that the generation procedure of the fuzzy extractor is efficiently invertible by an injective function. Our result implies that to circumvent the limitations of information-theoretic fuzzy extractors, we need to employ computational fuzzy extractors without efficient invertibility with injective functions. As positive results, we present constructions of computational fuzzy extractors based on a leakage-resilient key encapsulation mechanism and a strong decisional Diffie-Hellman assumption.