On the Limitations of Computational Fuzzy Extractors

We present a negative result of fuzzy extractors with computational security. Specifically, 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 that are not invertible by injective functions.