Robustly reusable fuzzy extractor with imperfect randomness

Fuzzy extractor (FE) extracts and reproduces a uniform string from a fuzzy source. Robustly reusable fuzzy extractor (rrFE) considers reusability and robustness simultaneously. Reusability of rrFE allows multiple extractions of pseudorandom strings from the same source and robustness detects active attacks. To achieve reusability and robustness, the existing constructions of rrFE make heavy use of perfect random coins (which are uniformly distributed and independent of each other), besides the fuzzy source. However, efficiently sampling unbiased random bits only exists in the ideal world. In this paper, we show how to construct rrFE resorting to imperfect randomness (non-uniform but of high entropy), which is easy to sample in practice. We propose two generic constructions of rrFE in the CRS model, with one construction dealing with perfect randomness and the other dealing with imperfect randomness. We also present two instantiations of rrFE from the DDH and LPN assumptions working with perfect randomness, and another two instantiations of rrFE from DDH and LPN working with imperfect randomness. All instantiations support linear fraction of errors between samples of the fuzzy source. Our DDH-based rrFE (both rrFE with perfect randomness and rrFE with imperfect randomness) are the first tightly secure rrFEs in the standard model, i.e., the reusability and robustness are tightly reduced to the DDH assumption. Compared with the DDH-based rrFE scheme in PKC2019 by Wen et al., our rrFE enjoys tighter security, better efficiency, and support of usage of imperfect randomness. Our LPN-based rrFE (both rrFE with perfect randomness and rrFE with imperfect randomness) are the first rrFEs from the LPN assumption in the standard model.