Computational fuzzy extractor from LWE

Abstract

Fuzzy extractors are able to derive uniform and stable strings from noisy sources. Traditional fuzzy extractors are defined as information-theoretical primitive. Unfortunately, the components of information-theoretical fuzzy extractors consume the entropy of the sources, which results in extracted strings being too short to be applied in practice. Fuller et al. introduced the notion of Computational Fuzzy Extractor (CFE) and proposed a CFE scheme, which extracts nearly all entropy from the sources, based on the Learning with Errors (LWE) assumption. However, their construction applies to a limited type of sources and only supports sub-linear error correctness rate. In this paper, we propose a generic construction of CFE from Computationally Private Secure Sketch (CPSS) and Lossy Computational Extractor (LCExt). By instantiating CPSS and LCExt based on the LWE assumption, we obtain specific CFE schemes from LWE. Compared with the CFE scheme by Fuller et al., our CFE scheme not only extracts almost all entropy from the source, but also supports linear error correctness rate, as long as the source has enough entropy.