Computational fuzzy extractors

Abstract

Fuzzy extractors derive strong keys from noisy sources. Their security is usually defined information-theoretically, with gaps between known negative results, existential constructions, and polynomial-time constructions. We ask whether using computational security can close these gaps. We show the following:•Negative result: Noise tolerance in fuzzy extractors is usually achieved using an information reconciliation component called a secure sketch. We show that secure sketches defined using pseudoentropy (Håstad et al., SIAM J. Comput. 1999) instead of information-theoretic security are still subject to upper bounds from coding theory.•Positive result: We show that our negative result can be avoided by constructing and analyzing a computational fuzzy extractor directly. We modify the code-offset construction (Juels and Wattenberg, CCS 1999) to use random linear codes. Security is based on the Learning with Errors problem and holds when the noisy source is uniform or symbol-fixing (that is, each dimension is either uniform or fixed).