Computational fuzzy extractors

Abstract

Fuzzy extractors derive strong keys from noisy sources. Their security is usually defined informationtheoretically, 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 are subject to upper bounds from coding theory even when the information-theoretic security requirement is relaxed. Specifically, we define computational secure sketches using conditional HILL pseudoentropy (Håstad et al., SIAM J. Computing 1999). We show that a computational secure sketch implies an error-correcting code. Thus, HILL pseudoentropy is bounded by the size of the best error-correcting code. Similar bounds apply to information-theoretic secure sketches.

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