Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data

TLDR

Biometric data and other noisy sources are not reproducible precisely and are not uniformly distributed, limiting their use as cryptographic keys. The paper defines and provides efficient secure techniques for converting noisy information into usable cryptographic keys, particularly for biometric authentication. The authors introduce two formally secure primitives—a fuzzy extractor that reliably extracts uniform randomness from noisy input and a secure sketch that enables exact recovery without revealing the input—and present nearly optimal constructions for various distance metrics. These primitives allow the extracted randomness to serve as a cryptographic key and enable secure, error‑tolerant biometric authentication without exposing sensitive data.

Abstract

We provide formal definitions and efficient secure techniques for turning noisy information into keys usable for any cryptographic application, and, in particular, reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is error-tolerant in the sense that R will be the same even if the input changes, as long as it remains reasonably close to the original. Thus, R can be used as a key in a cryptographic application. A secure sketch produces public information about its input w that does not reveal w and yet allows exact recovery of w given another value that is close to w. Thus, it can be used to reliably reproduce error-prone biometric inputs without incurring the security risk inherent in storing them. We define the primitives to be both formally secure and versatile, generalizing much prior work. In addition, we provide nearly optimal constructions of both primitives for various measures of “closeness” of input data, such as Hamming distance, edit distance, and set difference.