Key Extraction From General Nondiscrete Signals

Abstract

We address the problem of designing optimal schemes for the generation of secure cryptographic keys from continuous noisy data. We argue that, contrary to the discrete case, a universal fuzzy extractor does not exist. This implies that in the continuous case, key extraction schemes have to be designed for particular probability distributions. We extend the known definitions of the correctness and security properties of fuzzy extractors. Our definitions apply to continuous as well as discrete variables. We propose a generic construction for fuzzy extractors from noisy continuous sources, using independent partitions. The extra freedom in the choice of discretization, which does not exist in the discrete case, is advantageously used to give the extracted key a uniform distribution. We analyze the privacy properties of the scheme and the error probabilities in a one-dimensional toy model with simplified noise. Finally, we study the security implications of incomplete knowledge of the source's probability distribution${\BBP }$. We derive a bound on the min-entropy of the extracted key under the worst-case assumption, where the attacker knows${\BBP }$exactly.