General Constructions of Fuzzy Extractors for Continuous Sources

Yucheng Ma, Peisong Shen, Kewei Lv, Xue Tian, Chi Chen

Abstract: Fuzzy extractors are cryptographic primitives designed to generate cryptographic keys from noisy sources. While most existing fuzzy extractors are designed for discrete sources, our work focuses on fuzzy extractors for continuous sources. To evaluate the feasibility of key extraction from continuous sources, we introduce the notion of max-divergence, as classical entropy definitions are not directly applicable in this context. Building upon the concept of max-divergence, we extend the definition of fuzzy extractors to accommodate continuous sources. In addition, we introduce the notion of continuous-source fuzzy conductors, which generates strings with sufficient entropy from continuous noisy sources, and present a general approach for constructing continuous-source fuzzy extractors from continuous-source fuzzy conductors. Furthermore, we provide two constructions using lattice codes for error correction in the Euclidean space, and analyze the security of our constructions. Finally, we discuss the practical implementation of our proposed constructions.