Computational Robust Fuzzy Extractor. (27th July 2018) - Wen, Yunhua; Liu, Shengli; Hu, Ziyuan; Han, Shuai
Abstract: Robust fuzzy extractor is able to distill almost uniform strings from non-uniform noisy sources while robustness enables the extractor to detect adversaries' active attacks. Its security used to be defined information-theoretically. Information-theoretical security model is nice but too restricted and the extracted uniform string output by robust fuzzy extractors might be too short to be useful. This occurs even for the nearly optimal statistical robust fuzzy extractor constructed by Cramer et al. (Eurocrypt 2008). In this paper, we introduce the notion of computational robust fuzzy extractor by relaxing information-theoretical security to computational security and defining computational privacy and computational robustness for it. We give a simple construction of computational robust fuzzy extractor based on the hardness of Subgroup Membership Problem and Discrete Logarithm assumption. Thanks to computational security, our construction obtains much longer extracted uniform string than the nearly optimal (information-theoretically) robust fuzzy extractor proposed by Cramer et al.