Lossless fuzzy extractor enabled secure authentication using low entropy noisy sources

Fuzzy extractor provides a way for key generation from biometrics and other noisy data. It has been widely applied in biometric authentication systems that provides natural and passwordless user authentication. In general, given a random sample, a fuzzy extractor extracts a nearly uniform random string, and subsequently regenerates the string using a different yet similar noisy sample. However, due to error tolerance between the two samples, fuzzy extractor imposes high information loss (entropy) and thus, it only works for an input with high enough entropy. In this work, we propose a lossless fuzzy extractor for a large family of sources. The proposed lossless fuzzy extractor can be adopted for a wider range of random sources to extract an arbitrary number of nearly uniform random strings. Besides, we formally defined a new entropy measurement, named as equal error entropy, to measure the entropy loss in reproducing a bounded number of random strings. When the number of random strings is large enough, the equal error entropy is minimized and necessary for performance evaluation on the authentication using the extracted random strings.