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.

模糊提取器提供了一种从生物识别和其他嘈杂数据生成密钥的方法。它已被广泛应用于提供自然和无密码用户认证的生物认证系统中。通常，在给定随机样本的情况下，模糊提取器会提取几乎均匀的随机字符串，然后使用其他但类似的有噪样本重新生成字符串。但是，由于两个样本之间的容错性，模糊提取器会带来较高的信息损失（熵），因此，它仅适用于具有足够高的熵的输入。在这项工作中，我们为大量的来源提出了一种无损模糊提取器。所提出的无损模糊提取器可用于更广泛的随机源，以提取任意数量的几乎均匀的随机字符串。此外，我们正式定义了新的熵测度 称为等误差熵，用于在再现有限数量的随机字符串时测量熵损失。当随机字符串的数量足够大时，相等的误差熵会最小化，这对于使用提取的随机字符串进行身份验证的性能评估是必要的。