Information Leakage of Continuous-Source Zero Secrecy Leakage Helper Data Schemes

A Helper Data Scheme is a cryptographic primitive that extracts a high-entropy noise-free string from noisy data. Helper Data Schemes are used for privacy-preserving databases and for Physical Unclonable Functions. We refine the theory of Helper Data schemes with Zero Secrecy Leakage (ZSL), i.e. the mutual information between the helper data and the extracted secret is zero. We prove that ZSL necessitates particular properties of the helper data generating function, which also allows us to show the existence of `Sibling Points'. In the special case that our generated secret is uniformly distributed (Fuzzy Extractors) our results coincide with the continuum limit of a recent construction by Verbiskiy et al. Yet our results cover secure sketches as well. Moreover we present an optimal reconstruction algorithm for this scheme, that not only provides the lowest possible reconstruction error rate but also yields an attractive, simple implementation of the verification. Further, we introduce Diagnostic Category Leakage (DCL), which quantifies what an attacker can infer from helper data about a particular medical indication of the enrolled user, or reversely what probabilistic knowledge of a diagnose can leak about the secret. If the attacker has a priori knowledge about the enrolled user (medical indications, race, gender), then the ZSL property does not guarantee that there is no secrecy leakage from the helper data. However, this effect is typically very small.