Quantization in zero leakage helper data schemes

A helper data scheme (HDS) is a cryptographic primitive that extracts a high-entropy noise-free string from noisy data. Helper data schemes are used for preserving privacy in biometric databases and for physical unclonable functions. HDSs are known for the guided quantization of continuous-valued sources as well as for repairing errors in discrete-valued (digitized) sources. We refine the theory of helper data schemes with the zero leakage (ZL) property, i.e., the mutual information between the helper data and the extracted secret is zero. We focus on quantization and prove that ZL necessitates particular properties of the helper data generating function: (1) the existence of “sibling points”, enrollment values that lead to the same helper data but different secrets and (2) quantile helper data. We present an optimal reconstruction algorithm for our ZL scheme, that not only minimizes the reconstruction error rate but also yields a very efficient implementation of the verification. We compare the error rate to schemes that do not have the ZL property.