Nested Tailbiting Convolutional Codes for Secrecy, Privacy, and Storage

The key agreement problem with biometric or physical identifiers and two terminals for key enrollment and reconstruction is considered. A nested convolutional code construction that performs lossy compression with side information is proposed. Nested convolutional codes are an alternative to nested polar codes and nested random linear codes that achieve all points of the key-leakage-storage regions of the generated-secret and chosen-secret models for long block lengths. Our design uses a convolutional code for vector quantization during enrollment and a subcode of it for error correction during reconstruction. Physical identifiers with small bit error probability are considered to illustrate the gains of the proposed construction. One variant of nested convolutional codes improves on all previous constructions in terms of the key vs. storage rate ratio but it has high complexity. Another variant of nested convolutional codes with lower complexity performs similarly to previously designed nested polar codes. The results suggest that the choice of convolutional or polar codes for key agreement with identifiers depends on the complexity constraints.