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Key Agreement with Correlated Noise and Multiple Entities or Enrollments

We extend a basic key agreement model with a hidden identifier source to a multi-user model with joint secrecy and privacy constraints over all entities that do not trust each other. Different entities that use different measurements of the same remote source through broadcast channels (BCs) to agree on mutually-independent local secret keys are considered. This model is the proper multi-user extension of the basic model since the encoder and decoder pairs are not assumed to trust other pairs, unlike assumed in the literature. Strong secrecy constraints imposed jointly on all secret keys, which is more stringent than separate secrecy leakage constraints for each secret key considered in the literature, are satisfied. Inner bounds for maximum key rate, and minimum privacy-leakage and storage rates are proposed for any finite number of entities. Inner and outer bounds for degraded and less-noisy BCs are given to illustrate cases with strong privacy. A multi-enrollment model that is used for common physical unclonable functions (PUFs) is also considered to establish inner and outer bounds for keyleakage-storage regions that differ only in the Markov chains imposed. For this special case, the encoder and decoder measurement channels have the same channel transition matrix and secrecy leakage is measured for each secret key separately. We illustrate cases for which it is useful to have multiple enrollments as compared to a single enrollment and vice versa.