Secret key agreement (SKA) is an essential primitive in cryptography and
information security. In a multiterminal key agreement problem, there are a set
of terminals each having access to a component of a vector random variable, and
the goal of the terminals is to establish a shared key among a designated
subset of terminals. This problem has been studied under different assumptions
about the adversary. In the most general model, the adversary has access to a
random variable $Z$, that is correlated with all terminals’ variables. The
single-letter characterization of the secret key capacity of this model, known
as the wiretap secret key capacity, is not known for an arbitrary $Z$. In this
paper, we calculate the wiretap secret key capacity of a Tree-PIN, when $Z$
consists of noisy version of terminals’ variables. We also derive an upper
bound and a lower bound for the wiretap secret key capacity of a PIN, and prove
their tightness for some special cases.

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