  Distributed detection over a blockchain-aided Internet of Things (BIoT)
network in the presence of attacks is considered, where the integrated
blockchain is employed to secure data exchanges over the BIoT as well as data
storage at the agents of the BIoT. We consider a general adversary model where
attackers jointly exploit the vulnerability of IoT devices and that of the
blockchain employed in the BIoT. The optimal attacking strategy which minimizes
the Kullback-Leibler divergence is pursued. It can be shown that this
optimization problem is nonconvex, and hence it is generally intractable to
find the globally optimal solution to such a problem. To overcome this issue,
we first propose a relaxation method that can convert the original nonconvex
optimization problem into a convex optimization problem, and then the analytic
expression for the optimal solution to the relaxed convex optimization problem
is derived. The optimal value of the relaxed convex optimization problem
provides a detection performance guarantee for the BIoT in the presence of
attacks. In addition, we develop a coordinate descent algorithm which is based
on a capped water-filling method to solve the relaxed convex optimization
problem, and moreover, we show that the convergence of the proposed coordinate
descent algorithm can be guaranteed.
