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.

翻译：本文针对存在攻击场景下区块链辅助物联网（BIoT）网络的分布式检测问题展开研究，其中集成的区块链技术用于保障BIoT网络数据交换以及各代理节点数据存储的安全性。我们构建了一个通用对抗模型，该模型中攻击者联合利用物联网设备漏洞及BIoT中区块链系统的脆弱性。研究聚焦于使Kullback-Leibler散度最小化的最优攻击策略。研究表明该优化问题具有非凸性，故其全局最优解通常难以求解。为解决这一难题，我们首先提出一种松弛方法，将原始非凸优化问题转化为凸优化问题，进而推导出松弛后凸优化问题最优解的解析表达式。该松弛凸优化问题的最优值可为受攻击场景下的BIoT系统提供检测性能保障。此外，我们开发了一种基于截断注水法的坐标下降算法用于求解该松弛凸优化问题，并证明了所提坐标下降算法的收敛性。