Supplementary information files for "A robust shard inspection framework with efficient throughput and energy consumption for secure geolocation-based sharded blockchains"

<p dir="ltr">Supplementary files for article "A robust shard inspection framework with efficient throughput and energy consumption for secure geolocation-based sharded blockchains"<br><br>In sharded blockchains, peers are divided into smaller groups (shards) that generate and verify blocks in parallel, offering enhanced throughput and reduced delays. These properties make sharded blockchains a promising solution for secure data management in Internet of Things (IoT) systems. Particularly, geolocation-based sharded blockchains assign geographically proximate peers to the same shard, enabling faster IoT transaction processing. Yet, peers in each shard can easily collude to falsely accept/reject blocks. To resolve this issue, in this paper, we propose a robust reputation-based shard inspection framework. The framework adopts the shard inspection mechanism where a group of inspectors selected from the most reputable peers randomly verify blocks in each shard. This enables avoiding collusion attacks and enhancing the security of each shard. However, additional block verifications during the inspection process can incur significant block delays and energy overheads. To reduce these overheads, we formulate an optimization problem that jointly determines the number of inspectors and the inspection interval to maximize the system utility, which is proportional to the blockchain throughput and energy consumption. We then develop a distributed algorithm that enables dividing the optimization problem into sub-problems solvable independently by each shard. Experimental results show that our framework can maximize the system utility, while maintaining high levels of security in each shard.<br><br>©IEEE, CC BY 4.0</p>