Selfish Mining Attacks in Sharded Blockchains

Sharding is a promising technology to improve scalability of a blockchain. A blockchain is partitioned into a number of shards each of which is maintained by a subset of miners. The multiple shards constitute a sharded blockchain and are able to process transactions concurrently such that the overall throughput is increased. However, decreasing the number of miners in a blockchain increases the possibility to be attacked. In this paper, we consider how selfish mining attacks sharded blockchains. To the best of our knowledge, the problem has not been studied before. We first formulate an optimization problem to maximize the rewards earned by selfish miners by using an accurate analytical model. An algorithm for selfish miners to earn most rewards is proposed. Numerical results show that robustness of blockchains becomes weak when the blockchain is sharded. However, no matter how many number shards in a sharded blockchain, the rewards earned by selfish miners are close to each other. Furthermore, when the honest mining rate is uniformly assigned to each shard, the selfish miners earns the smallest amount of rewards.

I. Introduction

Blockchain is a decentralized ledger which is originally used in Bitcoin network [1]. In a blockchain, transactions are securely stored in the blocks and the blocks are concatenated using cryptography. Besides the Bitcon transactions, blockchains are widely used in processing various aspects of data nowadays. For example, Ethereum provides blockchain platforms for developing smart contracts which process a large number of various transactions such as financial, health or sports records [2].