Nonce Distribution in Bitcoin Blockchain

Abstract

In a Proof-of-Work (PoW) blockchain such as Bitcoin, mining is a competitive process of finding a feasible nonce which makes a block valid. The feasible nonce shall be a random number for the purpose of security and fairness. However, by exploring the mined nonces in first 875,000 blocks in Bitcoin blockchain, we observed that the number of even mined nonces is significantly larger than the odd ones. If the number of even feasible nonces is larger than that of odd ones, the miner may only attempt the even nonce in order to mine the block more quickly such that the fairness of Proof-of-Work mechanism cannot be maintained. In this paper, we conduct an experiment to show that the feasible nonce is inherently uniformly distributed. We also observe the mined nonces and the mining rounds which indirectly proves that the feasible nonces are uniformly distributed. Finally, we provide an explanation why the nonces mined in the block are not uniformly distributed; this is the result of selection bias from miners’ strategies.