Evolutionary Game for Mining Pool Selection in Blockchain Networks

In blockchain networks adopting the proof-of-work schemes, the monetary incentive is introduced by the Nakamoto consensus protocol to guide the behaviors of the full nodes (i.e., block miners) in the process of maintaining the consensus about the blockchain state. The block miners have to devote their computation power measured in hash rate in a crypto-puzzle solving competition to win the reward of publishing (a.k.a., mining) new blocks. Due to the exponentially increasing difficulty of the crypto-puzzle, individual block miners tends to join mining pools, i.e., the coalitions of miners, in order to reduce the income variance and earn stable profits. In this paper, we study the dynamics of mining pool selection in a blockchain network, where mining pools may choose arbitrary block mining strategies. We identify the hash rate and the block propagation delay as two major factors determining the outcomes of mining competition, and then model the strategy evolution of the individual miners as an evolutionary game. We provide the theoretical analysis of the evolutionary stability for the pool selection dynamics in a case study of two mining pools. The numerical simulations provide the evidence to support our theoretical discoveries as well as demonstrating the stability in the evolution of miners' strategies in a general case.Comment: Submitted to IEEE Wireless Communication Letter

On the Security of a Novel Probabilistic Signature Based on Bilinear Square Diffie-Hellman Problem and Its Extension

Probabilistic signature scheme has been widely used in modern electronic commerce since it could provide integrity, authenticity, and nonrepudiation. Recently, Wu and Lin proposed a novel probabilistic signature (PS) scheme using the bilinear square Diffie-Hellman (BSDH) problem. They also extended it to a universal designated verifier signature (UDVS) scheme. In this paper, we analyze the security of Wu et al.’s PS scheme and UDVS scheme. Through concrete attacks, we demonstrate both of their schemes are not unforgeable. The security analysis shows that their schemes are not suitable for practical applications