A Note on the Non-proportionality of Winning Probabilities in Bitcoin

The security of any proof-of-work blockchain protocol is based upon the assumption that the probability of a miner finding the next valid block is proportional to that miner’s hashing power and constant throughout the process of mining that block (i.e., that the mining process is a “memoryless” process). While the literature assumes that the mining process is indeed memoryless, in this paper we use deductive reasoning to show how, given the finiteness of hashing functions’ domains, this is not the case. This implies that the Bitcoin protocol induces a centralization of miners’ hashing power, which in turn threatens the long-term viability of Bitcoin and of other cryptocurrencies based on similar protocols. The novelty of this paper stems from our documenting of a previously unrecognized flaw in the incentive system sustaining Bitcoin’s security.