The Power of Random Symmetry-Breaking in Nakamoto Consensus

Nakamoto consensus underlies the security of many of the world's largest cryptocurrencies, such as Bitcoin and Ethereum. Common lore is that Nakamoto consensus only achieves consistency and liveness under a regime where the difficulty of its underlying mining puzzle is very high, negatively impacting overall throughput and latency. In this work, we study Nakamoto consensus under a wide range of puzzle difficulties, including very easy puzzles. We first analyze an adversary-free setting and show that, surprisingly, the common prefix of the blockchain grows quickly even with easy puzzles. In a setting with adversaries, we provide a small backwards-compatible change to Nakamoto consensus to achieve consistency and liveness with easy puzzles. Our insight relies on a careful choice of \emph{symmetry-breaking strategy}, which was significantly underestimated in prior work. We introduce a new method -- \emph{coalescing random walks} -- to analyzing the correctness of Nakamoto consensus under the uniformly-at-random symmetry-breaking strategy. This method is more powerful than existing analysis methods that focus on bounding the number of {\it convergence opportunities}.