A Permissionless Proof-of-Stake Blockchain with Best-Possible Unpredictability

To eliminate the unnecessary waste of energy and computing power in Bitcoin, in this paper, we develop a novel proof-of-stake consensus in the permissionless se‹ing. Among other features, our design achieves the “best possible” unpredictability for permissionless proof-of-stake protocols. As shown by Brown-Cohen et al (EC 2019), unpredictability property is critical for proof-of-stake consensus in the rational se‹ing; the ƒip side of unpredictability property, i.e., predictability can be abused by the a‹ackers for launching strengthened version of multiple a‹acks such as sel€sh-mining and bribing, against proof-of-stake systems. We are inspired by Bitcoin’s “block-by-block” design, and we show that a direct and natural mimic of Bitcoin’s design via proof-of-stake is secure if the majority 73% of stake is honest. Our result relies on an interesting upper bound of extending proof-of-stake blockchain we establish: players (who may extend all chains) can generate blockchain at most 2.72× faster than playing the basic strategy of extending the longest chain. We introduce a novel strategy called “D-distance-greedy” strategy, which enables us to construct a class of secure proof-of-stake blockchain protocols, against an arbitrary adversary, even assuming much smaller (than 73% of) stake is honest. To enable a thorough security analysis in the cryptographic se‹ing, we develop several new techniques: for example, to show the chain growth property, we represent the chain extension process via a Markov chain, and then develop a random walk on the Markov chain; to prove the common pre€x property, we introduce a new concept called “virtual chains”, and then present a reduction from the regular version of common pre€x to “common pre€x w.r.t. virtual chains”. Finally, we note that, ours is the €rst “block-by-block” style of proof-of-stake in the permissionless se‹ing, naturally mimicking Bitcoin’s design; it turns out that this feature, again allows us to achieve the “best possible” unpredictability property. Other existing provably secure permissionless proof-of-stake solutions are all in an “epoch-by-epoch” style, and thus cannot achieve the best possible unpredictability. ∗‘is is a replacement of earlier versions of the work [30, 31, 29]. Several technical issues in previous versions have been addressed; please see Section 6.3 for details. †Shanghai Jiaotong University, Email: fanlei@sjtu.edu.cn ‡University of Maryland, Email: jkatz@cs.umd.edu §Virginia Commonwealth University, Email: thaipd@vcu.edu ¶Virginia Commonwealth University, Email: hszhou@vcu.edu