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Register a new userCompounding of Wealth in Proof-of-Stake Cryptocurrencies
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Giulia Fanti
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Proof-of-stake (PoS) is a promising approach for designing efficient blockchains, where block proposers are randomly chosen with probability proportional to their stake. A primary concern with PoS systems is the rich getting richer phenomenon, whereby wealthier nodes are more likely to get elected, and hence reap the block reward, making them even wealthier. In this paper, we introduce the notion of equitability, which quantifies how much a proposer can amplify her stake compared to her initial investment. Even with everyone following protocol (i.e., honest behavior), we show that existing methods of allocating block rewards lead to poor equitability, as does initializing systems with small stake pools and/or large rewards relative to the stake pool. We identify a emph{geometric} reward function, which we prove is maximally equitable over all choices of reward functions under honest behavior and bound the deviation for strategic actions; the proofs involve the study of optimization problems and stochastic dominances of Polya urn processes, and are of independent mathematical interest. These results allow us to provide a systematic framework to choose the parameters of a practical incentive system for PoS cryptocurrencies.
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In the proof-of-stake (PoS) paradigm for maintaining decentralized, permissionless cryptocurrencies, Sybil attacks are prevented by basing the distribution of roles in the protocol execution on the stake distribution recorded in the ledger itself. However, for various reasons this distribution cannot be completely up-to-date, introducing a gap between the present stake distribution, which determines the parties current incentives, and the one used by the protocol. In this paper, we investigate this issue, and empirically quantify its effects. We survey existing provably secure PoS proposals to observe that the above time gap between the two stake distributions, which we call stake distribution lag, amounts to several days for each of these protocols. Based on this, we investigate the ledgers of four major cryptocurrencies (Bitcoin, Bitcoin Cash, Litecoin and Zcash) and compute the average stake shift (the statistical distance of the two distributions) for each value of stake distribution lag between 1 and 14 days, as well as related statistics. We also empirically quantify the sublinear growth of stake shift with the length of the considered lag interval. Finally, we turn our attention to unusual stake-shift spikes in these currencies: we observe that hard forks trigger major stake shifts and that single real-world actors, mostly exchanges, account for major stake shifts in established cryptocurrency ecosystems.
Fault-tolerant distributed systems move the trust in a single party to a majority of parties participating in the protocol. This makes blockchain based crypto-currencies possible: they allow parties to agree on a total order of transactions without a trusted third party. To trust a distributed system, the security of the protocol and the correctness of the implementation must be indisputable. We present the first machine checked proof that guarantees both safety and liveness for a consensus algorithm. We verify a Proof of Stake (PoS) Nakamoto-style blockchain (NSB) protocol, using the foundational proof assistant Coq. In particular, we consider a PoS NSB in a synchronous network with a static set of corrupted parties. We define execution semantics for this setting and prove chain growth, chain quality, and common prefix which together imply both safety and liveness.
The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $Theta(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $Theta(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a recursive relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
A blockchain is a database of sequential events that is maintained by a distributed group of nodes. A key consensus problem in blockchains is that of determining the next block (data element) in the sequence. Many blockchains address this by electing a new node to propose each new block. The new block is (typically) appended to the tip of the proposers local blockchain, and subsequently broadcast to the rest of the network. Without network delay (or adversarial behavior), this procedure would give a perfect chain, since each proposer would have the same view of the blockchain. A major challenge in practice is forking. Due to network delays, a proposer may not yet have the most recent block, and may, therefore, create a side chain that branches from the middle of the main chain. Forking reduces throughput, since only one a single main chain can survive, and all other blocks are discarded. We propose a new P2P protocol for blockchains called Barracuda, in which each proposer, prior to proposing a block, polls $ell$ other nodes for their local blocktree information. Under a stochastic network model, we prove that this lightweight primitive improves throughput as if the entire network were a factor of $ell$ faster. We provide guidelines on how to implement Barracuda in practice, guaranteeing robustness against several real-world factors.
The Nakamoto longest chain protocol is remarkably simple and has been proven to provide security against any adversary with less than 50% of the total hashing power. Proof-of-stake (PoS) protocols are an energy efficient alternative; however existing protocols adopting Nakamotos longest chain design achieve provable security only by allowing long-term predictability (which have serious security implications). In this paper, we prove that a natural longest chain PoS protocol with similar predictability as Nakamotos PoW protocol can achieve security against any adversary with less than 1/(1+e) fraction of the total stake. Moreover we propose a new family of longest chain PoS protocols that achieve security against a 50% adversary, while only requiring short-term predictability. Our proofs present a new approach to analyzing the formal security of blockchains, based on a notion of adversary-proof convergence.
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