Abstract
Nakamoto’s longest-chain consensus paradigm now powers the bulk of the world’s cryptocurrencies and distributed finance infrastructure. An emblematic property of longest-chain consensus is that it provides probabilistic settlement guarantees that strengthen over time. This makes the exact relationship between settlement error and settlement latency a critical aspect of the protocol that both users and system designers must understand to make informed decisions. A recent line of work has finally provided a satisfactory rigorous accounting of this relationship for proof-of-work longest-chain protocols, but those techniques do not appear to carry over to the proof-of-stake setting.
This article develops a new analytic approach for establishing such settlement guarantees that yields explicit, rigorous settlement bounds for proof-of-stake longest-chain protocols, placing them on equal footing with their proof-of-work counterparts. Our techniques apply with some adaptations to the proof-of-work setting where they provide improvements to the state-of-the-art settlement bounds for proof-of-work protocols.
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Notes
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https://ethereum.org/, prior to its shift to PoS in September 2022. The analysis also applies to currently deployed Ethereum Classic (ETC) and PoW Ethereum (ETHW) blockchains. In the rest of the paper, we refer to all these three instances together as “PoW-based Ethereum,” or simply Ethereum if no confusion can arise.
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This is a slight simplification in the case of Ouroboros Praos, where the probability of a party that holds an s-fraction of stake (for \(s\in [0,1]\)) becoming a slot leader is in fact \(1-(1-f)^{s}\) for a constant f set to 1/20 in Cardano. We adopt this simplification for the sake of broader applicability of our bounds.
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This work is funded in part by National Science Foundation award 2143058.
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Gaži, P., Ren, L., Russell, A. (2023). Practical Settlement Bounds for Longest-Chain Consensus. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_4
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