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Continuous-Time Analysis of the Bitcoin and Prism Backbone Protocols
arXiv - CS - Cryptography and Security Pub Date : 2020-01-16 , DOI: arxiv-2001.05644
Jing Li and Dongning Guo

Bitcoin is a peer-to-peer payment system proposed by Nakamoto in 2008. Based on the Nakamoto consensus, Bagaria, Kannan, Tse, Fanti, and Viswanath proposed the Prism protocol in 2018 and showed that it achieves near-optimal blockchain throughput while maintaining a similar level of security as bitcoin. Previous probabilistic security guarantees for the bitcoin and Prism backbone protocols were either established under a simplified discrete-time model or expressed in terms of exponential order results. This paper presents a streamlined and strengthened analysis under a more realistic continuous-time model. A fully rigorous model for blockchains is developed with no restrictions on adversarial miners except for an upper bound on their aggregate mining rate. The only assumption on the peer-to-peer network is that all block propagation delays are upper bounded by a constant. A new notion of "t-credible blockchains" is introduced, which, together with some carefully defined "typical" events concerning block production over time intervals, is crucial to establish probabilisitic security guarantees in continuous time. A blockchain growth theorem, a blockchain quality theorem, and a common prefix theorem are established with explicit probability bounds. Moreover, under a certain typical event which occurs with probability close to $1$, a valid transaction that is deep enough in one credible blockchain is shown to be permanent in the sense that it must be found in} in all future credible blockchains.

中文翻译:

比特币和棱镜主干协议的连续时间分析

比特币是中本聪于 2008 年提出的点对点支付系统。 基于中本聪共识,Bagaria、Kannan、Tse、Fanti 和 Viswanath 于 2018 年提出了 Prism 协议,并表明它在保持接近最优的区块链吞吐量的同时与比特币类似的安全级别。之前比特币和 Prism 主干协议的概率安全保证要么是在简化的离散时间模型下建立的,要么是用指数顺序结果表示的。本文在更现实的连续时间模型下提出了一种简化和强化的分析。开发了一个完全严格的区块链模型,对对抗性矿工没有任何限制,除了其总采矿率的上限。对等网络的唯一假设是所有块传播延迟的上限是一个常数。引入了“t-可信区块链”的新概念,连同一些精心定义的关于时间间隔内区块生产的“典型”事件,对于在连续时间内建立概率安全保证至关重要。一个区块链增长定理、一个区块链质量定理和一个公共前缀定理是用显式的概率界限建立的。此外,在发生概率接近 $1$ 的某个典型事件下,在一个可信区块链中足够深的有效交易被证明是永久性的,因为它必须在所有未来可信区块链中找到。引入,连同一些仔细定义的关于时间间隔内出块的“典型”事件,对于在连续时间内建立概率安全保证至关重要。区块链增长定理、区块链质量定理和公共前缀定理是建立在显式概率边界下的。此外,在发生概率接近 $1$ 的某个典型事件下,在一个可信区块链中足够深的有效交易被证明是永久性的,因为它必须在所有未来可信区块链中找到。引入,连同一些仔细定义的关于时间间隔内出块的“典型”事件,对于在连续时间内建立概率安全保证至关重要。一个区块链增长定理、一个区块链质量定理和一个公共前缀定理是用显式的概率界限建立的。此外,在发生概率接近 $1$ 的某个典型事件下,在一个可信区块链中足够深的有效交易被证明是永久性的,因为它必须在所有未来可信区块链中找到。一个区块链质量定理和一个公共前缀定理是用明确的概率界限建立的。此外,在发生概率接近 $1$ 的某个典型事件下,在一个可信区块链中足够深的有效交易被证明是永久性的,因为它必须在所有未来可信区块链中找到。一个区块链质量定理和一个公共前缀定理是用明确的概率界限建立的。此外,在发生概率接近 $1$ 的某个典型事件下,在一个可信区块链中足够深的有效交易被证明是永久性的,因为它必须在所有未来可信区块链中找到。
更新日期:2020-04-27
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