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We correct the double spend race analysis given in Nakamoto's foundational Bitcoin article and give a closed-form formula for the probability of success of a double spend attack using the Regularized Incomplete Beta Function. We give a…

Cryptography and Security · Computer Science 2020-05-07 Cyril Grunspan , Ricardo Pérez-Marco

Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view. The simplest strategy that can be profitable incorporates…

Cryptography and Security · Computer Science 2021-02-24 Cyril Grunspan , Ricardo Pérez-Marco

We study the incentives behind double-spend attacks on Nakamoto-style Proof-of-Work cryptocurrencies. In these systems, miners are allowed to choose which transactions to reference with their block, and a common strategy for selecting…

Computer Science and Game Theory · Computer Science 2023-12-14 Yanni Georghiades , Rajesh Mishra , Karl Kreder , Sriram Vishwanath

The fundamental attack against blockchain systems is the double-spend attack. In this tutorial, we provide a very detailed explanation of just one section of Satoshi Nakamoto's original paper where the attack's probability of success is…

Cryptography and Security · Computer Science 2017-01-17 A. Pinar Ozisik , Brian Neil Levine

Simple closed-form upper and lower bounds are developed for the security of the Nakamoto consensus as a function of the confirmation depth, the honest and adversarial block mining rates, and an upper bound on the block propagation delay.…

Cryptography and Security · Computer Science 2022-08-30 Dongning Guo , Ling Ren

We study security-latency bounds for Nakamoto consensus, i.e., how secure a block is after it becomes $k$-deep in the chain. We improve the state-of-the-art bounds by analyzing the race between adversarial and honest chains in three…

Cryptography and Security · Computer Science 2024-07-25 Mustafa Doger , Sennur Ulukus

We analyze how secure a block is after the block becomes $k$-deep, i.e., security-latency, for Nakamoto consensus under an exponential network delay model. We provide the fault tolerance and extensive bounds on safety violation…

Cryptography and Security · Computer Science 2025-10-22 Mustafa Doger , Sennur Ulukus

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-24 Lili Su , Quanquan C. Liu , Neha Narula

In this paper we revisit some major orthodoxies which lie at the heart of the bitcoin crypto currency and its numerous clones. In particular we look at The Longest Chain Rule, the monetary supply policies and the exact mechanisms which…

Cryptography and Security · Computer Science 2014-12-11 Nicolas T. Courtois

The security of blockchain systems depends on the distribution of mining power across participants. If sufficient mining power is controlled by one entity, they can force their own version of events. This may allow them to double spend…

Cryptography and Security · Computer Science 2024-03-21 Mary Milad , Christina Ovezik , Dimitris Karakostas , Daniel W. Woods

This paper investigates the fundamental trade-offs between block safety, confirmation latency, and transaction throughput of proof-of-work (PoW) longest-chain fork-choice protocols, also known as PoW Nakamoto consensus. New upper and lower…

Cryptography and Security · Computer Science 2024-12-05 Shu-Jie Cao , Dongning Guo

Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle.…

Cryptography and Security · Computer Science 2026-03-23 Mustafa Doger , Sennur Ulukus

Extensive research on Nakamoto-style consensus protocols has shown that network delays degrade the security of these protocols. Established results indicate that, perhaps surprisingly, maximal security is achieved when the network is as…

Cryptography and Security · Computer Science 2024-04-16 Jannik Albrecht , Sebastien Andreina , Frederik Armknecht , Ghassan Karame , Giorgia Marson , Julian Willingmann

In the Bitcoin white paper, Nakamoto proposed a very simple Byzantine fault tolerant consensus algorithm that is also known as Nakamoto consensus. Despite its simplicity, some existing analysis of Nakamoto consensus appears to be long and…

Cryptography and Security · Computer Science 2019-10-22 Jianyu Niu , Chen Feng , Hoang Dau , Yu-Chih Huang , Jingge Zhu

In 2008, Satoshi Nakamoto proposed an electronic cash system (bitcoin) that is completely realized by peer-to-peer technology. The core value of this scheme is that it proposes a solution based on Proof-of Work, so that the cash system can…

Cryptography and Security · Computer Science 2018-11-19 Zhiniang Peng , Yuki Chen

Safety guarantees and security-latency problem of Nakamoto consensus have been extensively studied in the last decade with a bounded delay model. Recent studies have shown that PoW protocol is secure under random delay models as well. In…

Cryptography and Security · Computer Science 2024-05-13 Mustafa Doger , Sennur Ulukus , Nail Akar

This paper presents a new consensus protocol based on verifiable delay function. First, we introduce the concept of verifiable delay puzzle (VDP), which resembles the hashing puzzle used in the PoW mechanism but can only be solved…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-07-21 Jieyi Long

We describe and analyze perishing mining, a novel block-withholding mining strategy that lures profit-driven miners away from doing useful work on the public chain by releasing block headers from a privately maintained chain. We then…

Cryptography and Security · Computer Science 2023-02-10 Tong Cao , Jérémie Decouchant , Jiangshan Yu

This paper studies proof-of-work Nakamoto consensus protocols under bounded network delays, settling two long-standing questions in blockchain security: What is the most effective attack on block safety under a given block confirmation…

Cryptography and Security · Computer Science 2025-09-16 Shu-Jie Cao , Dongning Guo

Formal analyses of blockchain protocols have received much attention recently. Consistency results of Nakamoto's blockchain protocol are often expressed in a quantity $c$, which denotes the expected number of network delays before some…

Cryptography and Security · Computer Science 2020-03-16 Jun Zhao , Jing Tang , Li Zengxiang , Huaxiong Wang , Kwok-Yan Lam , Kaiping Xue
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