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Bitcoin uses blockchain technology to maintain transactions order and provides probabilistic guarantee to prevent double-spending, assuming that an attacker's computational power does not exceed %50 of the network power. In this paper, we…

Cryptography and Security · Computer Science 2024-11-19 Ghader Ebrahimpour , Mohammad Sayad Haghighi

A proof of the security of the Bitcoin protocol is made rigorous, and simplified in certain parts. A computational model in which an adversary can delay transmission of blocks by time $\Delta$ is considered. The protocol is generalized to…

Cryptography and Security · Computer Science 2026-04-17 Christopher Blake , Chen Feng , Xuechao Wang , Qianyu Yu

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

We review the so called selfish mining strategy in the Bitcoin network and compare its profitability to honest mining.We build a rigorous profitability model for repetition games. The time analysis of the attack has been ignored in the…

Computer Science and Game Theory · Computer Science 2019-01-23 Cyril Grunspan , Ricardo Pérez-Marco

We revisit the fundamental question of Bitcoin's security against double spending attacks. While previous work has bounded the probability that a transaction is reversed, we show that no such guarantee can be effectively given if the…

Cryptography and Security · Computer Science 2016-06-01 Yonatan Sompolinsky , Aviv Zohar

Cryptocurrencies have gained popularity due to their transparency, security, and accessibility compared to traditional financial systems, with Bitcoin, introduced in 2009, leading the market. Bitcoin's security relies on blockchain…

Cryptography and Security · Computer Science 2024-11-12 Dinitha Wijewardhana , Sugandima Vidanagamachchi , Nalin Arachchilage

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

We survey recent results on the mathematical stability of Bitcoin protocol. Profitability and probability of a double spend are estimated in closed form with classical special functions. The stability of Bitcoin mining rules is analyzed and…

History and Overview · Mathematics 2020-03-03 Cyril Grunspan , Ricardo Pérez-Marco

Authorization is challenging in distributed systems that cannot rely on the identification of nodes. Proof-of-work offers an alternative gate-keeping mechanism, but its probabilistic nature is incompatible with conventional security…

Cryptography and Security · Computer Science 2022-09-20 Patrik Keller , Rainer Böhme

We present Bitcoin Security Tables computing the probability of success p(z,q,t) of a double spend attack by an attacker controlling a share q of the hashrate after z confirmations in time t.

Cryptography and Security · Computer Science 2017-02-20 Cyril Grunspan , Ricardo Pérez-Marco

Bitcoin derives a verifiable temporal order from probabilistic block discovery and cumulative proof-of-work rather than from a trusted global clock. We show that block arrivals exhibit stable exponential behavior across difficulty epochs,…

Information Theory · Computer Science 2026-02-11 Bin Chen , Pan Feng

A widespread security claim of the Bitcoin system, presented in the original Bitcoin white-paper, states that the security of the system is guaranteed as long as there is no attacker in possession of half or more of the total computational…

Cryptography and Security · Computer Science 2013-12-30 Lear Bahack

We present a strategy for a single quantum miner with relatively low hashing power, with the same ramifications as a 51% attack. Bitcoin nodes consider the chain with the highest cumulative proof-of-work to be the valid chain. A quantum…

Quantum Physics · Physics 2024-10-01 Bolton Bailey , Or Sattath

Grover's algorithm confers on quantum computers a quadratic advantage over classical computers for searching in an arbitrary data set, a scenario that describes Bitcoin mining. It has previously been argued that the only side-effect of…

Quantum Physics · Physics 2020-03-17 Or Sattath

In this paper, we explore the partitioning attacks on the Bitcoin network, which is shown to exhibit spatial bias, and temporal and logical diversity. Through data-driven study we highlight: 1) the centralization of Bitcoin nodes across…

Networking and Internet Architecture · Computer Science 2019-02-12 Muhammad Saad , Victor Cook , Lan Nguyen , My T. Thai , Aziz Mohaisen

Stubborn mining attack greatly downgrades Bitcoin throughput and also benefits malicious miners (attackers). This paper aims to quantify the impact of block receiving delay on stubborn mining attack severity in imperfect Bitcoin networks.…

Cryptography and Security · Computer Science 2023-09-14 Haoran Zhu , Xiaolin Chang , Jelena Mišić , Vojislav B. Mišić

The consensus protocol named proof of work (PoW) is widely applied by cryptocurrencies like Bitcoin. Although security of a PoW cryptocurrency is always the top priority, it is threatened by mining attacks like selfish mining. Researchers…

Cryptography and Security · Computer Science 2019-07-09 Hanqing Liu , Na Ruan , Joseph K. Liu

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

Most current assessments use ex post proxies that miss uncertainty and fail to consistently capture the rapid change in bitcoin mining. We introduce a unified, ex ante statistical model that derives expected return, downside risk, and…

Computational Engineering, Finance, and Science · Computer Science 2025-12-24 Yuting Cai , Ruthav Sadali , Korok Ray , Chao Tian

The key cryptographic protocols used to secure the internet and financial transactions of today are all susceptible to attack by the development of a sufficiently large quantum computer. One particular area at risk are cryptocurrencies, a…

Quantum Physics · Physics 2020-06-07 Divesh Aggarwal , Gavin K. Brennen , Troy Lee , Miklos Santha , Marco Tomamichel
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