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Eyal and Sirer's selfish mining strategy has demonstrated that Bitcoin system is not secure even if 50% of total mining power is held by altruistic miners. Since then, researchers have been investigating either to improve the efficiency of…

Multiagent Systems · Computer Science 2018-02-08 Tin Leelavimolsilp , Long Tran-Thanh , Sebastian Stein

Selfish mining is strategic rule-breaking to maximize rewards in proof-of-work protocols. Markov Decision Processes (MDPs) are the preferred tool for finding optimal strategies in Bitcoin and similar linear chain protocols. Protocols…

Cryptography and Security · Computer Science 2025-06-24 Patrik Keller

In the context of the `selfish-mine' strategy proposed by Eyal and Sirer, we study the effect of propagation delay on the evolution of the Bitcoin blockchain. First, we use a simplified Markov model that tracks the contrasting states of…

Cryptography and Security · Computer Science 2015-05-22 Johannes Göbel , Paul Keeler , Anthony E. Krzesinski , Peter G. Taylor

The Bitcoin cryptocurrency has received much attention recently. In the network of Bitcoin, transactions are recorded in a ledger. In this network, the process of recording transactions depends on some nodes called miners that execute a…

Cryptography and Security · Computer Science 2023-02-15 Ali Nikhalat-Jahromi , Ali Mohammad Saghiri , Mohammad Reza Meybodi

Mining attacks aim to gain an unfair share of extra rewards in the blockchain mining. Selfish mining can preserve discovered blocks and strategically release them, wasting honest miners' computing resources and getting higher profits.…

Cryptography and Security · Computer Science 2024-04-09 Jiaping Yu , Shang Gao , Rui Song , Zhiping Cai , Bin Xiao

Bitcoin and Ethereum are the top two blockchain-based cryptocurrencies whether from cryptocurrency market cap or popularity. However, they are vulnerable to selfish mining and stubborn mining due to that both of them adopt Proof-of-Work…

Cryptography and Security · Computer Science 2021-12-07 Runkai Yang , Xiaolin Chang , Jelena Mišić , Vojislav B. Mišić

In this paper, we provide a new theoretical framework of pyramid Markov processes to solve some open and fundamental problems of blockchain selfish mining under a rigorous mathematical setting. We first describe a more general model of…

Cryptography and Security · Computer Science 2021-09-14 Quan-Lin Li , Yan-Xia Chang , Xiaole Wu , Guoqing Zhang

In this paper we revisit the mining strategies in proof of work based cryptocurrencies and propose two strategies, we call smart and smarter mining, that in many cases strictly dominate honest mining. In contrast to other known attacks,…

Cryptography and Security · Computer Science 2019-02-13 Guy Goren , Alexander Spiegelman

Many of the recent works on the profitability of rogue mining strategies hinge on a parameter called $\gamma$ that measures the proportion of the honest network attracted by the attacker to mine on top of his fork. These works, see…

Cryptography and Security · Computer Science 2022-08-23 Pantelis Tassopoulos , Yorgos Protonotarios

Major cryptocurrency networks have relied on random peering choice rules for making connections in their peer-to-peer networks. Generally, these choices have good properties, particularly for open, permissionless networks. Random peering…

Computer Science and Game Theory · Computer Science 2024-02-23 Lucianna Kiffer , Rajmohan Rajaraman

Blockchain security is threatened by selfish mining, where a miner (operator) deviates from the protocol to increase their revenue. Selfish mining is exacerbated by adverse conditions: rushing (network propagation advantage for the selfish…

Cryptography and Security · Computer Science 2025-11-27 Roi Bar-Zur , Aviv Tamar , Ittay Eyal

We compute and compare profitabilities of stubborn mining strategies that are variations of selfish mining. These are deviant mining strategies violating Bitcoin's network protocol rules. We apply the foundational set-up from our previous…

Cryptography and Security · Computer Science 2018-08-06 Cyril Grunspan , Ricardo Pérez-Marco

Proof-of-Stake blockchains based on a longest-chain consensus protocol are an attractive energy-friendly alternative to the Proof-of-Work paradigm. However, formal barriers to "getting the incentives right" were recently discovered, driven…

Computer Science and Game Theory · Computer Science 2023-10-31 Matheus V. X. Ferreira , S. Matthew Weinberg

Mining processes of Bitcoin and similar cryptocurrencies are currently incentivized with voluntary transaction fees and fixed block rewards which will halve gradually to zero. In the setting where optional and arbitrary transaction fee…

Cryptography and Security · Computer Science 2022-07-14 Tiantian Gong , Mohsen Minaei , Wenhai Sun , Aniket Kate

We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are…

Computer Science and Game Theory · Computer Science 2016-07-11 Aggelos Kiayias , Elias Koutsoupias , Maria Kyropoulou , Yiannis Tselekounis

Proof-of-Stake systems randomly choose, on each round, one of the participants as a consensus leader that extends the chain with the next block such that the selection probability is proportional to the owned stake. However, distributed…

Cryptography and Security · Computer Science 2020-05-20 Mansoor Ahmed-Rengers , Kari Kostiainen

A proof of work (PoW) blockchain protocol distributes rewards to its participants, called miners, according to their share of the total computational power. Sufficiently large miners can perform selfish mining - deviate from the protocol to…

Cryptography and Security · Computer Science 2020-09-16 Roi Bar-Zur , Ittay Eyal , Aviv Tamar

The value of proof-of-work cryptocurrencies critically depends on miners having incentives to follow the protocol. However, the Bitcoin mining protocol proposed by Nakamoto (2008) and implemented in practice is well known not to constitute…

Cryptography and Security · Computer Science 2026-04-08 Manuel Mueller-Frank , Minghao Pan , Omer Tamuz

Proof-of-Stake consensus protocols give rise to complex modeling challenges. We analyze the recently-updated Tezos Proof-of-Stake protocol and demonstrate that, under certain conditions, rational participants are incentivized to behave…

Cryptography and Security · Computer Science 2020-04-09 Michael Neuder , Daniel J. Moroz , Rithvik Rao , David C. Parkes

Most public blockchain protocols, including the popular Bitcoin and Ethereum blockchains, do not formally specify the order in which miners should select transactions from the pool of pending (or uncommitted) transactions for inclusion in…

Cryptography and Security · Computer Science 2021-10-25 Johnnatan Messias , Mohamed Alzayat , Balakrishnan Chandrasekaran , Krishna P. Gummadi , Patrick Loiseau , Alan Mislove