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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

Machine learning is data hungry; the more data a model has access to in training, the more likely it is to perform well at inference time. Distinct parties may want to combine their local data to gain the benefits of a model trained on a…

Cryptography and Security · Computer Science 2019-01-09 Jamie Hayes , Olga Ohrimenko

Bitcoin mining presents a significant economic incentive for efficient hashing and broadcast of data, both parameters stemming from the Proofs of Work used to advance the network. This incentive has led to the development of Bitcoin…

Cryptography and Security · Computer Science 2016-03-17 Jonathan Harvey-Buschel , Can Kisagun

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

The main goal of this article is to present a direct approach for the formula giving the long-term apparent hashrates of Selfish Mining strategies using only elementary probabilities and combinatorics, more precisely, Dyck words. We can…

Cryptography and Security · Computer Science 2019-04-17 Cyril Grunspan , Ricardo Pérez-Marco

We give a straightforward proof for the formula giving the long-term apparent hashrate of the Selfish Mining strategy in Bitcoin using only elementary probabilities and combinatorics, and more precisely, Dyck words. There is no need to…

Cryptography and Security · Computer Science 2019-02-06 Cyril Grunspan , Ricardo Pérez-Marco

A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…

Quantum Physics · Physics 2023-08-03 Bernhard K Meister , Henry C W Price

Punishing those who refuse to participate in common efforts is a known and intensively studied way to maintain cooperation among self-interested agents. But this act is costly, hence punishers who are generally also engaged in the original…

Physics and Society · Physics 2021-11-29 Hsuan-Wei Lee , Colin Cleveland , Attila Szolnoki

Sustainable resource use in large societies requires social institutions that specify acceptable behavior and punish violators. Because mutual monitoring becomes prohibitively costly as populations grow, we examine whether sustainability…

Physics and Society · Physics 2025-07-31 Kenji Itao , Kunihiko Kaneko

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

Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users for information that will lead to better…

Machine Learning · Computer Science 2018-07-04 Manish Raghavan , Aleksandrs Slivkins , Jennifer Wortman Vaughan , Zhiwei Steven Wu

Detecting defection and alarming partners about the possible danger could be essential to avoid being exploited. This act, however, may require a huge individual effort from those who take this job, hence such a strategy seems to be…

Physics and Society · Physics 2017-05-25 Attila Szolnoki , Xiaojie Chen

Diversification is the typical investment strategy of risk-averse agents. However, non-diversified positions that allocate all resources to a single asset, state of the world or revenue stream are common too. We show that whenever finitely…

Theoretical Economics · Economics 2024-10-18 Christopher P. Chambers , Georgios Gerasimou

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 investigate pooling problems in which multiple players vie with one another to maximize individual profit in a non-cooperative competitive market. This competitive setting is interesting and worthy of study because the majority of…

Optimization and Control · Mathematics 2022-11-24 Dimitri J. Papageorgiou , Stuart M. Harwood , Francisco Trespalacios

In this paper, we address the critical challenges of double-spending and selfish mining attacks in blockchain-based digital currencies. Double-spending is a problem where the same tender is spent multiple times during a digital currency…

Cryptography and Security · Computer Science 2024-03-11 Seyed Ardalan Ghoreishi , Mohammad Reza Meybodi

We consider protocols where users communicate with multiple servers to perform a computation on the users' data. An adversary exerts semi-honest control over many of the parties but its view is differentially private with respect to honest…

Cryptography and Security · Computer Science 2022-08-19 Albert Cheu , Chao Yan

We consider a team of autonomous agents that navigate in an adversarial environment and aim to achieve a task by allocating their resources over a set of target locations. An adversary in the environment observes the autonomous team's…

Optimization and Control · Mathematics 2023-10-09 Shenghui Chen , Yagiz Savas , Mustafa O. Karabag , Brian M. Sadler , Ufuk Topcu

Although Bitcoin was intended to be a decentralized digital currency, in practice, mining power is quite concentrated. This fact is a persistent source of concern for the Bitcoin community. We provide an explanation using a simple model to…

Cryptography and Security · Computer Science 2018-11-22 Nick Arnosti , S. Matthew Weinberg

In this study, we examine the behavior and profitability of modern malware that mines cryptocurrency. Unlike previous studies, we look at the cryptocurrency market as a whole, rather than just Bitcoin. We not only consider PCs, but also…

Computers and Society · Computer Science 2019-01-31 Radhesh Krishnan Konoth , Rolf van Wegberg , Veelasha Moonsamy , Herbert Bos