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Related papers: The mathematics of Bitcoin

200 papers

This paper presents a stochastic model for block arrival times based on the difficulty retargeting rule used in Bitcoin, as well as other proof-of-work blockchains. Unlike some previous work, this paper explicitly models the difficulty…

Cryptography and Security · Computer Science 2018-12-31 Daniel Fullmer , A. S. Morse

The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth…

Cryptography and Security · Computer Science 2019-11-25 Erica Blum , Aggelos Kiayias , Cristopher Moore , Saad Quader , Alexander Russell

Bitcoin, as one of the most popular cryptocurrency, is recently attracting much attention of investors. Bitcoin price prediction task is consequently a rising academic topic for providing valuable insights and suggestions. Existing bitcoin…

Statistical Finance · Quantitative Finance 2020-08-25 Xiao Li , Weili Wu

In this work, we propose to apply a new model fusion and learning paradigm, known as Combinatorial Fusion Analysis (CFA), to the field of Bitcoin price prediction. Price prediction of financial product has always been a big topic in…

Statistical Finance · Quantitative Finance 2026-03-10 Yuanhong Wu , Wei Ye , Jingyan Xu , D. Frank Hsu

The Bitcoin transaction graph is a public data structure organized as transactions between addresses, each associated with a logical entity. In this work, we introduce a complete probabilistic model of the Bitcoin Blockchain. We first…

Cryptography and Security · Computer Science 2018-12-14 Marc Jourdan , Sebastien Blandin , Laura Wynter , Pralhad Deshpande

We show that the behaviour of Bitcoin has interesting similarities to stock and precious metal markets, such as gold and silver. We report that whilst Litecoin, the second largest cryptocurrency, closely follows Bitcoin's behaviour, it does…

Statistical Finance · Quantitative Finance 2014-11-10 Daniel Wilson-Nunn , Hector Zenil

Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^{\beta}$ with $\hat\beta \approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant…

Applications · Statistics 2026-05-21 Carlos Baquero , Raquel Menezes

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

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

Blockchain systems run consensus rules as code to agree on the state of the distributed ledger and secure the network. Changing these rules can be risky and challenging. In addition, it can often be controversial and take much effort to…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-02-15 Jakob Svennevik Notland , Mariusz Nowostawski , Jingyue Li

Increasingly machine learning systems are being deployed to edge servers and devices (e.g. mobile phones) and trained in a collaborative manner. Such distributed/federated/decentralized training raises a number of concerns about the…

Machine Learning · Computer Science 2020-10-20 Lie He , Sai Praneeth Karimireddy , Martin Jaggi

Ethereum has undergone a recent change called \textit{the Merge}, which made Ethereum a Proof-of-Stake blockchain, shifting closer to BFT consensus. Ethereum, which wished to keep the best of the two protocol designs (BFT and…

Cryptography and Security · Computer Science 2023-09-15 Ulysse Pavloff , Yackolley Amoussou-Guenou , Sara Tucci-Piergiovanni

This paper introduces a structural game-theoretic model to value decentralized digital assets like Bitcoin. Instead of relying on speculative beliefs, it frames the asset's price within a Rational-Expectations Security-Utility Nash…

Cryptography and Security · Computer Science 2025-08-12 Liang Chen

Blockchains have sparked global interest in recent years, gaining importance as they increasingly influence technology and finance. This thesis investigates the robustness of blockchain protocols, specifically focusing on Ethereum…

Cryptography and Security · Computer Science 2024-12-02 Ulysse Pavloff

After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner,…

Quantum Physics · Physics 2011-03-02 Roger Colbeck

A collection of questions about Bitcoin and its hypothetical relatives Bitguilder and Bitpenny is formulated. These questions concern technical issues about protocols, security issues, issues about the formalizations of informational monies…

Computers and Society · Computer Science 2013-12-30 Jan A. Bergstra , Karl de Leeuw

Bitcoins have recently become an increasingly popular cryptocurrency through which users trade electronically and more anonymously than via traditional electronic transfers. Bitcoin's design keeps all transactions in a public ledger. The…

Cryptography and Security · Computer Science 2015-02-06 Michael Fleder , Michael S. Kester , Sudeep Pillai

Bitcoin operates as a macroeconomic paradox: it combines a strictly predetermined, inelastic monetary issuance schedule with a stochastic, highly elastic demand for scarce block space. This paper empirically validates the Endogenous…

Statistical Finance · Quantitative Finance 2025-12-10 Hamoon Soleimani

In this literature review, we first briefly provide an introduction on the privacy aspect of blockchain systems and why it is a difficult quality to achieve, especially using traditional methods. Next, we go over a wide range of different…

Cryptography and Security · Computer Science 2018-09-28 Jad Wahab

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