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Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic…

Cryptography and Security · Computer Science 2025-11-20 Bin Chen

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

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

In Proof-of-Work blockchains, difficulty algorithms serve the crucial purpose of maintaining a stable transaction throughput by dynamically adjusting the block difficulty in response to the miners' constantly changing computational power.…

Cryptography and Security · Computer Science 2021-05-03 Dragos I. Ilie , Sam M. Werner , Iain Stewart , William J. Knottenbelt

Distributed ledger technologies have opened up a wealth of fine-grained transaction data from cryptocurrencies like Bitcoin and Ethereum. This allows research into problems like anomaly detection, anti-money laundering, pattern mining and…

Social and Information Networks · Computer Science 2024-10-07 Naomi A. Arnold , Peijie Zhong , Cheick Tidiane Ba , Ben Steer , Raul Mondragon , Felix Cuadrado , Renaud Lambiotte , Richard G. Clegg

We prove Bitcoin is secure under temporary dishonest majority. We assume the adversary can corrupt a specific fraction of parties and also introduce crash failures, i.e., some honest participants are offline during the execution of the…

Cryptography and Security · Computer Science 2019-08-02 Georgia Avarikioti , Lukas Kaeppeli , Yuyi Wang , Roger Wattenhofer

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

Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of…

Statistical Finance · Quantitative Finance 2021-12-15 Andrés García-Medina , Toan Luu Duc Huynh3

Proof-of-work allows Bitcoin to boast security amidst arbitrary fluctuations in participation of miners throughout time, so long as, at any point in time, a majority of hash power is honest. In recent years, however, the pendulum has…

Cryptography and Security · Computer Science 2025-08-12 Yuval Efron , Joachim Neu , Toniann Pitassi

We investigate a stationary process's crypticity---a measure of the difference between its hidden state information and its observed information---using the causal states of computational mechanics. Here, we motivate crypticity and cryptic…

Data Analysis, Statistics and Probability · Physics 2015-05-30 John R. Mahoney , Christopher J. Ellison , Ryan G. James , James P. Crutchfield

Bitcoin is a electronic payment system where payment transactions are verified and stored in a data structure called the blockchain. Bitcoin miners work individually to solve a computationally intensive problem, and with each solution a…

Cryptography and Security · Computer Science 2018-01-24 R. Bowden , H. P. Keeler , A. E. Krzesinski , P. G. Taylor

Bitcoin provides freshness properties by forming a blockchain where each block is associated with its timestamp and the previous block. Due to these properties, the Bitcoin protocol is being used as a decentralized, trusted, and secure…

Cryptography and Security · Computer Science 2018-05-21 Pawel Szalachowski

We study the probabilistic distribution of the confirmation time of Bitcoin transactions, conditional on the current memory pool (i.e., the queue of transactions awaiting confirmation). The results of this paper are particularly interesting…

Performance · Computer Science 2018-10-22 David Koops

As distributed ledgers, blockchains run consensus protocols which trade capacity for consistency, especially in non-ideal networks with incomplete connectivity and erroneous links. Existing studies on the tradeoff between capacity and…

Cryptography and Security · Computer Science 2021-06-29 Xu Wang , Wei Ni , Xuan Zha , Guangsheng Yu , Ren Ping Liu , Nektarios Georgalas , Andrew Reeves

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

Blockchain offers a decentralized, immutable, transparent system of records. It offers a peer-to-peer network of nodes with no centralised governing entity making it unhackable and therefore, more secure than the traditional paper-based or…

Cryptography and Security · Computer Science 2019-11-27 Harsh Jot Singh , Abdelhakim Senhaji Hafid

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

A new variation of blockchain proof of work algorithm is proposed to incentivize the timely execution of image processing algorithms. A sample image processing algorithm is proposed to determine interesting images using analysis of the…

Cryptography and Security · Computer Science 2017-07-17 Jake Billings

Bitcoin is the most successful cryptocurrency so far. This is mainly due to its novel consensus algorithm, which is based on proof-of-work combined with a cryptographically-protected data structure and a rewarding scheme that incentivizes…

Cryptography and Security · Computer Science 2019-05-24 Pawel Szalachowski , Daniel Reijsbergen , Ivan Homoliak , Siwei Sun

The functioning of the cryptocurrency Bitcoin relies on the open availability of the entire history of its transactions. This makes it a particularly interesting socio-economic system to analyse from the point of view of network science.…

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