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We introduce and study reward sharing schemes (RSS) that promote the fair formation of {\em stake pools}\ in collaborative projects that involve a large number of stakeholders such as the maintenance of a proof-of-stake (PoS) blockchain.…

Computer Science and Game Theory · Computer Science 2020-06-09 Lars Brünjes , Aggelos Kiayias , Elias Koutsoupias , Aikaterini-Panagiota Stouka

Blockchain systems are designed to produce blocks at a constant average rate. The most popular systems currently employ a Proof of Work (PoW) algorithm as a means of creating these blocks. Bitcoin produces, on average, one block every 10…

Cryptography and Security · Computer Science 2019-08-15 George Bissias , Brian Neil Levine

The resource-consuming mining of blocks on a blockchain equipped with a proof of work consensus protocol bears the risk of ruin, namely when the operational costs for the mining exceed the received rewards. In this paper we investigate to…

Cryptography and Security · Computer Science 2021-09-08 Hansjoerg Albrecher , Dina Finger , Pierre-Olivier Goffard

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

Bitcoin's Proof of Work (PoW) mechanism, while central to achieving decentralized consensus, has long been criticized for excessive energy use and hardware inefficiencies \cite{devries2018bitcoin, truby2018decarbonizing}. This paper…

Cryptography and Security · Computer Science 2025-08-19 Mohammad Ishzaz Asif Rafid , Morsalin Sakib

Bitcoin is a popular cryptocurrency that records alltransactions in a distributed append-only public ledger calledblockchain. The security of Bitcoin heavily relies on the incentive-compatible proof-of-work (PoW) based distributed consensus…

Cryptography and Security · Computer Science 2018-06-05 Mauro Conti , Sandeep Kumar E , Chhagan Lal , Sushmita Ruj

In this paper, we provide a novel dynamic decision method of blockchain selfish mining by applying the sensitivity-based optimization theory. Our aim is to find the optimal dynamic blockchain-pegged policy of the dishonest mining pool. To…

Cryptography and Security · Computer Science 2021-11-16 Jing-Yu Ma , Quan-Lin Li

In a Proof-of-Work blockchain such as Bitcoin mining hashrate is increasing in the block reward. An increase in hashrate reduces network vulnerability to attack (a reduction in security cost) while increasing carbon emissions and…

Cryptography and Security · Computer Science 2025-08-25 Daniel Aronoff

Decentralized data-feed systems enable blockchain-based smart contracts to access off-chain information by aggregating values from multiple oracles. To improve accuracy, these systems typically use an aggregation function, such as majority…

Computer Science and Game Theory · Computer Science 2025-09-16 Sina Aeeneh , Nikola Zlatanov , Jiangshan Yu

Several emerging PoW blockchain protocols rely on a "parallel-chain" architecture for scaling, where instead of a single chain, multiple chains are run in parallel and aggregated. A key requirement of practical PoW blockchains is to adapt…

Cryptography and Security · Computer Science 2021-05-11 Xuechao Wang , Viswa Virinchi Muppirala , Lei Yang , Sreeram Kannan , Pramod Viswanath

Bitcoin blockchain uses hash-based Proof-of-Work (PoW) that prevents unwanted participants from hogging the network resources. Anyone entering the mining game has to prove that they have expended a specific amount of computational power.…

Cryptography and Security · Computer Science 2025-04-22 Diptendu Chatterjee , Avishek Majumder , Subhra Mazumdar

We revisit the longstanding open problem of implementing Nakamoto's proof-of-work (PoW) consensus based on a real-world computational task $T(x)$ (as opposed to artificial random hashing), in a truly permissionless setting where the miner…

Cryptography and Security · Computer Science 2025-11-14 Ilan Komargodski , Omri Weinstein

Conventional double-spending attack models ignore the revenue losses stemming from the orphan blocks. On the other hand, selfish mining literature usually ignores the chance of the attacker to double-spend at no-cost in each attack cycle.…

Cryptography and Security · Computer Science 2026-03-23 Mustafa Doger , Sennur Ulukus

Mining fairness in blockchain refers to equality between the computational resources invested in mining and the block rewards received. There exists a dilemma wherein increasing the transaction processing capacity of a blockchain…

Cryptography and Security · Computer Science 2025-09-10 Akira Sakurai , Kazuyuki Shudo

In this paper, the authors propose to increase the efficiency of blockchain mining by using a population-based approach. Blockchain relies on solving difficult mathematical problems as proof-of-work within a network before blocks are added…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-27 Tosin P. Adewumi , Marcus Liwicki

Blockchain-based cryptocurrencies, such as Bitcoin, have seen on the rise in their popularity and value, making them a target to several forms of Denial-of-Service (DoS) attacks, and calling for a better understanding of their attack…

Cryptography and Security · Computer Science 2021-01-05 Muhammad Saad , Joongheon Kim , DaeHun Nyang , David Mohaisen

Blockchain is a technology that provides a distributed ledger that stores previous records while maintaining consistency and security. Bitcoin is the first and largest decentralized electronic cryptographic system that uses blockchain…

Cryptography and Security · Computer Science 2021-11-05 Befekadu G. Gebraselase , Bjarne E. Helvik , Yuming Jiang

We study an adversary who attacks a Proof-of-Work (POW) blockchain by selfishly constructing an alternative longest chain. We characterize optimal strategies employed by the adversary when a difficulty adjustment rule al\`a Bitcoin applies.…

Cryptography and Security · Computer Science 2023-08-30 Tzuo Hann Law , Selman Erol , Lewis Tseng

Proof-of-Work (PoW) is the most widely adopted incentive model in current blockchain systems, which unfortunately is energy inefficient. Proof-of-Stake (PoS) is then proposed to tackle the energy issue. The rich-get-richer concern of PoS…

Cryptography and Security · Computer Science 2021-03-31 Yuming Huang , Jing Tang , Qianhao Cong , Andrew Lim , Jianliang Xu

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