Table of Links Abstract and 1. Introduction 2 Methodology 3 Hardware 4 Software 5 Network 6 Consensus 7 Cryptocurrency Economics 8 Client API 9 Governance 10 Geography 11 Case Studies 12 Discussion and References A. Decentralization and Policymaking B. Software Testing C. Brief Evaluations per Layer D. Measuring decentralization E. Fault Tolerance and Decentralization D Measuring decentralization Our work offers a framework for analyzing blockchain decentralization, but not specific metrics to quantitatively measure it. For example, a metric could assign a single number to reflect how close a system is to a single point of failure, given a distribution of resources over a set of relevant parties. Here, we briefly review some metrics, at a high level, and leave for future work the exploration of alternatives and the computations over real-world data. A first option is Shannon entropy [159]. Briefly, a random variable’s entropy measures the uncertainty of its possible outcomes. In our setting, the more bits of entropy in the resource distribution, the more diverse it is, thus the more decentralized the measured component is. Min-entropy, i.e., the smallest of the R´enyi family of entropies [150] can be also used instead since it also offers a lower bound. An alternative is the Gini coefficient [154]. Gini expresses the percentage of space between the 45o line and the curve that plots the cumulative wealth y owned by the bottom x of the population. Intuitively, a Gini value of 0 implies perfect equality, where each person owns the same amount of resources, while 1 reveals extreme inequality. Alternative metrics could also help evaluate different aspects of decentralization. Examples from traditional economics are the Theil [164], Atkinson [8], and Herfindahl-Hirschman [151] indices. Drawing from the blockchain space, an often-used metric is the Nakamoto coefficient [144], which measures the minimum number of parties that control a majority of resources. Nonetheless, a systematic comparison of all alternatives is an interesting question for future research. E Fault Tolerance and Decentralization Decentralization disperses control across a large set of parties. This is seemingly beneficial for Byzantine Fault Tolerant (BFT) systems. On the other hand, it may be counterproductive for other notions of faults. Specifically, the goal of BFT systems is to sustain corruptions of some (bounded) number of participants. Therefore, avoiding single points of failure and distributing the system’s operation is particularly useful in this context. The more decentralized a BFT system is, the more parties an adversary needs to corrupt. Non-BFT systems, which are e.g., crash fault tolerant, may not be able to sustain the corruption of any participant. In other words, even if a single participant behaves in a Byzantine manner, the system’s properties cannot be guaranteed. Thus, the more decentralized a non-BFT system is, the larger its attack surface. Therefore, its security relies on the security of the weakest participant. For larger numbers of participants, i.e., if the system is more decentralized, the likelihood that an adversary can corrupt any one participant typically increases, since participants often do not have the same level of security. Therefore, exploring the relationship between decentralization and fault tolerance, as well as the settings where decentralization is beneficial and those where it is not, is another interesting topic of future research. Authors:
(1) Christina Ovezik, University of Edinburgh (c.ovezik@ed.ac.uk);
(2) Dimitris Karakostas, University of Edinburgh (dkarakos@ed.ac.uk);
(3) Aggelos Kiayias, University of Edinburgh and IOG (akiayias@ed.ac.uk). This paper is available on arxiv under CC BY 4.0 DEED license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2 Methodology 2 Methodology 3 Hardware 3 Hardware 4 Software 4 Software 5 Network 5 Network 6 Consensus 6 Consensus 7 Cryptocurrency Economics 7 Cryptocurrency Economics 8 Client API 8 Client API 9 Governance 9 Governance 10 Geography 10 Geography 11 Case Studies 11 Case Studies 12 Discussion and References 12 Discussion and References A. Decentralization and Policymaking A. Decentralization and Policymaking B. Software Testing B. Software Testing C. Brief Evaluations per Layer C. Brief Evaluations per Layer D. Measuring decentralization D. Measuring decentralization E. Fault Tolerance and Decentralization E. Fault Tolerance and Decentralization D Measuring decentralization Our work offers a framework for analyzing blockchain decentralization, but not specific metrics to quantitatively measure it. For example, a metric could assign a single number to reflect how close a system is to a single point of failure, given a distribution of resources over a set of relevant parties. Here, we briefly review some metrics, at a high level, and leave for future work the exploration of alternatives and the computations over real-world data. A first option is Shannon entropy [159]. Briefly, a random variable’s entropy measures the uncertainty of its possible outcomes. In our setting, the more bits of entropy in the resource distribution, the more diverse it is, thus the more decentralized the measured component is. Min-entropy, i.e., the smallest of the R´enyi family of entropies [150] can be also used instead since it also offers a lower bound. An alternative is the Gini coefficient [154]. Gini expresses the percentage of space between the 45o line and the curve that plots the cumulative wealth y owned by the bottom x of the population. Intuitively, a Gini value of 0 implies perfect equality, where each person owns the same amount of resources, while 1 reveals extreme inequality. Alternative metrics could also help evaluate different aspects of decentralization. Examples from traditional economics are the Theil [164], Atkinson [8], and Herfindahl-Hirschman [151] indices. Drawing from the blockchain space, an often-used metric is the Nakamoto coefficient [144], which measures the minimum number of parties that control a majority of resources. Nonetheless, a systematic comparison of all alternatives is an interesting question for future research. E Fault Tolerance and Decentralization Decentralization disperses control across a large set of parties. This is seemingly beneficial for Byzantine Fault Tolerant (BFT) systems. On the other hand, it may be counterproductive for other notions of faults. Specifically, the goal of BFT systems is to sustain corruptions of some (bounded) number of participants. Therefore, avoiding single points of failure and distributing the system’s operation is particularly useful in this context. The more decentralized a BFT system is, the more parties an adversary needs to corrupt. Non-BFT systems, which are e.g., crash fault tolerant, may not be able to sustain the corruption of any participant. In other words, even if a single participant behaves in a Byzantine manner, the system’s properties cannot be guaranteed. Thus, the more decentralized a non-BFT system is, the larger its attack surface. Therefore, its security relies on the security of the weakest participant. For larger numbers of participants, i.e., if the system is more decentralized, the likelihood that an adversary can corrupt any one participant typically increases, since participants often do not have the same level of security. Therefore, exploring the relationship between decentralization and fault tolerance, as well as the settings where decentralization is beneficial and those where it is not, is another interesting topic of future research. Authors: (1) Christina Ovezik, University of Edinburgh (c.ovezik@ed.ac.uk); (2) Dimitris Karakostas, University of Edinburgh (dkarakos@ed.ac.uk); (3) Aggelos Kiayias, University of Edinburgh and IOG (akiayias@ed.ac.uk). Authors: Authors: (1) Christina Ovezik, University of Edinburgh (c.ovezik@ed.ac.uk); (2) Dimitris Karakostas, University of Edinburgh (dkarakos@ed.ac.uk); (3) Aggelos Kiayias, University of Edinburgh and IOG (akiayias@ed.ac.uk). This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv available on arxiv

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