Besides attracting a billion dollar economy, Bitcoin revolutionized the field of digital currencies and influenced many adjacent areas. This also induced significant scientific interest. In this survey, we unroll and structure the manyfold results and research directions. We start by introducing the Bitcoin protocol and its building blocks. From there we continue to explore the design space by discussing existing contributions and results. In the process, we deduce the fundamental structures and insights at the core of the Bitcoin protocol and its applications. As we show and discuss, many key ideas are likewise applicable in various other fields, so that their impact reaches far beyond Bitcoin itself.

Bitcoin and Beyond: A Technical Survey on Decentralized Digital Currencies

Bitcoin is a decentralized crypto-currency, and an accompanying protocol, created in 2008. Bitcoin nodes continuously generate and propagate blocks---collections of newly approved transactions that are added to Bitcoin's ledger. Block creation requires nodes to invest computational resources, but also carries a reward in the form of bitcoins that are paid to the creator. While the protocol requires nodes to quickly distribute newly created blocks, strong nodes can in fact gain higher payoffs by withholding blocks they create and selectively postponing their publication. The existence of such selfish mining attacks was first reported by Eyal and Sirer, who have demonstrated a specific deviation from the standard protocol (a strategy that we name SM1). 
In this paper we extend the underlying model for selfish mining attacks, and provide an algorithm to find $\epsilon$-optimal policies for attackers within the model, as well as tight upper bounds on the revenue of optimal policies. As a consequence, we are able to provide lower bounds on the computational power an attacker needs in order to benefit from selfish mining. We find that the profit threshold -- the minimal fraction of resources required for a profitable attack -- is strictly lower than the one induced by the SM1 scheme. Indeed, the policies given by our algorithm dominate SM1, by better regulating attack-withdrawals. 
Using our algorithm, we show that Eyal and Sirer's suggested countermeasure to selfish mining is slightly less effective than previously conjectured. Next, we gain insight into selfish mining in the presence of communication delays, and show that, under a model that accounts for delays, the profit threshold vanishes, and even small attackers have incentive to occasionally deviate from the protocol. We conclude with observations regarding the combined power of selfish mining and double spending attacks.

Optimal Selfish Mining Strategies in Bitcoin

Achieve faster and more efficient network design and optimization with this comprehensive guide. Some of the most prominent researchers in the field explain the very latest analytic techniques and results from stochastic geometry for modelling the signal-to-interference-plus-noise ratio (SINR) distribution in heterogeneous cellular networks. This book will help readers to understand the effects of combining different system deployment parameters on key performance indicators such as coverage and capacity, enabling the efficient allocation of simulation resources. In addition to covering results for network models based on the Poisson point process, this book presents recent results for when non-Poisson base station configurations appear Poisson, due to random propagation effects such as fading and shadowing, as well as non-Poisson models for base station configurations, with a focus on determinantal point processes and tractable approximation methods. Theoretical results are illustrated with practical Long-Term Evolution (LTE) applications and compared with real-world deployment results.

Stochastic Geometry Analysis of Cellular Networks

As low Earth orbit (LEO) satellite communication systems are gaining increasing popularity, new theoretical methodologies are required to investigate such networks’ performance at large. This is because deterministic and location-based models that have previously been applied to analyze satellite systems are typically restricted to support simulations only. In this paper, we derive analytical expressions for the downlink coverage probability and average data rate of generic LEO networks, regardless of the actual satellites’ locality and their service area geometry. Our solution stems from stochastic geometry, which abstracts the generic networks into uniform binomial point processes. Applying the proposed model, we then study the performance of the networks as a function of key constellation design parameters. Finally, to fit the theoretical modeling more precisely to real deterministic constellations, we introduce the effective number of satellites as a parameter to compensate for the practical uneven distribution of satellites on different latitudes. In addition to deriving exact network performance metrics, the study reveals several guidelines for selecting the design parameters for future massive LEO constellations, e.g., the number of frequency channels and altitude.

Downlink Coverage and Rate Analysis of Low Earth Orbit Satellite Constellations Using Stochastic Geometry

We study optimal geographic content placement for device-to-device (D2D) networks in which each file's popularity follows the Zipf distribution. The locations of the D2D users (caches) are modeled by a Poisson point process (PPP) and have limited communication range and finite storage. Inspired by the Matern hard-core (type II) point process that captures pairwise interactions between nodes, we devise a novel spatially correlated caching strategy called {\em hard-core placement} (HCP) such that the D2D nodes caching the same file are never closer to each other than the {\em exclusion radius}. The exclusion radius plays the role of a substitute for caching probability. We derive and optimize the exclusion radii to maximize the {\em hit probability}, which is the probability that a given D2D node can find a desired file at another node's cache within its communication range. Contrasting it with independent content placement, which is used in most prior work, our HCP strategy often yields a significantly higher cache hit probability. We further demonstrate that the HCP strategy is effective for small cache sizes and a small communication radius, which are likely conditions for D2D.

Spatially Correlated Content Caching for Device-to-Device Communications

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 belief about the blockchain of a small pool of miners and the `rest of the community' to establish that the use of block-hiding strategies, such as selfish-mine, causes the rate of production of orphan blocks to increase. Then we use a spatial Poisson process model to study values of Eyal and Sirer's parameter $\gamma$, which denotes the proportion of the honest community that mine on a previously-secret block released by the pool in response to the mining of a block by the honest community. Finally, we use discrete-event simulation to study the behaviour of a network of Bitcoin miners, a proportion of which is colluding in using the selfish-mine strategy, under the assumption that there is a propagation delay in the communication of information between miners.

Bitcoin Blockchain Dynamics: the Selfish-Mine Strategy in the Presence of Propagation Delay

A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical, and simulation techniques. It gives a new point process that can serve as a network model exhibiting repulsion. The properties and functions of the new point process, such as moment measures, the Laplace functional, the void probabilities, as well as conditional (Palm) characteristics can be estimated accurately by simulating the underlying (non-thinned) point process, which can be taken, for example, to be Poisson. This is in contrast (and preference to) finite Gibbs point processes, which, instead of thinning, require weighting the Poisson realizations, involving usually intractable normalizing constants. Models based on determinantal point processes are also well suited for statistical (supervised) learning techniques, allowing the models to be fitted to observed network patterns with some particular geometric properties. We illustrate this approach by imitating with determinantal thinning the well-known Mat{e}rn~II hard-core thinning, as well as a soft-core thinning depending on nearest-neighbour triangles. These two examples demonstrate how the proposed approach can lead to new, statistically optimized, probabilistic transmission scheduling schemes.

Determinantal thinning of point processes with network learning applications

Keeler, Ross and Xia (2016) recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation model can be modelled by an inhomogeneous Poisson point process on the positive real line. The basic requirement for the results to apply is that there must be a large number of transmitters with different locations and random propagation effects.The aim of this note is to apply some of the main results of Keeler, Ross and Xia (2016) in a less general but more easily applicable form to illustrate how the results can be applied in practice. New results are derived that show that it is the strongest signals, after being weakened by random propagation effects, that behave like a Poisson process, which supports recent experimental work.

Stronger wireless signals appear more Poisson

Keeler et al. recently derived approximation and convergence results, which imply that the point process formed from the signal strengths received by an observer in a wireless network under a general statistical propagation model can be modeled by an inhomogeneous Poisson point process on the positive real line. The basic requirement for the results to apply is that there must be a large number of transmitters with different locations and random propagation effects. The aim of this letter is to apply some of the main results in a less general but more easily applicable form to illustrate how the results can be applied in practice. New results are derived that show, it is the strongest signals, after being weakened by random propagation effects, that behave like a Poisson process, which supports recent experimental work.

Paul Keeler

Papers

Stochastic Geometry Analysis of Cellular Networks

Bitcoin Blockchain Dynamics: the Selfish-Mine Strategy in the Presence of Propagation Delay

Determinantal thinning of point processes with network learning applications

Stronger wireless signals appear more Poisson

Stronger Wireless Signals Appear More Poisson