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Rapidly growing distributed ledger technologies (DLTs) have recently received attention among researchers in both industry and academia. While a lot of existing analysis (mainly) of the Bitcoin and Ethereum networks is available, the lack of measurements for other crypto projects is observed. This article addresses questions about tokenomics and wealth distributions in cryptocurrencies. We analyze the time-dependent statistical properties of top cryptocurrency holders for 14 different distributed ledger projects. The provided metrics include approximated Zipf coefficient, Shannon entropy, Gini coefficient, and Nakamoto coefficient. We show that there are quantitative differences between the coins (cryptocurrencies operating on their own independent network) and tokens (which operate on top of a smart contract platform). Presented results show that coins and tokens have different values of approximated Zipf coefficient and centralization levels. This work is relevant for DLTs as it might be useful in modeling and improving the committee selection process, especially in decentralized autonomous organizations (DAOs) and delegated proof of stake (DPoS) blockchains., Comment: 5 figures

The security of any Distributed Ledger Technology (DLT) depends on the safety of the network layer. Much effort has been put into understanding the consensus layer of DLTs. However, many network layer designs seem ad-hoc and lack a careful analysis of the influence of the design decisions on the whole DLT system. We propose a salt-based automated neighbor selection protocol that shows the inherent tradeoffs of certain design decisions and allows a quantitative treatment of some network topology requirements. This example may serve as a design framework and facilitate future research. We provide a selection of results from simulations to highlight some tradeoffs in the design decisions., Comment: 4 pages

Number of zeros seen by a particle around small clusters of other particles is encoded in the root partition, and partly characterizes the correlations in fractional quantum Hall trial wavefunctions. We explore a generalization wherein we consider the counting of zeros seen by a cluster of particles on another cluster. Numbers of such zeros between clusters in the Laughlin wavefunctions are fully determined by the root partition. However, such a counting is unclear for general Jain states where a polynomial expansion is difficult. Here we consider the simplest state beyond the Laughlin wavefunction, namely a state containing a single quasiparticle of the Laughlin state. We show numerically and analytically that in the trial wavefunction for the quasiparticle of the Laughlin state, counting of zeros seen by a cluster on another cluster depends on the relative dimensions of the two clusters. We further ask if the patterns in the counting of zeros extend, in at least an approximate sense, to wavefunctions beyond the trial states. Using numerical computations in systems up to $N=9$, we present results for the statistical distribution of zeros around particle clusters at the center of an FQH droplet in the ground state of a Hamiltonian that is perturbed away from the $V_1$ interaction (short-range repulsion). Evolution of this distribution with the strength of the perturbation shows that the counting of zeros is altered by even a weak perturbation away from the parent Hamiltonian, though the perturbations do not change the phase of the system., Comment: 14 pages, 11 figures

In this paper, we propose several solutions to the committee selection problem among participants of a DAG distributed ledger. Our methods are based on a ledger intrinsic reputation model that serves as a selection criterion. The main difficulty arises from the fact that the DAG ledger is a priori not totally ordered and that the participants need to reach a consensus on participants' reputation. Furthermore, we outline applications of the proposed protocols, including: (i) self-contained decentralized random number beacon; (ii) selection of oracles in smart contracts; (iii) applications in consensus protocols and sharding solutions. We conclude with a discussion on the security and liveness of the proposed protocols by modeling reputation with a Zipf law.

The fast probabilistic consensus (FPC) is a voting consensus protocol that is robust and efficient in Byzantine infrastructure. We propose an adaption of the FPC to a setting where the voting power is proportional to the nodes reputations. We model the reputation using a Zipf law and show using simulations that the performance of the protocol in Byzantine infrastructure increases with the Zipf exponent. Moreover, we propose several improvements of the FPC that decrease the failure rates significantly and allow the protocol to withstand adversaries with higher weight. We distinguish between cautious and berserk strategies of the adversaries and propose an efficient method to detect the more harmful berserk strategies. Our study refers at several points to a specific implementation of the IOTA protocol, but the principal results hold for general implementations of reputation models.

In recent years several distributed ledger technologies based on directed acyclic graphs (DAGs) have appeared on the market. Similar to blockchain technologies, DAG-based systems aim to build an immutable ledger and are faced with security concerns regarding the irreversibility of the ledger state. However, due to their more complex nature and recent popularity, the study of adversarial actions has received little attention so far. In this paper we are concerned with a particular type of attack on the IOTA cryptocurrency, more specifically a Parasite Chain attack that attempts to revert the history stored in the DAG structure, also called the Tangle. In order to improve the security of the Tangle, we present a detection mechanism for this type of attack. In this mechanism, we embrace the complexity of the DAG structure by sampling certain aspects of it, more particularly the distribution of the number of approvers. We initially describe models that predict the distribution that should be expected for a Tangle without any malicious actors. We then introduce metrics that compare this reference distribution with the measured distribution. Upon detection, measures can then be taken to render the attack unsuccessful. We show that due to a form of the Parasite Chain that is different from the main Tangle it is possible to detect certain types of malicious chains. We also show that although the attacker may change the structure of the Parasite Chain to avoid detection, this is done so at a significant cost since the attack is rendered less efficient., Comment: Accepted for publication at Tokenomics 2020, Toulouse, France

The growing number of applications for distributed ledger technologies is driving both industry and academia to solve the limitations of blockchain, particularly its scalability issues. Recent distributed ledger technologies have replaced the blockchain linear structure with a more flexible directed acyclic graph in an attempt to accommodate a higher throughput. Despite the fast-growing diffusion of directed acyclic graph based distributed ledger technologies, researchers lack a basic understanding of their behavior. In this paper we analyze the Tangle, a directed acyclic graph that is used (with certain modifications) in various protocols such as IOTA, Byteball, Avalanche or SPECTRE. Our contribution is threefold. First, we run simulations in a continuous-time model to examine tip count stability and cumulative weight evolution while varying the rate of incoming transactions. In particular we confirm analytical predictions on the number of tips with uniform random tip selection strategy. Second, we show how different tip selection algorithms affect the growth of the Tangle. Moreover, we explain these differences by analyzing the spread of exit probabilities of random walks. Our findings confirm analytically derived predictions and provide novel insights on the different phases of growth of cumulative weight as well as on the average time difference for a transaction to receive its first approval when using distinct tip selection algorithms. Lastly, we analyze simulation overhead and performance as a function of Tangle size and compare results for different tip selection algorithms., Comment: Published in: 2019 IEEE International Conference on Blockchain (Blockchain)

Trial wavefunctions like the Moore-Read and Read-Rezayi states which minimize short range multibody interactions are candidate states for describing the fractional quantum Hall effects at filling factors $\nu = 1/2$ and $\nu = 2/5$ in the second Landau level. These trial wavefunctions are unique zero energy states of three body and four body interaction Hamiltonians respectively but are not close to the ground states of the Coulomb interaction. Previous studies using extensive parameter scans have found optimal two body interactions that produce states close to these. Here we focus on short ranged four body interaction and study two mean field approximations that reduce the four body interactions to two body interactions by replacing composite operators with their incompressible ground state expectation values. We present the results for pseudopotentials of these approximate interactions. Comparison of finite system spectra of the four body and the approximate interactions at filling fraction $\nu=3/5$ show that these approximations produce good effective descriptions of the low energy structure of the four body ineraction Hamiltonian. The approach also independently reproduces the optimal two body interaction inferred from parameter scans. We also show that for $n=3$, but not for $n=4$, the mean field approximations of the $n$-body interaction is equivalent to particle hole symmetrization of the interaction., Comment: 12 pages

The family of "Jack states" related to antisymmetric Jack polynomials are the exact zero-energy ground states of particular model short-range {\em many-body} repulsive interactions, defined by a few non-vanishing leading pseudopotentials. Some Jack states are known or anticipated to accurately describe many-electron incompressible ground states emergent from the {\em two-body} Coulomb repulsion in fractional quantum Hall effect. By extensive numerical diagonalization we demonstrate emergence of Jack states from suitable pair interactions. We find empirically a simple formula for the optimal two-body pseudopotentials for the series of most prominent Jack states generated by {\em contact} many-body repulsion. Furthermore, we seek realization of arbitrary Jack states in realistic quantum Hall systems with Coulomb interaction, i.e., in partially filled lowest and excited Landau levels in quasi-two-dimensional layers of conventional semiconductors like GaAs or in graphene., Comment: 12 pages, 11 figures