Showing papers by "Amir Dembo published in 2020"
30 Oct 2020
TL;DR: The security analysis of three classes of longest chain protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes, resulting in exact characterization of the maximum tolerable adversary power for each protocol as a function of the average block time normalized by the network delay.
Abstract: Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes.
75 citations
TL;DR: The leading order of the exponential rate function for the probability that the number of copies of H in the Erdős-Renyi graph G ( n, p ) exceeds its expectation by a factor 1 + u, assuming n − κ ( H ) ≪ p ≪ 1, with κ( H ) = 1 / ( 2 Δ ), where Δ ≥ 1 is the maximum degree of H.
54 citations
TL;DR: In this article, the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed p-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the Gibbs measure concentrates at low temperature for the pure P-spin models and mixed perturbations of them, was derived.
Abstract: We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed p-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the Gibbs measure concentrates at low temperature for the pure p-spin models and mixed perturbations of them. We further relate the large time asymptotics of the resulting coupled non-linear integro-differential equations, to the geometric structure of the Gibbs measures (at low temperature), and derive their FDT solution (at high temperature).
11 citations
TL;DR: For any centered stationary Gaussian process of integrable covariance, whose spectral measure has compact support, or finite exponential moments (and some additional regularity), the number of zeros of the process in $[0,T]$ is within ε T$ of its mean value, up to an exponentially small in $T$ probability as discussed by the authors.
Abstract: We show that for any centered stationary Gaussian process of integrable covariance, whose spectral measure has compact support, or finite exponential moments (and some additional regularity), the number of zeroes of the process in $[0,T]$ is within $\eta T$ of its mean value, up to an exponentially small in $T$ probability.
8 citations
Posted Content•
TL;DR: In this article, the authors show that the trajectories of averaged observables of a dynamical system with random coefficients are universal, i.e., only depend on the choice of the distribution through its first and second moments.
Abstract: Consider $(X_{i}(t))$ solving a system of $N$ stochastic differential equations interacting through a random matrix $\mathbf J = (J_{ij})$ with independent (not necessarily identically distributed) random coefficients. We show that the trajectories of averaged observables of $(X_i(t))$, initialized from some $\mu$ independent of $\mathbf J$, are universal, i.e., only depend on the choice of the distribution $\mathbf{J}$ through its first and second moments (assuming e.g., sub-exponential tails). We take a general combinatorial approach to proving universality for dynamical systems with random coefficients, combining a stochastic Taylor expansion with a moment matching-type argument. Concrete settings for which our results imply universality include aging in the spherical SK spin glass, and Langevin dynamics and gradient flows for symmetric and asymmetric Hopfield networks.
3 citations
Posted Content•
TL;DR: In this article, the authors consider three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol, 2) Ouroboros and SnowWhite Proof of Stake protocols, 3) Chia Protocol.
Abstract: Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes.
2 citations