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The security of blockchain protocols is a combination of two properties: safety and liveness. It is well known that no blockchain protocol can provide both to sleepy (intermittently online) clients under adversarial majority. However, safety is more critical in that a single safety violation can cause users to lose money. At the same time, liveness must not be lost forever. We show that, in a synchronous network, it is possible to maintain safety for all clients even during adversarial majority, and recover liveness after honest majority is restored. Our solution takes the form of a recovery gadget that can be applied to any protocol with certificates (such as HotStuff, Streamlet, Tendermint, and their variants).

Classic BFT consensus protocols guarantee safety and liveness for all clients if fewer than one-third of replicas are faulty. However, in applications such as high-value payments, some clients may want to prioritize safety over liveness. Flexible consensus allows each client to opt for a higher safety resilience, albeit at the expense of reduced liveness resilience. We present the first construction that allows optimal safety--liveness tradeoff for every client simultaneously. This construction is modular and is realized as an add-on applied on top of an existing consensus protocol. The add-on consists of an additional round of voting and permanent locking done by the replicas, to sidestep a sub-optimal quorum-intersection-based constraint present in previous solutions. We adapt our construction to the existing Ethereum protocol to derive optimal flexible confirmation rules that clients can adopt unilaterally without requiring system-wide changes. This is possible because existing Ethereum protocol features can double as the extra voting and locking. We demonstrate an implementation using Ethereum's consensus API., Comment: To be published at the IEEE Symposium on Security & Privacy 2024

The InterPlanetary File System (IPFS) is currently the largest decentralized storage solution in operation, with thousands of active participants and millions of daily content transfers. IPFS is used as remote data storage for numerous blockchain-based smart contracts, Non-Fungible Tokens (NFT), and decentralized applications. We present a content censorship attack that can be executed with minimal effort and cost, and that prevents the retrieval of any chosen content in the IPFS network. The attack exploits a conceptual issue in a core component of IPFS, the Kademlia Distributed Hash Table (DHT), which is used to resolve content IDs to peer addresses. We provide efficient detection and mitigation mechanisms for this vulnerability. Our mechanisms achieve a 99.6\% detection rate and mitigate 100\% of the detected attacks with minimal signaling and computational overhead. We followed responsible disclosure procedures, and our countermeasures are scheduled for deployment in the future versions of IPFS., Comment: 17 pages (including references and appendices), 15 figures. Accepted to be published at the Network and Distributed System Security (NDSS) Symposium 2024

For Nakamoto's longest-chain consensus protocol, whose proof-of-work (PoW) and proof-of-stake (PoS) variants power major blockchains such as Bitcoin and Cardano, we revisit the classic problem of the security-performance tradeoff: Given a network of nodes with finite communication- and computation-resources, against what fraction of adversary power is Nakamoto consensus (NC) secure for a given block production rate? State-of-the-art analyses of NC fail to answer this question, because their bounded-delay model does not capture the rate limits to nodes' processing of blocks, which cause congestion when blocks are released in quick succession. We develop a new analysis technique to prove a refined security-performance tradeoff for PoW NC in a bounded-capacity model. In this model, we show that, in contrast to the classic bounded-delay model, Nakamoto's private attack is no longer the worst attack, and a new attack we call the teasing strategy, that exploits congestion, is strictly worse. In PoS, equivocating blocks can exacerbate congestion, making traditional PoS NC insecure except at very low block production rates. To counter such equivocation spamming, we present a variant of PoS NC we call Blanking NC (BlaNC), which achieves the same resilience as PoW NC., Comment: ACM Conference on Computer and Communications Security (CCS) 2024

Spamming attacks are a serious concern for consensus protocols, as witnessed by recent outages of a major blockchain, Solana. They cause congestion and excessive message delays in a real network due to its bandwidth constraints. In contrast, longest chain (LC), an important family of consensus protocols, has previously only been proven secure assuming an idealized network model in which all messages are delivered within bounded delay. This model-reality mismatch is further aggravated for Proof-of-Stake (PoS) LC where the adversary can spam the network with equivocating blocks. Hence, we extend the network model to capture bandwidth constraints, under which nodes now need to choose carefully which blocks to spend their limited download budget on. To illustrate this point, we show that 'download along the longest header chain', a natural download rule for Proof-of-Work (PoW) LC, is insecure for PoS LC. We propose a simple rule 'download towards the freshest block', formalize two common heuristics 'not downloading equivocations' and 'blocklisting', and prove in a unified framework that PoS LC with any one of these download rules is secure in bandwidth-constrained networks. In experiments, we validate our claims and showcase the behavior of these download rules under attack. By composing multiple instances of a PoS LC protocol with a suitable download rule in parallel, we obtain a PoS consensus protocol that achieves a constant fraction of the network's throughput limit even under worst-case adversarial strategies.

In this work, we consider the deterministic optimization using random projections as a statistical estimation problem, where the squared distance between the predictions from the estimator and the true solution is the error metric. In approximately solving a large scale least squares problem using Gaussian sketches, we show that the sketched solution has a conditional Gaussian distribution with the true solution as its mean. Firstly, tight worst case error lower bounds with explicit constants are derived for any estimator using the Gaussian sketch, and the classical sketching is shown to be the optimal unbiased estimator. For biased estimators, the lower bound also incorporates prior knowledge about the true solution. Secondly, we use the James-Stein estimator to derive an improved estimator for the least squares solution using the Gaussian sketch. An upper bound on the expected error of this estimator is derived, which is smaller than the error of the classical Gaussian sketch solution for any given data. The upper and lower bounds match when the SNR of the true solution is known to be small and the data matrix is well conditioned. Empirically, this estimator achieves smaller error on simulated and real datasets, and works for other common sketching methods as well., Comment: This work has been submitted to the IEEE Journal on Selected Areas in Information Theory (JSAIT) - Special Issue on Estimation and Inference, and is awaiting review. This document contains 37 pages and 14 figures

A photometric redshift sample of Luminous Red Galaxies (hereafter LRGs) obtained from The DECam Legacy Survey (DECaLS) is analysed to probe cosmic distances by exploiting the wedge approach of the two-point correlation function. Although the cosmological information is highly contaminated by the uncertainties existing in the photometric redshifts from the galaxy map, an angular diameter distance can be probed at the perpendicular configuration in which the measured correlation function is minimally contaminated. An ensemble of wedged correlation functions selected up to a given threshold based on having the least contamination was studied in the previous work (arXiv:1903.09651v2 [astro-ph.CO]) using simulations, and the extracted cosmological information was unbiased within this threshold. We apply the same methodology for analysing the LRG sample from DECaLS which will provide the optical imaging for targeting two-thirds of the DESI footprint and measure the angular diameter distances at $z=0.69$ and $z=0.87$ to be $D_{A}(0.697)=(1499 \pm 77\,\mathrm{Mpc})(r_{d}/r_{d,fid})$ and $D_{A}(0.874)=(1680 \pm 109\,\mathrm{Mpc})(r_{d}/r_{d,fid})$ with a fractional error of 5.14% and 6.48% respectively. We obtain a value of $H_{0}=67.59\pm5.52$ km/s/Mpc which supports the $H_0$ measured by all other BAO results and is consistent with $\Lambda$CDM model., Comment: 18 pages, 8 figures, DESI publication board APPROVED, submitted to ApJ

The galaxy distributions along the line-of-sight are significantly contaminated by the uncertainty on redshift measurements obtained through multiband photometry, which makes it difficult to get cosmic distance information measured from baryon acoustic oscillations, or growth functions probed by redshift distortions. We investigate the propagation of the uncertainties into large scale clustering by exploiting all known estimators, and propose the wedge approach as a promising analysis tool to extract cosmic distance information still remaining in the photometric galaxy samples. We test our method using simulated galaxy maps with photometric uncertainties of $\sigma_{0} =\left(0.01, 0.02, 0.03\right)$. The measured anisotropy correlation function $\xi$ is binned into the radial direction of $s$ and the angular direction of $\mu$, and the variations of $\xi(s,\mu)$ with perpendicular and radial cosmic distance measures of $D_A$ and $H^{-1}$ are theoretically estimated by an improved RSD model. Although the radial cosmic distance $H^{-1}$ is unable to be probed from any of the three photometric galaxy samples, the perpendicular component of $D_A$ is verified to be accurately measured even after the full marginalisation of $H^{-1}$. We measure $D_A$ with approximately 6% precision which is nearly equivalent to what we can expect from spectroscopic DR12 CMASS galaxy samples., Comment: 11 pages, 8 figures, MNRAS published New Figure 8 with constraints expected from upcoming surveys (LSST, Euclid)

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at $z < 1$, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at $2 < z < 5$, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $\sigma(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space., Comment: Science white paper submitted to the Astro2020 Decadal Survey

While Type Ia Supernovae (SNe Ia) are one of the most mature cosmological probes, the next era promises to be extremely exciting in the number of different ways SNe Ia are used to measure various cosmological parameters. Here we review the experiments in the 2020s that will yield orders of magnitudes more SNe Ia, and the new understandings and capabilities to constrain systematic uncertainties at a level to match these statistics. We then discuss five different cosmological probes with SNe Ia: the conventional Hubble diagram for measuring dark energy properties, the distance ladder for measuring the Hubble constant, peculiar velocities and weak lensing for measuring sigma8 and strong-lens measurements of H0 and other cosmological parameters. For each of these probes, we discuss the experiments that will provide the best measurements and also the SN Ia-related systematics that affect each one., Comment: Science White paper submitted to Astro2020 Decadal Survey. Additional co-authors added

Astrophysical observations currently provide the only robust, empirical measurements of dark matter. In the coming decade, astrophysical observations will guide other experimental efforts, while simultaneously probing unique regions of dark matter parameter space. This white paper summarizes astrophysical observations that can constrain the fundamental physics of dark matter in the era of LSST. We describe how astrophysical observations will inform our understanding of the fundamental properties of dark matter, such as particle mass, self-interaction strength, non-gravitational interactions with the Standard Model, and compact object abundances. Additionally, we highlight theoretical work and experimental/observational facilities that will complement LSST to strengthen our understanding of the fundamental characteristics of dark matter., Comment: 11 pages, 2 figures, Science Whitepaper for Astro 2020, more information at https://lsstdarkmatter.github.io

We investigate to which accuracy it is possible to recover the real-space two-point correlation function of galaxy clusters from cluster catalogues based on photometric redshifts, and test our ability to measure the redshift and mass evolution of the correlation length and the bias parameter as a function of the redshift uncertainty. We calculate the correlation function for cluster sub-samples covering various mass and redshift bins selected from a light-cone catalogue. To simulate the distribution of clusters in photometric redshift space, we assign to each cluster a redshift randomly extracted from a Gaussian distribution. The dispersion is varied in the range $\sigma_{(z=0)} = 0.001$ to $0.050$. The correlation function in real-space is computed through estimation and deprojection of $w_{p}(r_{p})$. Four mass ranges (from $M_{halo}> 2 \times 10^{13}$ to $M_{halo}> 2 \times 10^{14}$) and six redshift slices covering the redshift range [0,2] are investigated, using cosmological redshifts and photo-z configurations. We find a clear increase of the correlation amplitude as a function of redshift and mass for the $z_{c}$ samples. The evolution of the derived bias parameter is in agreement with theoretical expectations. From our pilot sample limited to $M_{halo}> 5 \times 10^{13} (0.4 < z < 0.7)$, we find that the real-space correlation function can be recovered by deprojection of $w_{p}(r_{p})$ within an accuracy of 5% for $\sigma_{z} = 0.001 \times (1 + z_{c})$ and within 10% for $\sigma_{z} = 0.03 \times (1 + z_{c})$. The evolution of the correlation in redshift and mass is clearly detected for all $\sigma_{z}$ tested. The best-fit parameters $(r_{0}$ and ${\gamma})$ as well as the bias obtained from the deprojection method for all $\sigma_{z}$ are within the $1 \sigma$ uncertainty of the $z_{c}$ sample., Comment: Final version after language correction. Accepted for publication in Astronomy&Astrophysics (A&A)

We measure the projected 2-point correlation function of galaxies in the 180 deg$^2$ equatorial regions of the GAMA II survey, for four different redshift slices between z = 0.0 and z=0.5. To do this we further develop the Cole (2011) method of producing suitable random catalogues for the calculation of correlation functions. We find that more r-band luminous, more massive and redder galaxies are more clustered. We also find that red galaxies have stronger clustering on scales less than ~3 $h^{-1}$ Mpc. We compare to two different versions of the GALFORM galaxy formation model, Lacey et al (in prep.) and Gonzalez-Perez et al. (2014), and find that the models reproduce the trend of stronger clustering for more massive galaxies. However, the models under predict the clustering of blue galaxies, can incorrectly predict the correlation function on small scales and under predict the clustering in our sample of galaxies with ~3$L_r$ . We suggest possible avenues to explore to improve these cluster- ing predictions. The measurements presented in this paper can be used to test other galaxy formation models, and we make the measurements available online to facilitate this., Comment: Accepted for publication by MNRAS