arXiv subjects

Marco Baldi

Publications and source records attributed to Marco Baldi.

At least 73 records · Page 4Linked to original sources

arXiv2022

On the road to percent accuracy VI: the nonlinear power spectrum for interacting dark energy with baryonic feedback and massive neutrinos

Understanding nonlinear structure formation is crucial for fully exploring the data generated by stage IV surveys, requiring accurate modelling of the power spectrum. This is challenging for deviations from $Λ$CDM, but we must ensure that alternatives are well tested, to avoid false detections. We present an extension of the halo model reaction framework for interacting dark energy. We modify the halo model including the additional force present in the Dark Scattering model and implement it into ReACT. The reaction is combined with a pseudo spectrum from EuclidEmulator2 and compared to N-body simulations. Using standard mass function and concentration-mass relation, we find predictions to be 1 % accurate at $z=0$ up to $k=0.8~h/{\rm Mpc}$ for the largest interaction strength tested ($ξ=50$ b/GeV), improving to $2~h/{\rm Mpc}$ at $z=1$. For smaller interaction strength ($10$ b/GeV), we find 1 % agreement at $z=1$ up to scales above $3.5~h/{\rm Mpc}$, being close to $1~h/{\rm Mpc}$ at $z=0$. Finally, we improve our predictions with the inclusion of baryonic feedback and massive neutrinos and study degeneracies between the effects of these contributions and those of the interaction. Limiting the scales to where our modelling is 1 % accurate, we find a degeneracy between the interaction and feedback, but not with massive neutrinos. We expect the degeneracy with feedback to be resolvable by including smaller scales. This work represents the first analytical tool for calculating the nonlinear spectrum for interacting dark energy models.

astro-ph.CO↗

arXiv2022

Optimization of a Reed-Solomon code-based protocol against blockchain data availability attacks

ASBK (named after the authors' initials) is a recent blockchain protocol tackling data availability attacks against light nodes, employing two-dimensional Reed-Solomon codes to encode the list of transactions and a random sampling phase where adversaries are forced to reveal information. In its original formulation, only codes with rate $1/4$ are considered, and a theoretical analysis requiring computationally demanding formulas is provided. This makes ASBK difficult to optimize in situations of practical interest. In this paper, we introduce a much simpler model for such a protocol, which additionally supports the use of codes with arbitrary rate. This makes blockchains implementing ASBK much easier to design and optimize. Furthermore, disposing of a clearer view of the protocol, some general features and considerations can be derived (e.g., nodes behaviour in largely participated networks). As a concrete application of our analysis, we consider relevant blockchain parameters and find network settings that minimize the amount of data downloaded by light nodes. Our results show that the protocol benefits from the use of codes defined over large finite fields, with code rates that may be even significantly different from the originally proposed ones.

cs.IT↗

arXiv2021

On the road to percent accuracy V: the non-linear power spectrum beyond $Λ$CDM with massive neutrinos and baryonic feedback

In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, percent-level accuracy is required when modelling the power spectrum. This calls for frameworks that can accurately capture the relevant physical effects, while allowing for deviations from $Λ$CDM. Massive neutrino and baryonic physics are two of the most relevant such effects. We present an integration of the halo model reaction frameworks for massive neutrinos and beyond-$Λ$CDM cosmologies. The integrated halo model reaction, combined with a pseudo power spectrum modelled by HMCode2020 is then compared against $N$-body simulations that include both massive neutrinos and an $f(R)$ modification to gravity. We find that the framework is 4% accurate down to at least $k\approx 3 \, h/{\rm Mpc}$ for a modification to gravity of $|f_{\rm R0}|\leq 10^{-5}$ and for the total neutrino mass $M_ν\equiv \sum m_ν\leq 0.15$ eV. We also find that the framework is 4% consistent with EuclidEmulator2 as well as the Bacco emulator for \B{most of the considered} $νw$CDM cosmologies down to at least $k \approx 3 \, h$/Mpc. Finally, we compare against hydrodynamical simulations employing HMCode2020's baryonic feedback modelling on top of the halo model reaction. For $νΛ$CDM cosmologies we find 2% accuracy for $M_ν\leq 0.48$eV down to at least $k\approx 5h$/Mpc. Similar accuracy is found when comparing to $νw$CDM hydrodynamical simulations with $M_ν= 0.06$eV. This offers the first non-linear, theoretically general means of accurately including massive neutrinos for beyond-$Λ$CDM cosmologies, and further suggests that baryonic, massive neutrino and dark energy physics can be reliably modelled independently.

astro-ph.CO↗

arXiv2021

Nuw CDM cosmology from the weak lensing convergence PDF

Pinning down the total neutrino mass and the dark energy equation of state is a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the total matter distribution whose non-Gaussian statistics can be quantified by the one-point probability distribution function (PDF) of the lensing convergence. We calculate the convergence PDF on mildly non-linear scales from first principles using large-deviation statistics, accounting for dark energy and the total neutrino mass. For the first time, we comprehensively validate the cosmology-dependence of the convergence PDF model against large suites of simulated lensing maps, demonstrating its percent-level precision and accuracy. We show that fast simulation codes can provide highly accurate covariance matrices, which can be combined with the theoretical PDF model to perform forecasts and eliminate the need for relying on expensive N-body simulations. Our theoretical model allows us to perform the first forecast for the convergence PDF that varies the full set of $Λ$CDM parameters. Our Fisher forecasts establish that the constraining power of the convergence PDF compares favourably to the two-point correlation function for a Euclid-like survey area at a single source redshift. When combined with a CMB prior from Planck, the PDF constrains both the neutrino mass $M_ν$ and the dark energy equation of state $w_0$ more strongly than the two-point correlation function.

astro-ph.CO↗

arXiv2021

Cryptanalysis of a code-based full-time signature

We present an attack against a code-based signature scheme based on the Lyubashevsky protocol that was recently proposed by Song, Huang, Mu, Wu and Wang (SHMWW). The private key in the SHMWW scheme contains columns coming in part from an identity matrix and in part from a random matrix. The existence of two types of columns leads to a strong bias in the distribution of set bits in produced signatures. Our attack exploits such a bias to recover the private key from a bunch of collected signatures. We provide a theoretical analysis of the attack along with experimental evaluations, and we show that as few as 10 signatures are enough to be collected for successfully recovering the private key. As for previous attempts of adapting Lyubashevsky's protocol to the case of code-based cryptography, the SHMWW scheme is thus proved unable to provide acceptable security. This confirms that devising secure code-based signature schemes with efficiency comparable to that of other post-quantum solutions (e.g., based on lattices) is still a challenging task.

cs.CR↗

arXiv2021

Cosmic voids in modified gravity models with massive neutrinos

Cosmic voids are progressively emerging as a new viable cosmological probe. Their abundance and density profiles are sensitive to modifications of gravity, as well as to dark energy and neutrinos. The main goal of this work is to investigate the possibility of exploiting cosmic void statistics to disentangle the degeneracies resulting from a proper combination of $f(R)$ modified gravity and neutrino mass. We use N-body simulations to analyse the density profiles and size function of voids traced by both dark matter particles and haloes. We find clear evidence of the enhancement of gravity in $f(R)$ cosmologies in the void density profiles at $z=1$. However, these effects can be almost completely overridden by the presence of massive neutrinos because of their thermal free-streaming. Despite the limited volume of the analysed simulations does not allow us to achieve a statistically relevant abundance of voids larger than $40 \ \mathrm{Mpc}/h$, we find that the void size function at high redshifts and for large voids is potentially an effective probe to disentangle these degenerate cosmological models, which is key in the prospective of the upcoming wide field redshift surveys.

astro-ph.CO↗

arXiv2021

Information set decoding of Lee-metric codes over finite rings

Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders exploiting the code structure are not known. Classically, ISD algorithms have been studied for codes in the Hamming metric. In this paper we switch from the Hamming metric to the Lee metric, and study ISD algorithms and their complexity for codes measured with the Lee metric over finite rings.

cs.CR↗

arXiv2021

A New Path to Code-based Signatures via Identification Schemes with Restricted Errors

In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the classical SDP, and describe algorithms which solve such new problem. We study the properties of random codes under this new decoding perspective, in the fashion of traditional coding theory results, and assess the complexity of solving a random R-SDP instance. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification schemes through the well-know Fiat-Shamir transformation.

cs.CR↗

arXiv2020

Comparison of Statistical and Machine Learning Techniques for Physical Layer Authentication

In this paper we consider authentication at the physical layer, in which the authenticator aims at distinguishing a legitimate supplicant from an attacker on the basis of the characteristics of a set of parallel wireless channels, which are affected by time-varying fading. Moreover, the attacker's channel has a spatial correlation with the supplicant's one. In this setting, we assess and compare the performance achieved by different approaches under different channel conditions. We first consider the use of two different statistical decision methods, and we prove that using a large number of references (in the form of channel estimates) affected by different levels of time-varying fading is not beneficial from a security point of view. We then consider classification methods based on machine learning. In order to face the worst case scenario of an authenticator provided with no forged messages during training, we consider one-class classifiers. When instead the training set includes some forged messages, we resort to more conventional binary classifiers, considering the cases in which such messages are either labelled or not. For the latter case, we exploit clustering algorithms to label the training set. The performance of both nearest neighbor (NN) and support vector machine (SVM) classification techniques is evaluated. Through numerical examples, we show that under the same probability of false alarm, one-class classification (OCC) algorithms achieve the lowest probability of missed detection when a small spatial correlation exists between the main channel and the adversary one, while statistical methods are advantageous when the spatial correlation between the two channels is large.

cs.CR↗

arXiv2020

Breaking the Dark Degeneracy with the Drifting Coefficient of the Field Cluster Mass Function

We present a numerical analysis supporting the evidence that the redshift evolution of the drifting coefficient of the field cluster mass function is capable of breaking several cosmic degeneracies. This evidence is based on the data from the CoDECS and DUSTGRAIN-pathfinder simulations performed separately for various non-standard cosmologies including coupled dark energy, $f(R)$ gravity and combinations of $f(R)$ gravity with massive neutrinos as well as for the standard $Λ$CDM cosmology. We first numerically determine the field cluster mass functions at various redshifts in the range of $0\le z\le 1$ for each cosmology. Then, we compare the analytic formula developed in previous works with the numerically obtained field cluster mass functions by adjusting its drifting coefficient, $β$, at each redshift. It is found that the analytic formula with the best-fit coefficient provides a good match to the numerical results at all redshifts for all of the cosmologies. The empirically determined redshift evolution of the drifting coefficient, $β(z)$, turns out to significantly differ among different cosmologies. It is also shown that even without using any prior information on the background cosmology the drifting coefficient, $β(z)$, can discriminate with high statistical significance the degenerate non-standard cosmologies not only from the $Λ$CDM but also from one another. It is concluded that the evolution of the departure from the Einstein-de Sitter state and spherically symmetric collapse processes quantified by $β(z)$ is a powerful probe of gravity and dark sector physics.

astro-ph.CO↗

arXiv2020

Dynamic Zoom Simulations: a fast, adaptive algorithm for simulating lightcones

The advent of a new generation of large-scale galaxy surveys is pushing cosmological numerical simulations in an uncharted territory. The simultaneous requirements of high resolution and very large volume pose serious technical challenges, due to their computational and data storage demand. In this paper, we present a novel approach dubbed Dynamic Zoom Simulations -- or DZS -- developed to tackle these issues. Our method is tailored to the production of lightcone outputs from N-body numerical simulations, which allow for a more efficient storage and post-processing compared to standard comoving snapshots, and more directly mimic the format of survey data. In DZS, the resolution of the simulation is dynamically decreased outside the lightcone surface, reducing the computational work load, while simultaneously preserving the accuracy inside the lightcone and the large-scale gravitational field. We show that our approach can achieve virtually identical results to traditional simulations at half of the computational cost for our largest box. We also forecast this speedup to increase up to a factor of 5 for larger and/or higher-resolution simulations. We assess the accuracy of the numerical integration by comparing pairs of identical simulations run with and without DZS. Deviations in the lightcone halo mass function, in the sky-projected lightcone, and in the 3D matter lightcone always remain below 0.1%. In summary, our results indicate that the DZS technique may provide a highly-valuable tool to address the technical challenges that will characterise the next generation of large-scale cosmological simulations.

astro-ph.CO↗

arXiv2020

Scaling relations of Fuzzy Dark Matter haloes I: individual systems in their cosmological environment

Dark matter models involving a very light bosonic particle, generally known as Fuzzy Dark Matter (FDM), have been recently attracting great interest in the cosmology community, as their wave-like phenomenology would simultaneously explain the longstanding mis-detection of a dark matter particle and help easing the small-scale issues related to the standard Cold Dark Matter (CDM) scenario. With the present work, we initiate a series of papers aiming at investigating the evolution of FDM structures in a cosmological framework performed with our N-body code AX-GADGET, detailing for the first time in the literature how the actual scaling relations between solitonic cores and host haloes properties are significantly affected by the dynamical state, morphology and merger history of the individual systems. In particular, in this first paper we confirm the ability of AX-GADGET to correctly reproduce the typical FDM solitonic core and we employ it to study the non-linear evolution of eight FDM haloes in their cosmological context through the zoom-in simulation approach. We find that the scaling relations identified in previous works for isolated systems are generally modified for haloes evolving in a realistic cosmological environment, and appear to be valid only as a limit for the most relaxed and spherically symmetric systems.

astro-ph.CO↗

arXiv2020

Testing the Reliability of Fast Methods for Weak Lensing Simulations: WL-MOKA on PINOCCHIO

The generation of simulated convergence maps is of key importance in fully exploiting weak lensing by Large Scale Structure (LSS) from which cosmological parameters can be derived. In this paper we present an extension of the PINOCCHIO code which produces catalogues of dark matter haloes so that it is capable of simulating weak lensing by LSS. Like WL-MOKA, the method starts with a random realisation of cosmological initial conditions, creates a halo catalogue and projects it onto the past-light-cone, and paints in haloes assuming parametric models for the mass density distribution within them. Large scale modes that are not accounted for by the haloes are constructed using linear theory. We discuss the systematic errors affecting the convergence power spectra when Lagrangian Perturbation Theory at increasing order is used to displace the haloes within PINOCCHIO, and how they depend on the grid resolution. Our approximate method is shown to be very fast when compared to full ray-tracing simulations from an N-Body run and able to recover the weak lensing signal, at different redshifts, with a few percent accuracy. It also allows for quickly constructing weak lensing covariance matrices, complementing PINOCCHIO's ability of generating the cluster mass function and galaxy clustering covariances and thus paving the way for calculating cross covariances between the different probes. This work advances these approximate methods as tools for simulating and analysing surveys data for cosmological purposes.

astro-ph.CO↗

arXiv2020

Non-linear damping of superimposed primordial oscillations on the matter power spectrum in galaxy surveys

Galaxy surveys are an important probe for superimposed oscillations on the primordial power spectrum of curvature perturbations, which are predicted in several theoretical models of inflation and its alternatives. In order to exploit the full cosmological information in galaxy surveys it is necessary to study the matter power spectrum to fully non-linear scales. We therefore study the non-linear clustering in models with superimposed linear and logarithmic oscillations to the primordial power spectrum by running high-resolution dark-matter-only N-body simulations. We fit a Gaussian envelope for the non-linear damping of superimposed oscillations in the matter power spectrum to the results of the N-body simulations for $k \lesssim 0.6\ h/$Mpc at $0 \leq z \leq 5$ with an accuracy below the percent. We finally use this fitting formula to forecast the capabilities of future galaxy surveys, such as Euclid and Subaru, to probe primordial oscillation down to non-linear scales alone and in combination with the information contained in CMB anisotropies.

astro-ph.CO↗

arXiv2020

Analysis of the error correction capability of LDPC and MDPC codes under parallel bit-flipping decoding and application to cryptography

Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through intensive Monte Carlo simulations. However, several applications, like code-based cryptography, need guaranteed low values of the error rate, which are infeasible to assess through simulations, thus requiring the development of theoretical models for the error rate of these codes under iterative decoding. Some models of this type already exist, but become computationally intractable for parameters of practical interest. Other approaches approximate the code ensemble behaviour through some assumptions, which may not hold true for a specific code. We propose a theoretical analysis of the error correction capability of LDPC and MDPC codes that allows deriving tight bounds on the error rate at the output of parallel bit-flipping decoders. Special attention is devoted to the case of codes with small girth; moreover, single-iteration decoding is investigated through a rigorous approach, which does not require any assumption and hence results in a guaranteed error correction capability for any single code. We show an example of application of the new bound to the context of code-based cryptography, where guaranteed error rates are needed to achieve some strong security levels.

cs.IT↗

arXiv2020

The stellar-to-halo mass relation over the past 12 Gyr

Understanding how galaxy properties are linked to the dark matter halos they reside in, and how they co-evolve is a powerful tool to constrain the processes related to galaxy formation. The stellar-to-halo mass relation (SHMR) and its evolution over the history of the Universe provides insights on galaxy formation models and allows to assign galaxy masses to halos in N-body dark matter simulations. We use a statistical approach to link the observed galaxy stellar mass functions on the COSMOS field to dark matter halo mass functions from the DUSTGRAIN simulation and from a theoretical parametrization from z=0 to z=4. We also propose an empirical model to describe the evolution of the stellar-to-halo mass relation as a function of redshift. We calculate the star-formation efficiency (SFE) of galaxies and compare results with previous works and semi-analytical models.

astro-ph.CO↗

arXiv2019

A Code-specific Conservative Model for the Failure Rate of Bit-flipping Decoding of LDPC Codes with Cryptographic Applications

Characterizing the decoding failure rate of iteratively decoded Low- and Moderate-Density Parity Check (LDPC/MDPC) codes is paramount to build cryptosystems based on them, able to achieve indistinguishability under adaptive chosen ciphertext attacks. In this paper, we provide a statistical worst-case analysis of our proposed iterative decoder obtained through a simple modification of the classic in-place bit-flipping decoder. This worst case analysis allows both to derive the worst-case behaviour of an LDPC/MDPC code picked among the family with the same length, rate and number of parity checks, and a code-specific bound on the decoding failure rate. The former result allows us to build a code-based cryptosystem enjoying the $δ$-correctness property required by IND-CCA2 constructions, while the latter result allows us to discard code instances which may have a decoding failure rate significantly different from the average one (i.e., representing weak keys), should they be picked during the key generation procedure.

cs.CR↗

arXiv2019

Emulators for the non-linear matter power spectrum beyond $Λ$CDM

Accurate predictions for the non-linear matter power spectrum are needed to confront theory with observations in current and near future weak lensing and galaxy clustering surveys. We propose a computationally cheap method to create an emulator for modified gravity models by utilizing existing emulators for $Λ$CDM. Using a suite of $N$-body simulations we construct a fitting function for the enhancement of both the linear and non-linear matter power spectrum in the commonly studied Hu-Sawicki $f(R)$ gravity model valid for wave-numbers $k \lesssim 5-10\, h\text{Mpc}^{-1}$ and redshifts $z \lesssim 3$. We show that the cosmology dependence of this enhancement is relatively weak so that our fit, using simulations coming from only one cosmology, can be used to get accurate predictions for other cosmological parameters. We also show that the cosmology dependence can, if needed, be included by using linear theory, approximate $N$-body simulations (such as COLA) and semi-analytical tools like the halo model. Our final fit can easily be combined with any emulator or semi-analytical models for the non-linear $Λ$CDM power spectrum to accurately, and quickly, produce a non-linear power spectrum for this particular modified gravity model. The method we use can be applied to fairly cheaply construct an emulator for other modified gravity models. As an application of our fitting formula we use it to compute Fisher-forecasts for how well galaxy clustering and weak lensing in a Euclid-like survey will be at constraining modifications of gravity.

astro-ph.CO↗