Lattice-based Methods Research Articles

Cryptographic Protocols Resilient to Quantum Attacks: Advancements in Post-Quantum Cryptography

New developments in quantum computing have made people worry that current security methods could be broken by quantum attacks. Some mathematical problems are hard to solve, which is how traditional encryption methods like RSA and ECC keep their secrets safe. However, quantum computers might be able to solve these issues a lot faster than regular computers, which makes these methods less safe. Because of this threat, experts have been working hard to make post-quantum cryptography methods that quantum computers can't break. These methods are made to stand up to the strength of quantum algorithms and protect the privacy, integrity, and validity of private data even when quantum attackers are present. Lattice-based cryptography is a potential method for post-quantum encryption. Its security comes from the difficulty of certain lattice problems. Lattice-based methods are thought to be safe from threats from both traditional and quantum computers because they offer good security promises. Lattice-based cryptography is a flexible way to build different types of cryptographic primitives, like encryption, digital signatures, and key sharing protocols. The study of code-based cryptography, which is based on how hard it is to decode some error-correcting codes, is another important advance. Code-based methods have been around for a long time and have been studied a lot, which makes them a good choice for security after quantum computing. Code-based cryptography is also easy to use and has strong security features, which makes it a good choice for real-world situations. Multivariate polynomial cryptography is another possible choice for cryptography after quantum computing. The safety of this method depends on how hard it is to solve systems of multivariate polynomial problems. Multivariate polynomial methods might not be as secure as lattice-based or code-based cryptography, but they are interesting options for some situations and places with limited resources.

Security in wireless body area networks via anonymous authentication: Comprehensive literature review, scheme classification, and future challenges

Authentication is a security practice that seeks to validate a user identity to various entities, yet doing so across a wireless network poses inherent risks. Wireless Body Area Networks (WBANs) are a unique form of network that contains e-healthcare patient data, thus WBANs require a high level of privacy and security. There are several anonymous WBAN authentication systems in the literature, but this is the first paper to conduct a complete review of all the various schemes, then tabulate and compare the results. Doing so reveals a number of research avenues that need either greater depth, or systems development. This article presents a thorough taxonomy and survey of the anonymous authentication methods, illustrating the security services and vulnerabilities, and then the properties of an ideal anonymous authentication scheme. The various schemes reviewed are also classified by their main encryption algorithm, such as bilinear parings-based schemes, elliptic curve cryptography-based solutions, lattice-based methods, and XOR-based approaches. The main authentication capabilities, cryptographic features, security advantages, evaluation metrics, and shortcomings are all specified and discussed. A thorough comparison of anonymous authentication methods is presented to demonstrate each scheme's resistance to a variety of security threats. The study concludes that very few schemes have addressed the group authentication problem, which is very important in healthcare systems. Also, in the multi-factor authentication context, which provides a higher level of security, only 11% of the schemes used three factors, and 1% of them utilized four factors. Besides, DDoS attacks, as a growing concern in all computing environments, are handled by a narrow number of schemes. At last, a set of recommendations for further research based on identified literature gaps.

Analysing the potential of transport triggered architecture for lattice-based cryptography algorithms

Lattice-based structures offer numerous possibilities for post-quantum cryptography. Recently, many post-quantum cryptography algorithms have been built on hard lattice problems. The three of the remaining four algorithms in the final round of the NIST Standardization Process rely on lattice-based methods. However, suitable processor architectures for these algorithms have not been sufficiently investigated. This study examines the potential advantages of transport triggered architecture for these algorithms. We compare popular 64-bit RISC-V processors with our conceptual transport triggered architecture processor over reference software implementations. Our processor provides better results than RISC-V competitors, regardless of the algorithm. It seems to be up to 3× faster, 1.6×-2× smaller, and consumes 1.3×-3.6× less energy than the compared RISC-V cores. Thus, an alternative base architecture is proposed for post-quantum cryptography processor development for embedded systems. The most critical shortcoming of the proposed architecture is the lack of compatible intellectual property core support for system-on-chip designs. We share comparative analyses with test results for different core configurations.

Lattice-based methods for regression and density estimation on complicated multidimensional regions

This paper illustrates the use of diffusion kernels to estimate smooth density and regression functions defined on highly complex domains. We generalize the two-dimensional lattice-based estimators of Barry and McIntyre (2011) and McIntyre and Barry (2018) to estimate any function defined on a domain that may be embedded in $$\mathbb {R}^d$$ , $$d\ge 1$$ . Examples include function estimation on the surface of a sphere, a sphere with boundaries and holes, a sphere over multiple time periods, a linear network, the surface of cylinder, a three-dimensional volume with boundaries, and a union of one- and two-dimensional subregions.

Deep Unsupervised Learning of 3D Point Clouds via Graph Topology Inference and Filtering.

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use lattice-based methods to process and learn 3D spatial information; however, this leads to inevitable discretization errors. In this work, we try to handle raw 3D points without such compromise. The proposed networks follow the autoencoder framework with a focus on designing the decoder. The encoder of the proposed networks adopts similar architectures as in PointNet, which is a well-acknowledged method for supervised learning of 3D point clouds. The decoder of the proposed networks involves three novel modules: the folding module, the graph-topology-inference module, and the graph-filtering module. The folding module folds a canonical 2D lattice to the underlying surface of a 3D point cloud, achieving coarse reconstruction; the graph-topology-inference module learns a graph topology to represent pairwise relationships between 3D points, pushing the latent code to preserve both coordinates and pairwise relationships of points in 3D point clouds; and the graph-filtering module couples the above two modules, refining the coarse reconstruction through a learnt graph topology to obtain the final reconstruction. The proposed decoder leverages a learnable graph topology to push the codeword to preserve representative features and further improve the unsupervised-learning performance. We further provide theoretical analyses of the proposed architecture. We provide an upper bound for the reconstruction loss and further show the superiority of graph smoothness over spatial smoothness as a prior to model 3D point clouds. In the experiments, we validate the proposed networks in three tasks, including 3D point cloud reconstruction, visualization, and transfer classification. The experimental results show that (1) the proposed networks outperform the state-of-the-art methods in various tasks, including reconstruction and transfer classification; (2) a graph topology can be inferred as auxiliary information without specific supervision on graph topology inference; (3) graph filtering refines the reconstruction, leading to better performances; and (4) designing a powerful decoder could improve the unsupervised-learning performance, just like a powerful encoder.

Flow-Simulation Model Improves Analysis of Perforated-Rock Cleanup and Productivity

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 190113, “Advanced Analysis of Cleanup and Productivity From Perforated Rocks Using Computational Fluid Dynamics,” by Rajani Satti, SPE, Stephen N. Zuklic, and Derek Bale, SPE, Baker Hughes, a GE company, and Nils Koliha, Andrew Fager, SPE, Gana Balasubramanian, Bernd Crouse, SPE, and David Freed, SPE, EXA, prepared for the 2018 SPE Western Regional Meeting, Garden Grove, California, USA, 22–27 April. The paper has not been peer reviewed. Because of inherent complexities, understanding the characteristics of perforations in downhole environments is a significant challenge. Perforation-flow laboratories have been used to provide insight into cleanup and productivity mechanisms around perforation tunnels. In contrast to previous studies, the model presented in this work uses the perforation-flow laboratory, micro-computed-tomography (CT) and conventional CT imaging, and, most importantly, an advanced simulation approach to provide an accurate assessment of cleanup techniques and productivity. This full-scale 3D flow model accounts for realistic aspects of tunnel geometry, perforation damage, and blockages that impede flow. Introduction In recent years, numerical tools increasingly have been used in conjunction with experiments to provide better insight into the flow characteristics of perforated cores and perforated well-scale formations. Several numerical studies on perforation fluid flow have been conducted for core scale. However, comprehensive details relating to the modeling of perforation-zone damage and thickness, flow directionality, debris mechanisms, and implications for cleanup have not been studied in detail. In addition, most computational fluid dynamics (CFD) studies have used traditional Navier-Stokes-based solvers. In this study, the authors have used a commercially available flow-simulation software based on the lattice Boltzmann method (LBM) to calculate the complex flow and cleanup mechanisms around the perforation tunnel. Lattice-based methods, an alternative to traditional CFD methods, track the advection and collisions of fluid particles on a computational grid. Because the average number of particles per grid cell far exceeds the computing power required to track them individually, the particles are grouped into an integer number of discrete velocities. LBM has been well validated and is in common use for many flow applications. The flow solver used here includes a turbulence model that is similar conceptually to the large-eddy simulation approach. The flow solver also includes a porous-media model that is used, in this study, to model the rock. The porous-media model invokes a Darcy-type pressure loss by applying a flow resistance determined from the known permeability of the rock. The resistance can include a viscous (linear) and an inertial (quadratic) term with respect to local velocity and can be made to vary spatially to model rock heterogeneity.

The Material Point Monte Carlo model: A discrete, off-lattice method for microstructural evolution simulations

A new kinetic Monte Carlo model, termed the Material Point Monte Carlo (MPMC) method, is developed to simulate microstructural evolution under a variety of driving forces. The MPMC operates on a spatially random set of discrete material points; at each time step, points are relocated and their material data are updated according to a statistical mechanics scheme. Because material points are randomly distributed, and remain so under affine deformations, the MPMC eliminates artifacts of the simulation grid that occur in lattice-based methods such as the Monte Carlo Potts model. For model systems the MPMC is verified to correctly reproduce grain boundary motion caused by bulk and interfacial driving forces. It is then applied to larger and more complex problems, including grain growth during plastic deformation.

An Analytic Method Pricing Convertible Bonds: Based on Path Decomposing

We develop analytic method using equivalent path decomposition for convertible bonds (CBs) with call and put provision. Since CBs embedded options are strictly path-dependent, equivalent path decomposition can clearly identify the risk exposure, and completely replicate the payoff features of CBs. Compared to simulation methods and lattice-based numerical methods, our method provides ordinary investors with an effective tool to analyze the effects and interactions of the different provisions contained in CBs. Finally we extend to pricing CBs with call protection.

Cryptanalysis of a Public Key Cryptosystem Based on the Matrix Combinatorial Problem

In this paper, we present a cryptanalysis of a public key cryptosystem based on the matrix combinatorial problem proposed by Wang and Hu (2010). Using lattice-based methods finding small integer solutions of modular linear equations, we recover the secret key of this cryptosystem for a certain range of parameters. In experiments, for the suggested parameters by Wang and Hu, the secret key can be recovered in seconds.

Improvement Comparison of Different Lattice-based Discriminative Training Methods in Chinese-monolingual and Chinese-English-bilingual Speech Recognition

Improvement Comparison of Different Lattice-based Discriminative Training Methods in Chinese-monolingual and Chinese-English-bilingual Speech Recognition

Cryptanalysis of a quadratic compact knapsack public-key cryptosystem

Recently, Wang and Hu have proposed a high-density quadratic compact knapsack public-key cryptosystem using the Chinese remainder theorem to disguise two secret cargo vectors. The system is claimed to be secure against certain known attacks; however, it has not been demonstrated to fulfill any provable security goals. In this work, we show that this system is not secure. Exploiting the special structure of system parameters, we first show that a candidate list for the secret modulus can be obtained by solving linear equations with small solutions. Next, we show that with this candidate list, all other secrets can be recovered in succession with lattice-based methods by solving certain modular linear equations with small solutions. As a result, recovering a private key can be done in about 11 h for the proposed system parameter n = 100 . We also discuss a method to thwart the proposed attack.

A multi-factor Markovian HJM model for pricing American interest rate derivatives

This article presents a numerically efficient approach for constructing an interest rate lattice for multi-state variable multi-factor term structure models in the Makovian HJM [Econometrica 70 (1992) 77] framework based on Monte Carlo simulation and an advanced extension to the Markov Chain Approximation technique. The proposed method is a mix of Monte Carlo and lattice-based methods and combines the best from both of them. It provides significant computational advantages and flexibility with respect to many existing multi-factor model implementations for interest rates derivatives valuation and hedging in the HJM framework.

Calculation of temperature-dependent hadronic correlation functions of pseudoscalar and vector currents

We make use of the Nambu--Jona-Lasinio (NJL) formalism and real-time finite-temperature field theory to calculate hadronic current correlation functions in the deconfined phase of quantum chromodynamics (QCD). Here, we consider both pseudoscalar and vector currents. Since the method used in the lattice analysis to calculate the spectral functions requires assumptions about the likelihood of a particular form for the spectral function, we believe our calculations will be useful to researchers who wish to calculate hadronic current correlation functions at finite temperature using lattice-based methods. Our model makes use of temperature-dependent coupling constants for the NJL model. We present various arguments that such temperature dependence is necessary, if the results of the model are to be consistent with what is known concerning QCD thermodynamics.

Introduction concept lattice-based theory, methods and tools for knowledge discovery in databases: Applications

Concept or Galois Lattices (CL) provide a productive framework for a variety of problems that arise in Knowledge Discovery in Databases (KDD). This paper introduces this special issue of Applied Artificial Intelligence devoted to applications of Concept Lattices for KDD (CLKDD). The papers in this volume come from a call for papers issued after the first International Workshop on Concept Lattice-based Theory, Methods and Tools for KDD held in July 2001 at Stanford University. Another special issue devoted to algorithms and methods of CLKDD will appear in the Journal of Experimental and Theoretical Artificial Intelligence.