Lattice-based Encryption Over Standard Lattices in Hardware

Lattice-based cryptography has gained credence recently as a replacement for current public-key cryptosystems, due to its quantum-resilience, versatility, and relatively low key sizes. To date, encryption based on the learning with errors (LWE) problem has only been investigated from an ideal lattice standpoint, due to its computation and size efficiencies. However, a thorough investigation of standard lattices in practice has yet to be considered. Standard lattices may be preferred to ideal lattices due to their stronger security assumptions and less restrictive parameter selection process. In this paper, an area-optimised hardware architecture of a standard lattice-based cryptographic scheme is proposed. The design is implemented on a FPGA and it is found that both encryption and decryption fit comfortably on a Spartan-6 FPGA. This is the first hardware architecture for standard lattice-based cryptography reported in the literature to date, and thus is a benchmark for future implementations.
Additionally, a revised discrete Gaussian sampler is proposed which is the fastest of its type to date, and also is the first to investigate the cost savings of implementing with lamda_2-bits of precision. Performance results are promising in comparison to the hardware designs of the equivalent ring-LWE scheme, which in addition to providing a stronger security proof; generate 1272 encryptions per second and 4395 decryptions per second.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

A29 NMR spin-lattice relaxation study of paramagnetics -doped orthosilictes

A ~si MAS NMR study of spin-lattice relaxation behaviour in paramagnetic-doped crystalline silicates was undertaken, using synthetic magnesium orthosilicate (forsterite) and synthetic zinc orthosilicate (willemite) doped with 0.1% to 20% of Co(II), Ni(II), or CU(II), as experimental systems. All of the samples studied exhibited a longitudinal magnetization return to the Boltzmann distribution of nuclear spin states which followed a stretched-exponential function of time: Y=exp [- (tjTn) n], O

Tintype of Girl Peering through Lattice [n.d.]

A young African American girl peers through a lattice window in an unknown photographer's studio in this small black and white tintype. The girl in the photo is unidentified. There are slight scratches on the surface of the tintype, which is cut in a hexagonal shape. This tintype was in the possession of Iris Sloman Bell, of St. Catharines, Ontario. The Sloman - Bell families have relatives who are descended from Black slaves from the United States."Tintypes were the invention of Prof. Hamilton Smith of Ohio. They begin as thin sheets of iron, covered with a layer of black paint. This serves as the base for the same iodized collodion coating and silver nitrate bath used in the ambrotype process. First made in 1856, millions were produced well into the twentieth century. When tintypes were finished in the same sorts of mats and cases used for ambrotypes, it can be almost impossible to distinguish which process was used without removing the image to examine the substrate." Source: American Museum of Photography http://www.photographymuseum.com/primer.html

Lipoprotein-associated phospholipase A2 (Lp-PLA2) in acute coronary syndrome

La phospholipase A2 liée aux lipoprotéines (Lp-PLA2) est une biomarqueur de plusieurs maladies inflammatoires et une niveau sérique élevé est associé à l’instabilité de la plaque artérioscléreuse. Comme son nom l’indique, la Lp-PLA2 est liée aux lipoprotéines plasmatiques (LDL et HDL) et son rôle est de prévenir l’accumulation de phospholipides oxidés a la surface des lipoprotéines. Toutefois, les produits de dégradation des phospholipides oxidés par la Lp-PLA2 - le lysophosphatidyl choline par les acides gras oxidés peuvent aussi promouvoir l’inflammation. Mieux comprendre le métabolisme de la Lp-PLA2 pourrait nous permettre de mieux apprécier son rôle dans la formation d’une plaque artérioscléreuse instable, car des études antérieures ont démontré une forte expression de la Lp-PLA2 dans la plaque. De plus, il existe une forte corrélation entre les niveaux et l’activité plasmatiques de la Lp-PLA2 et la maladie coronarienne, les accidents cérébraux-vasculaires et la mortalité cardiaque. L’inhibition de la Lp-PLA2 avec une petite molécule, le darapladib, n’a pas démontré de bénéfice sur les évènements cardiovasculaires dans deux études cliniques. Cette thèse présentera d’abord une revue de la littérature sur la Lp-PLA2 et les maladies cardiovasculaires et les deuxième et troisième chapitres, une étude clinique réalisée sur des patients avec un syndrome coronarien aigu.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

LDA or GGA? A combined experimental inelastic neutron scattering and ab initio lattice dynamics study of alkali metal hydrides

In a previous work, we carried out inelastic neutron scattering (INS) spectroscopy experiments and preliminary first principles calculations on alkali metal hydrides. The complete series of alkali metal hydrides, LiH, NaH, KH, RbH and CsH was measured in the high-resolution TOSCA INS spectrometer at ISIS. Here, we present the results of ab initio electronic structure calculations of the properties of the alkali metal hydrides using both the local density approximation (LDA) and the generalized gradient approximation (GGA), using the Perdew–Burke–Ernzerhof (PBE) parameterization. Properties calculated were lattice parameters, bulk moduli, dielectric constants, effective charges, electronic densities and inelastic neutron scattering (INS) spectra. We took advantage of the currently available computer power to use full lattice dynamics theory to calculate thermodynamic properties for these materials. For the alkali metal hydrides (LiH, NaH, KH, RbH and CsH) using lattice dynamics, we found that the INS spectra calculated using LDA agreed better with the experimental data than the spectra calculated using GGA. Both zero-point effects and thermal contributions to free energies had an important effect on INS and several thermodynamic properties.

Small-world effects in lattice stochastic diffusion search

Stochastic Diffusion Search is an efficient probabilistic bestfit search technique, capable of transformation invariant pattern matching. Although inherently parallel in operation it is difficult to implement efficiently in hardware as it requires full inter-agent connectivity. This paper describes a lattice implementation, which, while qualitatively retaining the properties of the original algorithm, restricts connectivity, enabling simpler implementation on parallel hardware. Diffusion times are examined for different network topologies, ranging from ordered lattices, over small-world networks to random graphs.