A Summary of the FV Homomorphic Encryption Scheme and the Average-Case Noise Growth

Homomorphic encryption is a method of encryption that allows for secure computation of data. Many industries are moving away from owning expensive high-powered computers and instead delegating costly computations to the cloud. In an age of data breaches, there is an inherent risk when putting sensitive data on the cloud. Homomorphic encryption allows one to securely perform computations on the cloud without allowing the host or any other party access to the raw data itself. One application being explored is encrypting health data on low-powered embedded devices, uploading it to a cloud application, performing computations to assess health risks, and send the results back to the user’s device for decryption and interpretation. Another application being explored is digital voting. This thesis aims to provide a summary of the current state-of-the-art of homomorphic encryption. We will begin by providing the reader with sources for the current main im- plementations and schemes they are based on. We will then present the mathematical background used in existing schemes. This includes a background on lattices, cyclotomic fields, rings of integers, and the underlying believed-to-be-hard problems existing schemes take advantage of. We will then shift our attention to the FV scheme which is based on the ring-LWE problem and is one of the main schemes used today. We will then briefly discuss some optimizations used in FV implementations. Finally, we will look at some probabilistic experiments which suggest the noise growth in FV is significantly lower than the theoretical maximum in the average case, and will explore some of the benefits that can be gained

Applicability of a cognitive model and treatment to worry in children and adolescents

Studies have found that the cognitive model of worry developed by Dugas, Gagnon, Ladouceur and Freeston (1998) involving Intolerance of Uncertainly (IU), Cognitive Avoidance (CA), Positive Beliefs about Worry (PB), and Negative Problem Orientation (NPO) accounts for approximately 40-50% of the variance in worry frequency in adults. A recent trial of the treatment based on this model (Dugas, Brillon, Savard et al., 2010) found it to be superior to no treatment and marginally superior to applied relaxation in adults with Generalized Anxiety Disorder (GAD). In this presentation the authors discuss the results of two studies testing the applicability of this cognitive model to children and adolescents. In the first study measures of IU, CA, PB, worry and anxiety were administered to 515 British primary and secondary school students (aged 7-19 years). A path analysis was undertaken to test whether IU acted as a higher order variable for CA and PB and whether the relationship between IU/CA/PB and anxiety was mediated by worry frequency. Significant (bivariate) correlations were observed between the measures of IU, PB, CA, worry and anxiety across the age range. However separate path models had to be fitted for children (aged 7-12 years) and adolescents (aged 13-19) with PB being dropped from the child model. CA was related to anxiety only through worry in children while IU showed direct paths to worry and anxiety in both children and adolescents. In the second study we present results from a case series where a modified version of the treatment based on the Dugas et al (1998) led to an 80% reduction in GAD diagnoses in 16 youth (aged 7-17 years) clinically referred for anxiety. Further testing and refinement of this cognitive model and its treatment may lead to further improvements in our understanding of worry in youth and its treatment. Possible modifications and refinements are discussed

CSIDH with Level Structure

We construct a new post-quantum cryptosystem which consists of enhancing CSIDH and similar cryptosystems by adding a full level $N$ structure. We discuss the size of the isogeny graph in this new cryptosystem which consists of components which are acted on by the ray class group for the modulus $N$. We conclude by showing that, if we can efficiently find rational isogenies between elliptic curves, then we can efficiently find rational isogenies that preserve the level structure. We show that one can reduce the group action problem for the ray class group to the group action problem for the ideal class group. This reduces the security of this new cryptosystem to that of the original on

The Astropy Problem

The Astropy Project (http://astropy.org) is, in its own words, "a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages." For five years this project has been managed, written, and operated as a grassroots, self-organized, almost entirely volunteer effort while the software is used by the majority of the astronomical community. Despite this, the project has always been and remains to this day effectively unfunded. Further, contributors receive little or no formal recognition for creating and supporting what is now critical software. This paper explores the problem in detail, outlines possible solutions to correct this, and presents a few suggestions on how to address the sustainability of general purpose astronomical software

Twinkle -- a small satellite spectroscopy mission for the next phase of exoplanet science

With a focus on off-the-shelf components, Twinkle is the first in a series of cost competitive small satellites managed and financed by Blue Skies Space Ltd. The satellite is based on a high-heritage Airbus platform that will carry a 0.45 m telescope and a spectrometer which will provide simultaneous wavelength coverage from 0.5-4.5 $\rm{\mu m}$. The spacecraft prime is Airbus Stevenage while the telescope is being developed by Airbus Toulouse and the spectrometer by ABB Canada. Scheduled to begin scientific operations in 2025, Twinkle will sit in a thermally-stable, sun-synchronous, low-Earth orbit. The mission has a designed operation lifetime of at least seven years and, during the first three years of operation, will conduct two large-scale survey programmes: one focused on Solar System objects and the other dedicated to extrasolar targets. Here we present an overview of the architecture of the mission, refinements in the design approach, and some of the key science themes of the extrasolar survey.Comment: Presented at SPIE Astronomical Telescopes & Instrumentation 202

The James Webb Space Telescope Mission: Optical Telescope Element Design, Development, and Performance

The James Webb Space Telescope (JWST) is a large, infrared space telescope that has recently started its science program which will enable breakthroughs in astrophysics and planetary science. Notably, JWST will provide the very first observations of the earliest luminous objects in the Universe and start a new era of exoplanet atmospheric characterization. This transformative science is enabled by a 6.6 m telescope that is passively cooled with a 5-layer sunshield. The primary mirror is comprised of 18 controllable, low areal density hexagonal segments, that were aligned and phased relative to each other in orbit using innovative image-based wavefront sensing and control algorithms. This revolutionary telescope took more than two decades to develop with a widely distributed team across engineering disciplines. We present an overview of the telescope requirements, architecture, development, superb on-orbit performance, and lessons learned. JWST successfully demonstrates a segmented aperture space telescope and establishes a path to building even larger space telescopes.Comment: accepted by PASP for JWST Overview Special Issue; 34 pages, 25 figure

The Science Performance of JWST as Characterized in Commissioning

This paper characterizes the actual science performance of the James Webb Space Telescope (JWST), as determined from the six month commissioning period. We summarize the performance of the spacecraft, telescope, science instruments, and ground system, with an emphasis on differences from pre-launch expectations. Commissioning has made clear that JWST is fully capable of achieving the discoveries for which it was built. Moreover, almost across the board, the science performance of JWST is better than expected; in most cases, JWST will go deeper faster than expected. The telescope and instrument suite have demonstrated the sensitivity, stability, image quality, and spectral range that are necessary to transform our understanding of the cosmos through observations spanning from near-earth asteroids to the most distant galaxies.Comment: 5th version as accepted to PASP; 31 pages, 18 figures; https://iopscience.iop.org/article/10.1088/1538-3873/acb29

Search for heavy resonances decaying to two Higgs bosons in final states containing four b quarks

A search is presented for narrow heavy resonances X decaying into pairs of Higgs bosons (H) in proton-proton collisions collected by the CMS experiment at the LHC at root s = 8 TeV. The data correspond to an integrated luminosity of 19.7 fb(-1). The search considers HH resonances with masses between 1 and 3 TeV, having final states of two b quark pairs. Each Higgs boson is produced with large momentum, and the hadronization products of the pair of b quarks can usually be reconstructed as single large jets. The background from multijet and t (t) over bar events is significantly reduced by applying requirements related to the flavor of the jet, its mass, and its substructure. The signal would be identified as a peak on top of the dijet invariant mass spectrum of the remaining background events. No evidence is observed for such a signal. Upper limits obtained at 95 confidence level for the product of the production cross section and branching fraction sigma(gg -> X) B(X -> HH -> b (b) over barb (b) over bar) range from 10 to 1.5 fb for the mass of X from 1.15 to 2.0 TeV, significantly extending previous searches. For a warped extra dimension theory with amass scale Lambda(R) = 1 TeV, the data exclude radion scalar masses between 1.15 and 1.55 TeV

Measurement of the top quark mass using charged particles in pp collisions at root s=8 TeV

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