Homomorphic Encryption and Cryptanalysis of Lattice Cryptography

The vast amount of personal data being collected and analyzed through internet connected devices is vulnerable to theft and misuse. Modern cryptography presents several powerful techniques that can help to solve the puzzle of how to harness data for use while at the same time protecting it---one such technique is homomorphic encryption that allows computations to be done on data while it is still encrypted. The question of security for homomorphic encryption relates to the broader field of lattice cryptography. Lattice cryptography is one of the main areas of cryptography that promises to be secure even against quantum computing. In this dissertation, we will touch on several aspects of homomorphic encryption and its security based on lattice cryptography. Our main contributions are: 1. proving some heuristics that are used in major results in the literature for controlling the error size in bootstrapping for fully homomorphic encryption, 2. presenting a new fully homomorphic encryption scheme that supports k-bit arbitrary operations and achieves an asymptotic ciphertext expansion of one, 3. thoroughly studying certain attacks against the Ring Learning with Errors problem, 4. precisely characterizing the performance of an algorithm for solving the Approximate Common Divisor problem

Space Station Rapid Sample Return Revisited

Rapid feedback of experiment results helps investigators to fine tune experiments, shorten experiment cycle times, and reduce development costs for new products. A rapid sample return (RSR) system was studied early in the Phase B Space Station Preliminary Design effort as a means of providing rapid feedback to increase station experimental productivity and reduce mission costs. However sufficient justification for baselining a RSR concept was not found. RSR was deemed nonessential because the Space Station would be serviced by a NSTS flight every 45 days and the design included thorough onboard analytical capabilities. Efforts at cost reduction have since reduced habitable station volume by 50%, combining separate life science and materials science modules into a single U.S. Laboratory (USL) module. Volume allocated for USL analytical instrumentation was reduced as a result. This decrease in onboard instrumentation has since been followed by a substantial reduction of NSTS station support flights

Bridging the Chasms: Contemporary Anarchists in the U.S.

Studies of anarchists across disciplines have largely focused on famous personalities and major historical events or on contentious protest actions and violence. In a 21st century context in which anarchism has an ever more significant influence on social movements in the U.S. and around the globe, understanding how anarchists understand that label is increasingly important. This paper aims to contribute to an understanding of the meaning of anarchism through the words of anarchists themselves. In this study, I interview 22 anarchists from three U.S. cities about what anarchism means to them and about if and how they practice their ideology in their everyday lives. I find a high level of unity around several core values regardless of the interviewees’ backgrounds or affiliations. Beyond that base level of unity, we see extensive variation across the sectarian divisions asserted by dominant theoretical works, both findings suggesting that such dichotomous, antagonistic frameworks may be overly simplistic. In addition, I explore a rhetorical device that appears frequently in the interviews and connect it to a pervasive sense of marginality. This “marginality within marginality” may have several sources, including punk music and subculture, which I argue contribute to the perpetuation of a notion of unbridgeability between types of anarchists

Inconvenient Truth About Boise Public Transportation

The Boise-Nampa metropolitan area is growing rapidly, and its transportation system must expand to account for this growth. However, in order for a public transportation system to be effective, citizens must have both the ability and the incentive to make use of it. Our research will focus on the demand for public transit in the Boise-Nampa metropolitan area. First, we will determine current ridership on the existing public transit system, frequency of use, reasons for using mass transit over other alternative modes of transportation, and what attributes of the system make it an attractive option. Next, we will determine what attributes of the system the public finds most problematic or inconvenient, and we will use this information to recommend policies and level-of-service adjustments that could make the system more user-friendly and efficient. Our research will examine the public’s awareness of available public transit options and the image that the current system projects in the public consciousness, and suggest measures for improvement where necessary

A Note on Sub-Gaussian Random Variables

A sub-Gaussian distribution is any probability distribution that has tails bounded by a Gaussian and has a mean of zero. It is well known that the sum of independent sub-Gaussians is again sub-Gaussian. This note generalizes this result to sums of sub- Gaussians that may not be independent, under the assumption a certain conditional distribution is also sub-Gaussian. This general result is useful in the study of noise growth in (fully) homomorphic encryption schemes [CGHX19, CGGI17], and hopefully useful for other applications

On the zero-dispersion limit of the Benjamin-Ono Cauchy problem for positive initial data

We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-disperion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg-de Vries equation.Comment: 54 pages, 11 figure