Physical Sciences and Mathematics Commons^™

Results On $K$-Covers In The Game Quads, Daniel Melvin Rose-Levine

Senior Projects Spring 2024

This project explores the $k$-cover conjecture for the game Quads. The conjecture states that for all $k\in\mathbb{N}$, there exists a $k$-cover if and only if $k = 2$ or $k = \frac{2^n-2}{6}$ for some odd $n\in\mathbb{N}$ with $n>1$. We show that if $k$ is one of these values, then there exists a $k$-cover. We discuss partial results in the other direction, i.e., that these are the only values of $k$ for which there exists a $k$-cover.

Symmetry And Structures Of Apn Functions And Sidon Sets, Darrion Thornburgh

Senior Projects Spring 2024

Let $\mathbb{F}_p^n$ be the $n$-dimensional vector space over $\mathbb{F}_p$. The graph $\mathcal{G}_F = \{ (x, F(x)) : x \in \mathbb{F}_p^n \}$ of a vectorial function $F \colon \mathbb{F}_p^n \to \mathbb{F}_p^m$ can have interesting combinatorial properties depending on varying cryptographic conditions on $F$. A vectorial Boolean function $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ is almost perfect nonlinear (APN) if there are at most $2$ solutions to the equation $F(x+a) + F(x) = b$ for all $a,b \in \mathbb{F}_2^n$ where $a \neq 0$. Equivalently, $F$ is APN if and only if $\mathcal{G}_F$ is a Sidon set, that is, a set in $\mathbb{F}_2^n$ where …

Attitudes And Perceptions Towards Privacy And Surveillance In Australia, Aleatha J. Shanley

Theses: Doctorates and Masters

Understanding attitudes towards privacy and surveillance technologies used to enhance security objectives is a complex, but crucial aspect for policy makers to consider. Historically, terrorism-related incidents justified the uptake of surveillance practices. More recently however, biosecurity concerns have motivated nation-states to adopt more intrusive surveillance measures. There is a growing body of literature that supports the public’s desire to maintain privacy despite fears of biological or physical threats.

This research set out to explore attitudes towards privacy and surveillance in an Australian context. Throughout the course of this endeavour, the COVID-19 pandemic emerged bringing with it a variety of track …