main.tex

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\title{Design and Implementation of a Generalized Elliptic Curve Library in Rust}
\author{Filip Schauer}
\begin{document}
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\hspace*{-20pt}{\huge\sffamily\textbf{BACHELOR THESIS}}
\vspace{10pt}

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    Thesis submitted in fulfillment of the requirements for the degree of Bachelor of Science in Engineering at the University of Applied Sciences Technikum Wien - Degree Program
    Information and Communication Systems and Services\vspace{5pt}
  \end{minipage}}

\vspace{47pt}\hspace*{-20pt}
\begin{minipage}{0.9625\linewidth}
  \huge\bfseries\sffamily Design and Implementation of a Generalized Elliptic Curve Library in Rust
\end{minipage}\vspace{47pt}

\Large
\hspace*{-20pt}%
By:~Filip Schauer

\hspace*{-20pt}%
Student Number:~52320085
\vspace{0.8\baselineskip}%

\hspace*{-20pt}%
Supervisor:~FH-Prof. DI Alexander Mense
\vspace{0.8\baselineskip}%

\hspace*{-20pt}%
Wien, \today%
\end{titlepage}

\chapter*{Declaration}
``As author and creator of this work to hand, I confirm with my
signature knowledge of the relevant copyright regulations
governed by higher education acts (see Urheberrechtsgesetz
/Austrian copyright law as amended as well as the Statute on
Studies Act Provisions / Examination Regulations of the UAS
Technikum Wien as amended).\\[\baselineskip]
I hereby declare that I completed the present work independently
and that any ideas, whether written by others or by myself, have
been fully sourced and referenced. I am aware of any consequences
I may face on the part of the degree program director if there
should be evidence of missing autonomy and independence or
evidence of any intent to fraudulently achieve a pass mark for
this work (see Statute on Studies Act Provisions / Examination
Regulations of the UAS Technikum Wien as amended).\\[\baselineskip]
I further declare that up to this date I have not published the work to
hand nor have I presented it to another examination board in the same or
similar form. I affirm that the version submitted matches the version in
the upload tool.``\vspace{4\baselineskip}

\noindent Wien, \today\hspace{0.4\linewidth}Digital Signature

\subfile{abstract.tex}

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\tableofcontents
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\subfile{introduction.tex}

\subfile{methodology.tex}

\subfile{1ec_intro/part1.tex}

\subfile{2ec_finite_field_intro/part2.tex}

\subfile{3ec_forms/part3.tex}

\subfile{4ec_advanced/part4.tex}

\subfile{5rs_library_manual/part5.tex}

\subfile{conclusion.tex}

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\addcontentsline{toc}{chapter}{Bibliography}
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\phantomsection
\addcontentsline{toc}{chapter}{Documentation table of AI-based tools}
\chapter*{Documentation table of AI-based tools}
\begin{tabularx}{\textwidth}{|p{3.078cm}|p{3.31cm}|X|}
    \hline
    AI-Based Tool & Intended Use & Prompt, Source, Page, Paragraph\dots \\
    \hline
    Gemini 2.5 Pro\newline
    Gemini 2.5 Flash\newline
    Gemini 3 Pro\newline
    Gemini 3 Flash\newline
    Gemini 3.1 Pro\newline
    Claude Sonnet 4.6 &
    Review and assistance with planning the structure &
    <SUMMARY AND OUTLINE OF THE THESIS>\newline
    <THESIS PROPOSAL \& CODE \& PAPER>\newline
    <ROUGH NOTES AND QUESTIONS ON STRUCTURE AND THESIS PRESENTATION> \\
    \hline
    GPT-5\newline GPT-5 Mini\newline GPT-5.2\newline GPT-5.3 & Review and assistance with tightening up prose & Should anything be tightened up? \newline <CHAPTER> \\
    \hline
    DeepL Write & Alternative phrasing suggestions and language polish & Used selectively for sentence-level improvements \\
    \hline
\end{tabularx}
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\phantomsection
\addcontentsline{toc}{chapter}{List of Abbreviations}
\chapter*{List of Abbreviations}
\begin{acronym}[ECDLP]
    \acro{crt}[CRT]{Chinese Remainder Theorem}
    \acro{ecc}[ECC]{Elliptic Curve Cryptography}
    \acro{ecdh}[ECDH]{Elliptic Curve Diffie-Hellman}
    \acro{ecdlp}[ECDLP]{Elliptic Curve Discrete Logarithm Problem}
    \acro{eea}[EEA]{Extended Euclidean Algorithm}
    \acro{gcd}[GCD]{Greatest Common Divisor}
    \acro{secg}[SECG]{Standards for Efficient Cryptography Group}
\end{acronym}

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