methodology.tex

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\chapter*{Methodology}
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The thesis follows a Design Science Research approach that employs an iterative and incremental development cycle.
Rather than strictly separating research, implementation, and evaluation into linear phases, the work proceeds in iterative cycles, with each cycle focusing on a single library component.
Each iteration consists of the following steps:
\begin{enumerate}
\item \textbf{Analyse} mathematical literature to derive formulas and algorithms required for the current component.
\item \textbf{Implement} the component into the elliptic curve library.
\item \textbf{Verify} the correctness of the implementation via unit tests, cross-referencing results against established software (e.g. SageMath, OpenSSL) and known standard test vectors.
\item \textbf{Benchmark} the component, identify bottlenecks and apply optimizations.
\end{enumerate}

The findings feed directly into the corresponding chapters of the thesis.

To answer \hyperref[research_question_1]{Research Question~\ref*{research_question_1}}, the resulting software architecture is evaluated to assess the extent to which Rust's type system can unify the underlying mathematical models.
Finally, a comprehensive performance comparison against specialized cryptographic libraries is conducted to answer \hyperref[research_question_2]{Research Question~\ref*{research_question_2}}.

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