main.tex

\documentclass[letterpaper]{article}

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\usepackage{arxiv}
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% tikz package and its libraries for drawing graphshttps://www.overleaf.com/project/5c6b6dc56db16163cf1f3609
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\renewcommand{\arraystretch}{1.2} % increase the height of the table rows

% new commands for definitions and theorems--------
\newtheorem{theorem}{Theorem}[subsection]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{remark}[theorem]{Remark} % [section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{definition}[theorem]{Definition} % [section] % definition numbers are dependent on theorem numbers
\newtheorem{example}[theorem]{Example} % [section] % same for example numbers
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% new commands for mathematical notations--------
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\N}{\mathbb{N}}
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\newcommand{\keygen}{\text{Keygen}}
\newcommand{\seckeygen}{\text{SecretKeygen}}
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\newcommand{\evalkeygen}{\text{EvalKeygen}}
\newcommand{\enc}{\text{Enc}}
\newcommand{\dec}{\text{Dec}}
\newcommand{\eval}{\text{Eval}}
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\newcommand{\bgv}{\text{BGV}}
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\newcommand{\bitdecomp}{\text{BitDecomp}}
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% make index page 
%\usepackage{imakeidx}
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\title{A Tutorial Introduction on Lattice-based Cryptography and Homomorphic Encryption}


\author{
  Yang Li \\
  %\thanks{Use footnote for providing further information about author} \\
  School of Computing\\
  Australian National University\\
  Canberra, ACT, 2600 \\
  \texttt{kelvin.li@anu.edu.au} \\
  %% examples of more authors
   \And
 Kee Siong Ng \\
  School of Computing\\
  Australian National University\\
  Canberra, ACT, 2600 \\
  \texttt{keesiong.ng@anu.edu.au} \\
  \And
  Michael Purcell \\
  School of Computing \\
  Australian National University \\
  Canberra, ACT, 2600 \\
  \texttt{michael.purcell1@anu.edu.au}\\
}

\setlength{\parindent}{1.5em}

\usepackage{subfiles} % Best loaded last in the preamble

\makeindex

\begin{document}
\maketitle

\tableofcontents

%\newpage
%\section{Course Design}
%\subfile{sections/course design}

\newpage
\section{Introduction}
\subfile{sections/introduction}

\newpage
\section{Computational Complexity Theory}\label{sec:computational complexity}
\subfile{sections/complexity theory}

\newpage
\section{Cryptography Basics}
\subfile{sections/crypto}


\newpage
\section{Lattice Theory}
\subfile{sections/lattice theory}

\newpage
\section{Discrete Gaussian Distribution}\label{sec:discrete gaussian}
\subfile{sections/discrete gaussian}

\newpage
\section{Learning with Errors}
\subfile{sections/lwe}

\newpage
\section{Cyclotomic Polynomials and Cyclotomic Extensions}
\subfile{sections/cyclotomic}

\newpage
\section{Algebraic Number Theory}\label{sec:ant short}
\subfile{sections/ant shorter}

\newpage
\section{Ring Learning with Errors}
\subfile{sections/ring lwe}

\newpage
\section{Homomorphic Encryption}
\subfile{sections/he}

\newpage
\appendix
\section{Abstract Algebra}
\subfile{sections/abstract algebra}

\newpage
\section{Galois Theory}
\subfile{sections/galois theory}

\newpage
\section{Algebraic Number Theory}
\subfile{sections/ant longer}

\newpage
\section{Mind Maps}\label{sec:mind maps}
\subfile{sections/mindmaps}


\newpage
\bibliography{references}\addcontentsline{toc}{section}{References}
\bibliographystyle{abbrvnat}

\newpage
\printindex

\end{document}