main.tex

\documentclass[10pt, a4paper]{report}

\usepackage{nonotation}


%%%%%%%%%%%%%%%%%%%%%%%%% FONTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{bold-extra} % Used for boldface-smallcaps combo in section headers
\usepackage[normalem]{ulem} % For strikethrough text


%%%%%%%%%%%%%%%%%%%%%%%%% HYPERLINKS %%%%%%%%%%%%%%%%%%%%%%%%%

\PassOptionsToPackage{hyphens}{url}
\usepackage{hyperref}

\hypersetup{
    colorlinks,
    linkcolor       = {red!70!black},
    citecolor       = {blue!50!black},
    urlcolor        = {blue!80!black}
}

% Hyperlink dingbat
\usepackage{pifont} 
\newcommand{\linkicon}{\ding{226}}


%%%%%%%%%%%%%%%%%%%%%%%%% TIKZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{datavisualization.formats.functions}

% Tikz styles used throughout all the figures
% Nodes
\tikzstyle{box}     = [draw, minimum size = 2em]
\tikzstyle{nobox}   = [minimum size = 2em]
% Pins
\tikzstyle{init}    = [pin edge = {-to, thin, black}]


%%%%%%%%%%%%%%%%%%%%%%%%% THEOREMS %%%%%%%%%%%%%%%%%%%%%%%%%%%

\usepackage{amsthm}

\newtheorem{theorem}                    {Theorem}       [chapter]
\newtheorem{lemma}          [theorem]   {Lemma}
\newtheorem{corollary}      [theorem]   {Corollary}
\newtheorem{claim}          [theorem]   {Claim}
\newtheorem{observation}    [theorem]   {Observation}
\newtheorem{proposition}    [theorem]   {Proposition}
\theoremstyle{definition}
\newtheorem{definition}     [theorem]   {Definition}
\newtheorem{exercise}       [theorem]   {Exercise}
\newtheorem{example}        [theorem]   {Example}
\newtheorem{construction}               {Construction}
\theoremstyle{remark}
\newtheorem{solution}       [theorem]   {Solution}


%%%%%%%%%%%%%%%%%%%%%%%%% TODOS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\usepackage{xcolor}
\usepackage{framed}

\newcounter{todocount}
\definecolor{shadecolor}{rgb}{1, 1, 0}
\newcommand{\todo}[1]{
    \stepcounter{todocount}
    \begin{shaded}
    \textsc{To-do} \arabic{todocount}: #1
    \end{shaded}
}


%%%%%%%%%%%%%%%%%%%%%%%%% OTHER %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Math?lap commands
\usepackage{mathtools}

% Custom chapter title
\newcommand{\mychapter}[2]{
    \setcounter{chapter}{#1}
    \setcounter{section}{0}
    \chapter*{#2}
    \addcontentsline{toc}{chapter}{#2}
}

\newcommand{\upto}{\text{---}} % Range ligature
\renewcommand{\mod}{\mathrel{\textup{mod}}} % Remainder operator
\newcommand{\groupgen}{\mathcal{GG}} % Group generators for standard assumptions
\newcommand{\quadres}{\mathcal{Q}uad} % Quadratic residue group
\newcommand{\keygen}{\textsf{\textup{Keygen}}} % Key generator for public-privte pairs
\newcommand{\C}{\mathcal{C}} % Cipherspace
\newcommand{\G}{\mathcal{G}} % Generally used for generators or groups
\newcommand{\K}{\mathcal{K}} % Keyspace
\newcommand{\M}{\mathcal{M}} % Messagespace
\newcommand{\T}{\mathcal{T}} % Tagspace
\newcommand{\RO}{\mathrm{RO}} % Random oracle
\newcommand{\Gen}{\mathrm{Gen}} % Generic generator
\newcommand{\otp}{\textsc{otp}} % One-Time Pad


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

    \tableofcontents

    \chapter{Introduction}

    Newcomers beware: this course will employ a great deal of math, especially:
    \begin{itemize}
        \item Probability;
        \item Algebra, especially group theory;
        \item Notions of complexity theory and asymptotic analysis;
        \item Some unique mathematical constructs, such as \emph{cryptographic games}
    \end{itemize}

    \subsubsection{Some terminology}

    % Some people might have heard terms similar to ``cryptography'', like ``cryptology'', or ``cryptanalysis''. While they are often deemed interchangeable, there exists indeed a differentiation between the three:

    % \begin{itemize}
    %     \item \emph{Cryptography} denotes the study and betterment of encryption techniques;
    %     \item \emph{Cryptanalysis} denotes the study of encrypted messages, and the ways of breaking the encryption to get to the message;
    %     \item \emph{Cryptology} refers collectively to cryptography and cryptanalisis.
    % \end{itemize}

    % This course has the intended main purpose of fostering better encryption techniques, hence its name.
    
    While cryptography is almost always associated with the idea of keeping something secret, it is worthwhile to carefully consider other aspects that it influences:

    \begin{itemize}
        \item \emph{Confidentiality}: the two parties using a form of encrypted communication can safely assume that they are communicating privately; this can be further split into:
              \begin{itemize}
                  \item \emph{Secrecy}: the particular aspect of privacy;
                  \item \emph{Authentication}: the particular aspect of identity verification.
              \end{itemize}

        \item \emph{Integrity}: this is about having a guarantee that data is not altered, a property which becomes essential especially in safety-critical scenarios.
    \end{itemize}

    \subsubsection{Principles}

    Modern cryptography systems are usually designed according to \emph{Kerckhoffs's principle}, which states that a secure system  shall only rely on the encryption keys, and not by the secrecy of the underlying algorithm; as Claude Shannon later summed up: \emph{``the enemy knows the scheme''}. The problem of sharing the key between two parties while retaining communication confidentiality thus becomes central in developing a good scheme, and is the main focus of almost every scheme described during the course.

    \part{Mathematical foundations}

    \input{lessons/lesson_1.tex}
    \input{lessons/lesson_2.tex}
    \input{lessons/lesson_3.tex}
    \input{lessons/lesson_4.tex}
    \input{lessons/lesson_5.tex}

    \part{Symmetric schemes}

    \input{lessons/lesson_6.tex}
    \input{lessons/lesson_7.tex}
    \input{lessons/lesson_8.tex}
    \input{lessons/lesson_9.tex}
    \input{lessons/lesson_10.tex}
    \input{lessons/lesson_11.tex}
    \input{lessons/lesson_12.tex}

    \part{Asymmetric schemes}

    \input{lessons/lesson_13.tex}
    \input{lessons/lesson_14.tex}
    \input{lessons/lesson_15.tex}
    \input{lessons/lesson_16.tex}
    \input{lessons/lesson_17.tex}
    \input{lessons/lesson_18.tex}
    \input{lessons/lesson_19.tex}

    \part{Proof-based schemes}

    \input{lessons/lesson_20.tex}
    \input{lessons/lesson_21.tex}
    \input{lessons/lesson_22.tex}
    \input{lessons/lesson_23.tex}
    \input{lessons/lesson_24.tex}
\end{document}