From 106106d0db344b43c4c723d22c0511e1346aba33 Mon Sep 17 00:00:00 2001
From: Dmytro Bogatov <dmytro@dbogatov.org>
Date: Mon, 27 Nov 2017 01:18:28 -0500
Subject: [PATCH] Add example section.
---
example/definitions.tex | 12 ++
example/final-map.tex | 9 ++
example/final-tree.tex | 67 ++++++++++++
example/initial-map.tex | 29 +++++
example/tree.tex | 107 ++++++++++++++++++
main.tex | 1 +
packages.tex | 3 +
sections/example.tex | 235 ++++++++++++++++++++++++++++++++++++++++
settings.tex | 2 +
9 files changed, 465 insertions(+)
create mode 100644 example/definitions.tex
create mode 100644 example/final-map.tex
create mode 100644 example/final-tree.tex
create mode 100644 example/initial-map.tex
create mode 100644 example/tree.tex
create mode 100644 sections/example.tex
diff --git a/example/definitions.tex b/example/definitions.tex
new file mode 100644
index 0000000..4862830
--- /dev/null
+++ b/example/definitions.tex
@@ -0,0 +1,12 @@
+\DeclareDocumentCommand
+ {\oramNode}
+ { O{$\varnothing$} O{$\varnothing$} O{$\varnothing$} }
+ {#1, #2, #3}
+
+\newif\ifselected
+\newif\ifpathread
+
+\newif\ifnodeonenew
+\newif\ifnodetwonew
+\newif\ifnodethreenew
+\newif\ifnodefournew
diff --git a/example/final-map.tex b/example/final-map.tex
new file mode 100644
index 0000000..adf8a69
--- /dev/null
+++ b/example/final-map.tex
@@ -0,0 +1,9 @@
+\begin{tabular}{ l | *{9}{c} } % chktex 44
+
+ Block ID & 1 & 2 & 3 & 4 & \textcolor{red}{$5$} & 6 & $\ldots$ & 37 \\
+
+ \midrule%
+
+ Leaf ID & 6 & 5 & 5 & 1 & \textcolor{red}{$3$} & 5 & $\ldots$ & 7 \\
+
+\end{tabular}
diff --git a/example/final-tree.tex b/example/final-tree.tex
new file mode 100644
index 0000000..bc3e9d8
--- /dev/null
+++ b/example/final-tree.tex
@@ -0,0 +1,67 @@
+\newcommand
+{\blockFive}
+{
+ \ifselected
+ \textcolor{red}{$5$}
+ \else
+ $5$
+ \fi
+}
+
+\newcommand
+ {\leafSix}
+{
+ \ifselected
+ \textcolor{red}{$6$}
+ \else
+ $6$
+ \fi
+}
+
+\ifpathread
+ \newcommand{\selectedNode}{blue}
+\else
+ \newcommand{\selectedNode}{black}
+\fi
+
+\begin{tikzpicture}[scale=0.8]
+\Tree
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\oramNode};
+ [.\node[rounded corners, draw]{\oramNode[$4$]};
+ [.\node[rounded corners, draw]{\oramNode[$12$][$17$]};
+ [.\node[rounded corners, draw]{\oramNode[$22$][$23$]};
+ 1
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$26$][$28$][$30$]};
+ 2
+ ]
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$24$][$29$][$33$]};
+ [.\node[rounded corners, draw]{\oramNode[$27$][$31$][$35$]};
+ 3
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$34$][$32$][$21$]};
+ 4
+ ]
+ ]
+ ]
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\oramNode[$10$][$1$]};
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\oramNode[$2$][\blockFive][$8$]};
+ [.\node[rounded corners, draw]{\oramNode[$3$][$6$][$11$]};
+ 5
+ ]
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\oramNode[$7$][$13$][$15$]};
+ \node[]{\leafSix};
+ ]
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$9$][$13$]};
+ [.\node[rounded corners, draw]{\oramNode[$20$][$14$][$16$]};
+ 7
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$25$][$18$][$19$]};
+ 8
+ ]
+ ]
+ ]
+ ]
+\end{tikzpicture}
diff --git a/example/initial-map.tex b/example/initial-map.tex
new file mode 100644
index 0000000..a55021d
--- /dev/null
+++ b/example/initial-map.tex
@@ -0,0 +1,29 @@
+\newcommand
+ {\blockFive}
+ {
+ \ifselected
+ \textcolor{red}{$5$}
+ \else
+ $5$
+ \fi
+ }
+
+\newcommand
+ {\leafSix}
+ {
+ \ifselected
+ \textcolor{red}{$6$}
+ \else
+ $6$
+ \fi
+ }
+
+\begin{tabular}{ l | *{9}{c} } % chktex 44
+
+ Block ID & 1 & 2 & 3 & 4 & \blockFive & 6 & $\ldots$ & 37 \\
+
+ \midrule%
+
+ Leaf ID & 6 & 5 & 5 & 1 & \leafSix & 5 & $\ldots$ & 7 \\
+
+\end{tabular}
diff --git a/example/tree.tex b/example/tree.tex
new file mode 100644
index 0000000..4cd17e0
--- /dev/null
+++ b/example/tree.tex
@@ -0,0 +1,107 @@
+\newcommand
+ {\blockFive}
+ {
+ \ifselected
+ \textcolor{red}{$5$}
+ \else
+ $5$
+ \fi
+ }
+
+\newcommand
+ {\leafSix}
+ {
+ \ifselected
+ \textcolor{red}{$6$}
+ \else
+ $6$
+ \fi
+ }
+
+\ifpathread
+ \newcommand{\selectedNode}{blue}
+\else
+ \newcommand{\selectedNode}{black}
+\fi
+
+\newcommand
+ {\nodeLevelOne}
+ {
+ \ifnodeonenew
+ \oramNode[\textcolor{blue}{$8$}][\textcolor{blue}{$7$}][\textcolor{blue}{$1$}]
+ \else
+ \oramNode[$7$][$13$][$15$]
+ \fi
+ }
+
+\newcommand
+ {\nodeLevelTwo}
+ {
+ \ifnodetwonew
+ \oramNode[\textcolor{blue}{$2$}][\textcolor{blue}{$10$}][\textcolor{blue}{$15$}]
+ \else
+ \oramNode[$2$][\blockFive][$8$]
+ \fi
+ }
+
+\newcommand
+ {\nodeLevelThree}
+ {
+ \ifnodethreenew
+ \oramNode[\textcolor{blue}{$13$}]
+ \else
+ \oramNode[$10$][$1$]
+ \fi
+ }
+
+\newcommand
+ {\nodeLevelFour}
+ {
+ \ifnodefournew
+ \oramNode[\textcolor{blue}{$5^\prime$}]
+ \else
+ \oramNode
+ \fi
+ }
+
+\begin{tikzpicture}[scale=0.8]
+ \Tree
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\nodeLevelFour};
+ [.\node[rounded corners, draw]{\oramNode[$4$]};
+ [.\node[rounded corners, draw]{\oramNode[$12$][$17$][$36$]};
+ [.\node[rounded corners, draw]{\oramNode[$22$][$23$]};
+ 1
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$26$][$28$][$30$]};
+ 2
+ ]
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$24$][$29$][$33$]};
+ [.\node[rounded corners, draw]{\oramNode[$27$][$31$][$35$]};
+ 3
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$34$][$32$][$21$]};
+ 4
+ ]
+ ]
+ ]
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\nodeLevelThree};
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\nodeLevelTwo};
+ [.\node[rounded corners, draw]{\oramNode[$3$][$6$][$11$]};
+ 5
+ ]
+ [.\node[rounded corners, draw/.expand once=\selectedNode]{\nodeLevelOne};
+ \node[]{\leafSix};
+ ]
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$9$][$13$][$37$]};
+ [.\node[rounded corners, draw]{\oramNode[$20$][$14$][$16$]};
+ 7
+ ]
+ [.\node[rounded corners, draw]{\oramNode[$25$][$18$][$19$]};
+ 8
+ ]
+ ]
+ ]
+ ]
+\end{tikzpicture}
diff --git a/main.tex b/main.tex
index 2480b10..58d965e 100644
--- a/main.tex
+++ b/main.tex
@@ -41,6 +41,7 @@
\input{sections/overview-of-other-orams}
\input{sections/problem-definition}
\input{sections/path-oram-protocol}
+ \input{sections/example}
\input{sections/recursion-and-parametrization}
\input{sections/bounds-on-stash-usage}
\input{sections/evaluation}
diff --git a/packages.tex b/packages.tex
index 20eb8a8..2542b46 100644
--- a/packages.tex
+++ b/packages.tex
@@ -13,6 +13,9 @@
\usepackage{hyperref}
\usepackage{hyperxmp}
\usepackage{multirow}
+\usepackage{tikz-qtree}
+\usepackage{xparse}
+\usepackage{caption}
\usepackage[
backend=biber,
diff --git a/sections/example.tex b/sections/example.tex
new file mode 100644
index 0000000..bda62a5
--- /dev/null
+++ b/sections/example.tex
@@ -0,0 +1,235 @@
+\input{example/definitions}
+
+\section{Example}
+
+ \begin{frame}{Initial state}
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Initial underlying tree}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{figure}
+ \centering
+
+ \input{example/initial-map}
+ \caption{Initial position map}
+ \end{figure}
+
+ \end{frame}
+
+ \begin{frame}{\textsc{Access}$(5)$}
+
+ \selectedtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Select block with ID 5}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{figure}
+ \centering
+
+ \input{example/initial-map}
+ \caption{Find leaf for block with ID 5}
+ \end{figure}
+
+ \end{frame}
+
+ \begin{frame}{Read path}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Select path $\mathcal{P}(6)$}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{figure}
+ \centering
+
+ \input{example/initial-map}
+ \caption{Find leaf for block with ID 5}
+ \end{figure}
+
+ \end{frame}
+
+ \begin{frame}{Remap block}
+
+ \begin{block}{Stash}
+
+ \begin{gather*}
+ S = \{ 10, 1, 2, \textcolor{red}{5}, 8, 7, 13, 15 \} \\
+ data = \textsc{DecryptBlock}(\textcolor{red}{5}) \\
+ \textcolor{blue}{5^\prime} \gets \textsc{EncryptData}(data^{\mbox{*}}) \\
+ S = \{ 10, 1, 2, \textcolor{blue}{5^\prime}, 8, 7, 13, 15 \}
+ \end{gather*}
+
+ \end{block}
+
+ \begin{block}{Remap}
+
+ Assign random leaf
+
+ \[
+ \text{position}[5] := 3
+ \]
+
+ \end{block}
+
+ \end{frame}
+
+ \begin{frame}{Write path back}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \nodeonenewtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Write bucket on level $L = 3$}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{block}{Stash}
+
+ \begin{gather*}
+ S^\prime = \{ 8, 7, 1 \} \\
+ S = \{ 10, 2, \textcolor{blue}{5}, 13, 15 \}
+ \end{gather*}
+
+ \end{block}
+
+ \end{frame}
+
+ \begin{frame}{Write path back}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \nodeonenewtrue
+ \nodetwonewtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Write bucket on level $L - 1 = 2$}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{block}{Stash}
+
+ \begin{gather*}
+ S^\prime = \{ 2, 10, 15 \} \\
+ S = \{ \textcolor{blue}{5}, 13 \}
+ \end{gather*}
+
+ \end{block}
+
+ \end{frame}
+
+ \begin{frame}{Write path back}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \nodeonenewtrue
+ \nodetwonewtrue
+ \nodethreenewtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Write bucket on level $L - 2 = 1$}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{block}{Stash}
+
+ \begin{gather*}
+ S^\prime = \{ 13 \} \\
+ S = \{ \textcolor{blue}{5} \}
+ \end{gather*}
+
+ \end{block}
+
+ \end{frame}
+
+ \begin{frame}{Write path back}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \nodeonenewtrue
+ \nodetwonewtrue
+ \nodethreenewtrue
+ \nodefournewtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Write bucket on level $0$}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{block}{Stash}
+
+ \begin{gather*}
+ S^\prime = \{ \textcolor{blue}{5} \} \\
+ S = \varnothing
+ \end{gather*}
+
+ \end{block}
+
+ \end{frame}
+
+ \begin{frame}{Final state}
+
+ \selectedtrue
+ \pathreadtrue
+
+ \nodeonenewtrue
+ \nodetwonewtrue
+ \nodethreenewtrue
+ \nodefournewtrue
+
+ \begin{figure}
+ \centering
+
+ \input{example/tree}
+ \caption{Tree after the execution}
+ \end{figure}
+
+ \vspace{-12pt}
+
+ \begin{figure}
+ \centering
+
+ \input{example/final-map}
+ \caption{Position map after the execution}
+ \end{figure}
+
+ \end{frame}
diff --git a/settings.tex b/settings.tex
index 9f8e682..575faee 100644
--- a/settings.tex
+++ b/settings.tex
@@ -68,3 +68,5 @@
pdfmenubar=false,
pdfpagelayout=SinglePage
}
+
+\captionsetup[figure]{labelformat=empty}
--
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