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presentation/pres.lyx

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+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\begin_preamble
+\usepackage{newpxtext,newpxmath}
+\end_preamble
+\use_default_options false
+\begin_modules
+theorems-ams
+theorems-sec
+eqs-within-sections
+figs-within-sections
+tabs-within-sections
+theorems-named
+\end_modules
+\maintain_unincluded_children false
+\language british
+\language_package default
+\inputencoding utf8
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
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+\papersize a5paper
+\use_geometry true
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+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation landscape
+\suppress_date false
+\justification true
+\use_refstyle 0
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1cm
+\topmargin 2cm
+\rightmargin 1cm
+\bottommargin 2cm
+\secnumdepth 3
+\tocdepth 2
+\paragraph_separation indent
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+\tracking_changes false
+\output_changes false
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+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Private Information Retrieval
+\end_layout
+
+\begin_layout Author
+Alexander, Casper, Thomas
+\end_layout
+
+\begin_layout Section
+Private Information Retrieval
+\end_layout
+
+\begin_layout Itemize
+Allows a user to retrieve an item from an database, without revealing the
+ item to the server
+\end_layout
+
+\begin_layout Itemize
+Naïve: Send the entire database to the user
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Simple Scheme — Definitions
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $n=2^{s}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $s=\log_{2}n$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $k=\log_{2}n+1=s+1$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $i\in\left[n\right]\equiv\left\{ 0,1\right\} ^{s}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $x=x_{1},\dots,x_{n}\in\left\{ 0,1\right\} ^{n}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Graphics
+	filename simpleprop.png
+	scale 60
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Simple Scheme — Protocol
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+	filename simpleprot.png
+	width 100text%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+General Case — Definitions
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $k$
+\end_inset
+
+ databases, where 
+\begin_inset Formula $k\leq\log_{2}n$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Integers represented using 
+\begin_inset Formula $s$
+\end_inset
+
+-bit long sequences with exactly 
+\begin_inset Formula $k-1$
+\end_inset
+
+ occurrences of 
+\begin_inset Formula $1$
+\end_inset
+
+ in them
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Formula $s$
+\end_inset
+
+ defined as minimum 
+\begin_inset Formula $s$
+\end_inset
+
+ satisfying 
+\begin_inset Formula $\left(\begin{array}{c}
+s\\
+k-1
+\end{array}\right)\geq n$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Our case: 
+\begin_inset Formula $k=2\implies s=n$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+\begin_inset Graphics
+	filename generalprops.png
+	scale 60
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+General Case — Protocol
+\end_layout
+
+\begin_layout Standard
+\begin_inset Graphics
+	filename advancedprot.png
+	width 100line%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage newpage
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document