From 41189ad927313c6dde35ef278c512cecd2b54128 Mon Sep 17 00:00:00 2001 From: "Casper V. Kristensen" Date: Tue, 19 Nov 2019 14:22:59 +0100 Subject: [PATCH] 20MinPres.lyx --- presentation/advancedprot.png | Bin 0 -> 52421 bytes presentation/generalprops.png | Bin 0 -> 4931 bytes presentation/pres.lyx | 302 ++++++++++++++++++++++++++++++++++ presentation/simpleprop.png | Bin 0 -> 9599 bytes presentation/simpleprot.png | Bin 0 -> 57191 bytes 5 files changed, 302 insertions(+) create mode 100644 presentation/advancedprot.png create mode 100644 presentation/generalprops.png create mode 100644 presentation/pres.lyx create mode 100644 presentation/simpleprop.png create mode 100644 presentation/simpleprot.png diff --git a/presentation/advancedprot.png b/presentation/advancedprot.png new file mode 100644 index 0000000000000000000000000000000000000000..9cea7244ff8e96576e3930fb90ae191e2eb15c3f GIT binary patch literal 52421 zcma&Oc{o*V8$P_1N+l#oW~GvlP-G@DM46J1IYWlbWKKz@Ovz9}q9jCyj159U<~d0+ zhlI%Zoy+t7zT@}TcYOOe-sjccYwxwzeP6?Qo!5D-Ahq)fyLK?{AdyJBloaJONF?$b 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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" +\font_typewriter "default" "default" +\font_math "auto" "auto" +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize default +\spacing other 1.15 +\use_hyperref true +\pdf_bookmarks true +\pdf_bookmarksnumbered false +\pdf_bookmarksopen false +\pdf_bookmarksopenlevel 1 +\pdf_breaklinks false +\pdf_pdfborder true +\pdf_colorlinks false +\pdf_backref false +\pdf_pdfusetitle true +\papersize a5paper +\use_geometry true +\use_package amsmath 2 +\use_package amssymb 2 +\use_package cancel 0 +\use_package esint 1 +\use_package mathdots 0 +\use_package mathtools 0 +\use_package mhchem 0 +\use_package stackrel 0 +\use_package stmaryrd 0 +\use_package undertilde 0 +\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 +\paragraph_indentation default +\is_math_indent 0 +\math_numbering_side default +\quotes_style english +\dynamic_quotes 0 +\papercolumns 1 +\papersides 1 +\paperpagestyle default +\tracking_changes false +\output_changes false +\html_math_output 0 +\html_css_as_file 0 +\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 + 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