From cef4ac5a73e6a7ede3b0a0a177f78e096bda3763 Mon Sep 17 00:00:00 2001
From: Matthias Beyer <mail@beyermatthias.de>
Date: Fri, 1 Jan 2021 18:18:02 +0100
Subject: Add content for chapter about blocks

Signed-off-by: Matthias Beyer <mail@beyermatthias.de>
---
 doc/paper/main.tex | 79 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)

diff --git a/doc/paper/main.tex b/doc/paper/main.tex
index 7789f02..976f2fc 100644
--- a/doc/paper/main.tex
+++ b/doc/paper/main.tex
@@ -8,8 +8,44 @@
 \usepackage{textcomp}
 \usepackage{xcolor}
 \usepackage{url}
+\usepackage{listings}
 \def\BibTeX{{\rm B\kern-.05em{\sc i\kern-.025em b}\kern-.08em
     T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
+
+\colorlet{punct}{red!60!black}
+\definecolor{background}{HTML}{EEEEEE}
+\definecolor{delim}{RGB}{20,105,176}
+\colorlet{numb}{magenta!60!black}
+
+\lstdefinelanguage{json}{
+    basicstyle=\normalfont\ttfamily,
+    numbers=left,
+    numberstyle=\scriptsize,
+    stepnumber=1,
+    numbersep=8pt,
+    showstringspaces=false,
+    breaklines=true,
+    frame=lines,
+    backgroundcolor=\color{background},
+    literate=
+     *{0}{{{\color{numb}0}}}{1}
+      {1}{{{\color{numb}1}}}{1}
+      {2}{{{\color{numb}2}}}{1}
+      {3}{{{\color{numb}3}}}{1}
+      {4}{{{\color{numb}4}}}{1}
+      {5}{{{\color{numb}5}}}{1}
+      {6}{{{\color{numb}6}}}{1}
+      {7}{{{\color{numb}7}}}{1}
+      {8}{{{\color{numb}8}}}{1}
+      {9}{{{\color{numb}9}}}{1}
+      {:}{{{\color{punct}{:}}}}{1}
+      {,}{{{\color{punct}{,}}}}{1}
+      {\{}{{{\color{delim}{\{}}}}{1}
+      {\}}{{{\color{delim}{\}}}}}{1}
+      {[}{{{\color{delim}{[}}}}{1}
+      {]}{{{\color{delim}{]}}}}{1},
+}
+
 \begin{document}
 
 \title{How to implement a distributed social network using IPFS}
@@ -77,6 +113,49 @@ types.
 % What a "block" is used for and what data it holds
 % - metadata pointer
 
+As described above, the "Block" data type is used for building the blockchain.
+Because this kind of object must be easy to distribute to ensure high
+availability of blocks of a single chain, this type must be small in size.
+Thus, it should only hold the following elements:
+
+\begin{itemize}
+    \item A version number, which describes the version of the format used
+    \item A list of pointers to parent blocks
+    \item A pointer to a metadata Block
+\end{itemize}
+
+A block may hold more than one pointer to a parent block to make merges possible
+on the block-level.
+
+\begin{lstlisting}[language=json,caption={Example of a Block},label=jsonblock]
+{
+"v": 1,
+"parents": ["Qmabc...", "Qmdef..."],
+"content": "Qmghi..."
+}
+\end{lstlisting}
+
+As shown in \ref{jsonblock}, minimal data is held in the "Block" object.
+Because of the small size, replication of block objects is cheap and every
+modern end-user device can easily hold millions of blocks.
+
+If $S_{parents}(b)$ is the size of the list of parents of a block $b$,
+and
+$S_{base}$ is the size of a block without any parents,
+the required disk space can be described by
+
+\begin{equation}
+    S_{sum} = n * S_{base} + \sum_{i=1}^{n} S_{parents}(b_i)
+\end{equation}
+
+where $b_i$ is a block and $n$ is the number of blocks.
+Depending on the overhead of the encoding technology used, the size of an
+individual block is in the lower bytes range.
+E.G. assuming a size of 46 bytes for a IPFS hash, a block with only one parent fits
+into 100 bytes, even if encoded as JSON. That means that one Gigabyte of storage
+could hold more than 10 Million blocks.
+
+
 \subsection{Metadata-Block}
 % What a "metadata-block" is used for and what data it holds
 % - mime
-- 
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