Test math

cw/cw.tex

@@ -0,0 +1,70 @@
+%%% Preamble
+\documentclass[11pt, a4paper]{article}
+
+\usepackage[english]{babel} % English language/hyphenation
+\usepackage{url}
+\usepackage{tabularx}
+\usepackage{pdfpages}
+\usepackage{float}
+
+\usepackage{graphicx}
+\graphicspath{ {../images for report/} }
+\usepackage[margin=2cm]{geometry}
+
+\usepackage{hyperref}
+\hypersetup{
+    colorlinks,
+    citecolor=black,
+    filecolor=black,
+    linkcolor=black,
+    urlcolor=black
+}
+
+\usepackage{cleveref}
+
+%%% Custom headers/footers (fancyhdr package)
+\usepackage{fancyhdr}
+\pagestyle{fancyplain}
+\fancyhead{}							% No page header
+\fancyfoot[L]{}							% Empty 
+\fancyfoot[C]{\thepage}					% Pagenumbering		
+\fancyfoot[R]{}						    % Empty
+\renewcommand{\headrulewidth}{0pt}		% Remove header underlines
+\renewcommand{\footrulewidth}{0pt}		% Remove footer underlines
+\setlength{\headheight}{13.6pt}
+
+% numeric
+\usepackage[style=ieee,sorting=none,backend=biber]{biblatex}
+\addbibresource{../main.bib}
+
+% Write the approved title of your dissertation
+\title{Automated image classification with expandable models}
+
+% Write your full name, as in University records
+\author{Andre Henriques, 6644818}
+
+\date{}
+
+%%% Begin document
+\begin{document}
+	\section*{5}
+	\subsection*{5.1}
+	The hash function is collision resistante for $n=1$, since if the block size is one the hash function is the encryption. Therefore:
+	if the message is only one block long:
+	$$H=E$$
+	$$m\ne m'$$
+	$$H(m)=E(K, IV \xor m) = C_1$$
+	$$H(m')=E(K, IV \xor m') = C_2$$
+	And if there the hashing function was not collision resistant that would imply
+	$$C_1=C_2\implies D(C_1)=D(C_2) \impies m=m'$$
+	and since $m !=m'$ the hash function is collision resistant, for messages with 1 block.
+	
+
+	
+
+	
+
+
+\end{document}
+
+