diff --git a/cw/cw.tex b/cw/cw.tex new file mode 100644 index 0000000..d3042f4 --- /dev/null +++ b/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} + +