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% Write the approved title of your dissertation
\title{Automated image classification with expandable models}

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\author{Andre Henriques, 6644818}

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	\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:
	$$H=E$$
	$$m\ne m'$$
	$$H(m)=E(K, IV \oplus m) = C_1$$
	$$H(m')=E(K, IV \oplus m') = C_2$$
	And if there the hashing function was not collision resistant that would imply
	$$C_1=C_2\Rightarrow D(C_1)=D(C_2) \Rightarrow m=m'$$
	and since $m !=m'$ the hash function is collision resistant, for messages with 1 block.
	

	

	


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