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Nt1330 Unit 1 Assignment 1 Algorithm Essay

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The algorithm is executed by the owner to encrypt the plaintext of $D$ as follows:
\begin {enumerate}
\item [1:]for each document $D_i \in D$ for $i \in [1,n]$ do
\item [2:]encrypt the plaintext of $D_i$ using also $\textit{El Gamal}$ cipher under $\textit{O's}$ private key $a$ and $\textit{U's}$ public key $U_{pub}$ as $Enc_{D_i}= U_{pub}^a \times D_i $
\item [3:]end for
\item[4:] return $\textit{EncDoc}$
\end{enumerate}

\subsubsection{\textit{\textbf {Retrieval phase}}} Include three algorithms as detailed below:
\begin{enumerate}
\item [I-] $\textit{Trapdoor Generator}$: To retrieve only the documents containing keywords $Q$, the data user $U$ has to ask the $O$ for public key $O_{pub}$ to generate trapdoors; If $O$ is offline these owners' data can't be retrieved in time. If not, $U$ will get the public key $O_{pub}$ and create one trapdoor for a conjunctive keyword set $Q=\{q_1,q_2,...,q_l\}$, using $\textsf{TrapdoorGen}(Q, PP, PR$) algorithm. Firstly, the data user combines the conjunctive queries to make them look like one query, $Tq=\{q_1\| q_2\|...\| q_l\}$, then $U$ will compute the trapdoor of the search request of concatenated conjunctive keywords $\textit{Tq}$ under his private key $b$, $Tw=H_1(Tq)^b \in \mathbb{G}_1 $. Finally, $U$ submits $Tw$ to the cloud server. …show more content…

Then $S$ test $\textit{BF}$ in all $r$ locations, if all $r$ locations of all independent hash functions in $\textit{BF}$ are 1, the remote server returns the relevant encrypted file corresponding the $ID_i$ to $U$. In other words searchable index $I_D$ can be used to check set membership without leaking the set items, and for accumulated

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