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\section{Some cryptographic applications}  This is not a book about cryptography, it is rather a book that helps the reader faces face  a course focused on cryptography, so we will not explain the general theory of cryptography. However, After after  having seen some mathematical background in the previous sections, it is possible to define rigorously a few cryptographic systems in an easy way. We believe these systems can motivate the reader to start a deeper subject of cryptography on her own. We will see:  \begin{itemize}  \item the classical Diffie-Helman key-exchange   \item the Rivest-Shamir-Adleman encryption/decryption system  \item the classical El Gamal encryption/decryption system  \end{itemize}  \subsection{Classical DH}  \subsection{RSA}  \subsection {El Gamal}