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Section 1.2 Why “mathematical” cryptography?

One can think of encryption as the act of changing a message into a cipher. If we let \(M\) stand for our message and \(C\) stand for the cipher, we get a simple visual model which looks like

\begin{equation*} M \xrightarrow{\rm encryption} C \end{equation*}

Typically, we'll want to encrypt a plaintext (that is, standard English words), consisting of letters and characters in the English alphabet. (Of course the same idea can be applied to data stored on a computer). The process of converting a plaintext into a message that can be encrypted numerically is called encoding.

\begin{equation*} T \xrightarrow{\rm encoding} M \xrightarrow{\rm encryption} C \end{equation*}

Mathematics provides a framework for this process by thinking of encoding and encryption as functions that have certain desirable properties. Our primary focus will be the functions that do encryption, though necessarily we will have to discuss encoding as well.