Suppose you encounter some ciphertext $(i,q,x,x,p,a,z,q)$ that you know has been encrypted using a simple shift permutation $\phi_n$ for some $n$.

1. Decode the ciphertext and state the original message. State the value of $n$ that was used to encode the original message.
2. Encode the plain text message “attack at dawn” into ciphertext using the same encryption key you discovered in the first part.
3. Are there any other $n$ that would have produced the same results as above?

• Make remarks with a list.

problem.first_encryption_key.tex

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\begin{problem}
Suppose you encounter some ciphertext $(i,q,x,x,p,a,z,q)$ that you know has been encrypted using a simple shift permutation $\phi_n$ for some $n$.
\begin{enumerate}
\item Decode the ciphertext and state the original message. State the value of $n$ that was used to encode the original message. 
\item Encode the plain text message "attack at dawn" into ciphertext using the same encryption key you discovered in the first part.
\item Are there any other $n$ that would have produced the same results as above?
\end{enumerate}
\end{problem}

• Dihedral group

problem ben