Assume the letters A-Z are labeled by 0, … , 25 and the blank is labeled by 26, i.e. the alphabet with a blank is identified with the ring 
. We define the key of an affine matrix cryptosystem to be 
, where 
and 
, which defines an enciphering transformation
Example 1: Encipher the message “WELCOME TO THE NEW AGE” using an affine cryptosystem with the key , where
![\[A=\begin{pmatrix} 5 & 4 \\ 2 & 2 \end{pmatrix} \text{ and } B=\begin{pmatrix} 3 \\ 2 \end{pmatrix}\]](https://malachialexander.com/wp-content/ql-cache/quicklatex.com-ec30caec1a805b3c905bb4f9060e0466_l3.svg "Rendered by QuickLaTeX.com")
Step 1: Translate the message to the labeling in
in matrix form:
Step 2: Apply the encipher transformation:
Step 3: Translate the message back to the alphabet from the labeling:
