Affine Encryption Key

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Definition (Affine Encryption Key)

Suppose we have an alphabet with $n$ letters. Set up a 1-1 correspondence between the letters in your alphabet and the integers 0 to $n-1$. As an example, we could let $n=27$ for the standard alphabet with 26 letters and a space (the 27th letter which we'll number 0), and then use the correspondence in the table below.

Pick an integer $m\geq n$. Then an affine encryption key is an invertible function \( f:\mathbb{Z}_m \to \mathbb{Z}_m\) defined by $$f(x)=ax+b\pmod {m}$$ for some $a,b\in\mathbb{Z}_m$.

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