Sentence:  In our example of the <WSD>affine</WSD> cryptosystem family, deciphering is also accomplished by an <WSD>affine</WSD> map, namely P \equiv a^{-1}C-a^{-1}b \bmod N, and so the deciphering transformation uses the same algorithm as the enciphering transformation, except with a different key, namely, the pair (a^{-1}, -a^{-1}b). 
Meaning of the word marked with <WSD> tags:  Of or pertaining to a function expressible as f(\vec x)= A \vec x + \vec b  (where A is a linear transformation and \vec b is a constant), which, regarded as a transformation, maps parallel lines to parallel lines and finite points to finite points.