We first need to show that for each pair of plaintext-ciphertext letters ( x,y ), there are exactly 12 keys that encrypt x to y . For each choice of a , the key ( a,y − ax ) encrypts the plaintext letter x to the ciphertext letter y , since ax + ( y − ax ) = y . There are twelve possible choices for a so there are exactly twelve keys that map a given plaintext letter to a given ciphertext letter.
This is an easy question, I'm just trying to make sense of this statement found on page three here www.maths.uq.edu.au/courses/MATH3302/2010/files/cryptotute2.pdf
In the affine cipher how is their only 12 keys that map a given plaintext x to a given ciphertext y? I learned that the affinecipher has 286 nontrivial keys. So if thats the case how can only 12 of them map a given plaintext x to a given ciphertext y.