This is the problem.
Assume that the letters from A to Z are numbered from 0 to 25, and let f be a cipher function such that f (x) = (ax + b) mod 26.
● Determine all the possible values that a (0≤ a <26) can take so that f be bijective.
● For those values of a that make f bijective, indicate which are the possible b-values that ensure that each letter will be mapped to a letter different.
This is my guess:
Being $f(x) = (ax + b)$ $mod$ $26$ and $a = 3,5,7,9,11,15,17,19,21,23,25$.
Now my question is:
Does $f (x)$ have to be a fixed points function?
Do I have to choose values of b that make the function be a fixed point function, in order to ensure that each letter will be mapped to a letter different.?